WorldWideScience

Sample records for bayesian markov random

  1. A Bayesian model for binary Markov chains

    Directory of Open Access Journals (Sweden)

    Belkheir Essebbar

    2004-02-01

    Full Text Available This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

  2. Bayesian analysis of Markov point processes

    DEFF Research Database (Denmark)

    Berthelsen, Kasper Klitgaard; Møller, Jesper

    2006-01-01

    Recently Møller, Pettitt, Berthelsen and Reeves introduced a new MCMC methodology for drawing samples from a posterior distribution when the likelihood function is only specified up to a normalising constant. We illustrate the method in the setting of Bayesian inference for Markov point processes...... a partially ordered Markov point process as the auxiliary variable. As the method requires simulation from the "unknown" likelihood, perfect simulation algorithms for spatial point processes become useful....

  3. A Bayesian method for construction of Markov models to describe dynamics on various time-scales.

    Science.gov (United States)

    Rains, Emily K; Andersen, Hans C

    2010-10-14

    The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This paper presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (τ,P,T), where τ is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N(P)×N(P) transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N(P) is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. (1) The method uses Bayesian analysis to determine the partition as well as the transition probabilities. (2) The method allows the construction of a Markov model for any chosen mesoscopic time-scale τ. (3) It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a "consistent mesoscopic Markov model" (CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time-scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P,T) for any chosen τ. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time-scale τ was generated by the CMMM specified by (P,T). An optimization algorithm is used to find the most

  4. A Bayesian Markov geostatistical model for estimation of hydrogeological properties

    International Nuclear Information System (INIS)

    Rosen, L.; Gustafson, G.

    1996-01-01

    A geostatistical methodology based on Markov-chain analysis and Bayesian statistics was developed for probability estimations of hydrogeological and geological properties in the siting process of a nuclear waste repository. The probability estimates have practical use in decision-making on issues such as siting, investigation programs, and construction design. The methodology is nonparametric which makes it possible to handle information that does not exhibit standard statistical distributions, as is often the case for classified information. Data do not need to meet the requirements on additivity and normality as with the geostatistical methods based on regionalized variable theory, e.g., kriging. The methodology also has a formal way for incorporating professional judgments through the use of Bayesian statistics, which allows for updating of prior estimates to posterior probabilities each time new information becomes available. A Bayesian Markov Geostatistical Model (BayMar) software was developed for implementation of the methodology in two and three dimensions. This paper gives (1) a theoretical description of the Bayesian Markov Geostatistical Model; (2) a short description of the BayMar software; and (3) an example of application of the model for estimating the suitability for repository establishment with respect to the three parameters of lithology, hydraulic conductivity, and rock quality designation index (RQD) at 400--500 meters below ground surface in an area around the Aespoe Hard Rock Laboratory in southeastern Sweden

  5. Learning Bayesian network classifiers for credit scoring using Markov Chain Monte Carlo search

    NARCIS (Netherlands)

    Baesens, B.; Egmont-Petersen, M.; Castelo, R.; Vanthienen, J.

    2001-01-01

    In this paper, we will evaluate the power and usefulness of Bayesian network classifiers for credit scoring. Various types of Bayesian network classifiers will be evaluated and contrasted including unrestricted Bayesian network classifiers learnt using Markov Chain Monte Carlo (MCMC) search.

  6. Invited commentary: Lost in estimation--searching for alternatives to markov chains to fit complex Bayesian models.

    Science.gov (United States)

    Molitor, John

    2012-03-01

    Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.

  7. Markov Chain Monte Carlo Bayesian Learning for Neural Networks

    Science.gov (United States)

    Goodrich, Michael S.

    2011-01-01

    Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

  8. Bayesian structure learning for Markov Random Fields with a spike and slab prior

    NARCIS (Netherlands)

    Chen, Y.; Welling, M.; de Freitas, N.; Murphy, K.

    2012-01-01

    In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of disadvantages such as the inability to assess model uncertainty and

  9. Bayesian posterior distributions without Markov chains.

    Science.gov (United States)

    Cole, Stephen R; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B

    2012-03-01

    Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.

  10. Metis: A Pure Metropolis Markov Chain Monte Carlo Bayesian Inference Library

    Energy Technology Data Exchange (ETDEWEB)

    Bates, Cameron Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Mckigney, Edward Allen [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2018-01-09

    The use of Bayesian inference in data analysis has become the standard for large scienti c experiments [1, 2]. The Monte Carlo Codes Group(XCP-3) at Los Alamos has developed a simple set of algorithms currently implemented in C++ and Python to easily perform at-prior Markov Chain Monte Carlo Bayesian inference with pure Metropolis sampling. These implementations are designed to be user friendly and extensible for customization based on speci c application requirements. This document describes the algorithmic choices made and presents two use cases.

  11. Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy

    Science.gov (United States)

    Sharma, Sanjib

    2017-08-01

    Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in the number of papers that employ Monte Carlo based Bayesian analysis. New, efficient Monte Carlo based methods are continuously being developed and explored. In this review, we first explain the basics of Bayesian theory and discuss how to set up data analysis problems within this framework. Next, we provide an overview of various Monte Carlo based methods for performing Bayesian data analysis. Finally, we discuss advanced ideas that enable us to tackle complex problems and thus hold great promise for the future. We also distribute downloadable computer software (available at https://github.com/sanjibs/bmcmc/ ) that implements some of the algorithms and examples discussed here.

  12. Bayesian networks precipitation model based on hidden Markov analysis and its application

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    Surface precipitation estimation is very important in hydrologic forecast. To account for the influence of the neighbors on the precipitation of an arbitrary grid in the network, Bayesian networks and Markov random field were adopted to estimate surface precipitation. Spherical coordinates and the expectation-maximization (EM) algorithm were used for region interpolation, and for estimation of the precipitation of arbitrary point in the region. Surface precipitation estimation of seven precipitation stations in Qinghai Lake region was performed. By comparing with other surface precipitation methods such as Thiessen polygon method, distance weighted mean method and arithmetic mean method, it is shown that the proposed method can judge the relationship of precipitation among different points in the area under complicated circumstances and the simulation results are more accurate and rational.

  13. Bayesian analysis for reversible Markov chains

    NARCIS (Netherlands)

    Diaconis, P.; Rolles, S.W.W.

    2006-01-01

    We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Pólya’s urn. We give closed form normalizing constants, a simple

  14. Unmixing hyperspectral images using Markov random fields

    International Nuclear Information System (INIS)

    Eches, Olivier; Dobigeon, Nicolas; Tourneret, Jean-Yves

    2011-01-01

    This paper proposes a new spectral unmixing strategy based on the normal compositional model that exploits the spatial correlations between the image pixels. The pure materials (referred to as endmembers) contained in the image are assumed to be available (they can be obtained by using an appropriate endmember extraction algorithm), while the corresponding fractions (referred to as abundances) are estimated by the proposed algorithm. Due to physical constraints, the abundances have to satisfy positivity and sum-to-one constraints. The image is divided into homogeneous distinct regions having the same statistical properties for the abundance coefficients. The spatial dependencies within each class are modeled thanks to Potts-Markov random fields. Within a Bayesian framework, prior distributions for the abundances and the associated hyperparameters are introduced. A reparametrization of the abundance coefficients is proposed to handle the physical constraints (positivity and sum-to-one) inherent to hyperspectral imagery. The parameters (abundances), hyperparameters (abundance mean and variance for each class) and the classification map indicating the classes of all pixels in the image are inferred from the resulting joint posterior distribution. To overcome the complexity of the joint posterior distribution, Markov chain Monte Carlo methods are used to generate samples asymptotically distributed according to the joint posterior of interest. Simulations conducted on synthetic and real data are presented to illustrate the performance of the proposed algorithm.

  15. Bayesian analysis for exponential random graph models using the adaptive exchange sampler

    KAUST Repository

    Jin, Ick Hoon

    2013-01-01

    Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the existence of intractable normalizing constants. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the issue of intractable normalizing constants encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

  16. Bayesian grid matching

    DEFF Research Database (Denmark)

    Hartelius, Karsten; Carstensen, Jens Michael

    2003-01-01

    A method for locating distorted grid structures in images is presented. The method is based on the theories of template matching and Bayesian image restoration. The grid is modeled as a deformable template. Prior knowledge of the grid is described through a Markov random field (MRF) model which r...

  17. Efficient Incorporation of Markov Random Fields in Change Detection

    DEFF Research Database (Denmark)

    Aanæs, Henrik; Nielsen, Allan Aasbjerg; Carstensen, Jens Michael

    2009-01-01

    of noise, implying that the pixel-wise classifier is also noisy. There is thus a need for incorporating local homogeneity constraints into such a change detection framework. For this modelling task Markov Random Fields are suitable. Markov Random Fields have, however, previously been plagued by lack...

  18. Bayesian Mixed Hidden Markov Models: A Multi-Level Approach to Modeling Categorical Outcomes with Differential Misclassification

    Science.gov (United States)

    Zhang, Yue; Berhane, Kiros

    2014-01-01

    Questionnaire-based health status outcomes are often prone to misclassification. When studying the effect of risk factors on such outcomes, ignoring any potential misclassification may lead to biased effect estimates. Analytical challenges posed by these misclassified outcomes are further complicated when simultaneously exploring factors for both the misclassification and health processes in a multi-level setting. To address these challenges, we propose a fully Bayesian Mixed Hidden Markov Model (BMHMM) for handling differential misclassification in categorical outcomes in a multi-level setting. The BMHMM generalizes the traditional Hidden Markov Model (HMM) by introducing random effects into three sets of HMM parameters for joint estimation of the prevalence, transition and misclassification probabilities. This formulation not only allows joint estimation of all three sets of parameters, but also accounts for cluster level heterogeneity based on a multi-level model structure. Using this novel approach, both the true health status prevalence and the transition probabilities between the health states during follow-up are modeled as functions of covariates. The observed, possibly misclassified, health states are related to the true, but unobserved, health states and covariates. Results from simulation studies are presented to validate the estimation procedure, to show the computational efficiency due to the Bayesian approach and also to illustrate the gains from the proposed method compared to existing methods that ignore outcome misclassification and cluster level heterogeneity. We apply the proposed method to examine the risk factors for both asthma transition and misclassification in the Southern California Children's Health Study (CHS). PMID:24254432

  19. Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo

    Science.gov (United States)

    Cheong, R. Y.; Gabda, D.

    2017-09-01

    Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.

  20. Bayesian tomography by interacting Markov chains

    Science.gov (United States)

    Romary, T.

    2017-12-01

    In seismic tomography, we seek to determine the velocity of the undergound from noisy first arrival travel time observations. In most situations, this is an ill posed inverse problem that admits several unperfect solutions. Given an a priori distribution over the parameters of the velocity model, the Bayesian formulation allows to state this problem as a probabilistic one, with a solution under the form of a posterior distribution. The posterior distribution is generally high dimensional and may exhibit multimodality. Moreover, as it is known only up to a constant, the only sensible way to addressthis problem is to try to generate simulations from the posterior. The natural tools to perform these simulations are Monte Carlo Markov chains (MCMC). Classical implementations of MCMC algorithms generally suffer from slow mixing: the generated states are slow to enter the stationary regime, that is to fit the observations, and when one mode of the posterior is eventually identified, it may become difficult to visit others. Using a varying temperature parameter relaxing the constraint on the data may help to enter the stationary regime. Besides, the sequential nature of MCMC makes them ill fitted toparallel implementation. Running a large number of chains in parallel may be suboptimal as the information gathered by each chain is not mutualized. Parallel tempering (PT) can be seen as a first attempt to make parallel chains at different temperatures communicate but only exchange information between current states. In this talk, I will show that PT actually belongs to a general class of interacting Markov chains algorithm. I will also show that this class enables to design interacting schemes that can take advantage of the whole history of the chain, by authorizing exchanges toward already visited states. The algorithms will be illustrated with toy examples and an application to first arrival traveltime tomography.

  1. Wind Farm Reliability Modelling Using Bayesian Networks and Semi-Markov Processes

    Directory of Open Access Journals (Sweden)

    Robert Adam Sobolewski

    2015-09-01

    Full Text Available Technical reliability plays an important role among factors affecting the power output of a wind farm. The reliability is determined by an internal collection grid topology and reliability of its electrical components, e.g. generators, transformers, cables, switch breakers, protective relays, and busbars. A wind farm reliability’s quantitative measure can be the probability distribution of combinations of operating and failed states of the farm’s wind turbines. The operating state of a wind turbine is its ability to generate power and to transfer it to an external power grid, which means the availability of the wind turbine and other equipment necessary for the power transfer to the external grid. This measure can be used for quantitative analysis of the impact of various wind farm topologies and the reliability of individual farm components on the farm reliability, and for determining the expected farm output power with consideration of the reliability. This knowledge may be useful in an analysis of power generation reliability in power systems. The paper presents probabilistic models that quantify the wind farm reliability taking into account the above-mentioned technical factors. To formulate the reliability models Bayesian networks and semi-Markov processes were used. Using Bayesian networks the wind farm structural reliability was mapped, as well as quantitative characteristics describing equipment reliability. To determine the characteristics semi-Markov processes were used. The paper presents an example calculation of: (i probability distribution of the combination of both operating and failed states of four wind turbines included in the wind farm, and (ii expected wind farm output power with consideration of its reliability.

  2. Evidence Estimation for Bayesian Partially Observed MRFs

    NARCIS (Netherlands)

    Chen, Y.; Welling, M.

    2013-01-01

    Bayesian estimation in Markov random fields is very hard due to the intractability of the partition function. The introduction of hidden units makes the situation even worse due to the presence of potentially very many modes in the posterior distribution. For the first time we propose a

  3. Markov Random Fields on Triangle Meshes

    DEFF Research Database (Denmark)

    Andersen, Vedrana; Aanæs, Henrik; Bærentzen, Jakob Andreas

    2010-01-01

    In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process label...

  4. Estimation of expected number of accidents and workforce unavailability through Bayesian population variability analysis and Markov-based model

    International Nuclear Information System (INIS)

    Chagas Moura, Márcio das; Azevedo, Rafael Valença; Droguett, Enrique López; Chaves, Leandro Rego; Lins, Isis Didier

    2016-01-01

    Occupational accidents pose several negative consequences to employees, employers, environment and people surrounding the locale where the accident takes place. Some types of accidents correspond to low frequency-high consequence (long sick leaves) events, and then classical statistical approaches are ineffective in these cases because the available dataset is generally sparse and contain censored recordings. In this context, we propose a Bayesian population variability method for the estimation of the distributions of the rates of accident and recovery. Given these distributions, a Markov-based model will be used to estimate the uncertainty over the expected number of accidents and the work time loss. Thus, the use of Bayesian analysis along with the Markov approach aims at investigating future trends regarding occupational accidents in a workplace as well as enabling a better management of the labor force and prevention efforts. One application example is presented in order to validate the proposed approach; this case uses available data gathered from a hydropower company in Brazil. - Highlights: • This paper proposes a Bayesian method to estimate rates of accident and recovery. • The model requires simple data likely to be available in the company database. • These results show the proposed model is not too sensitive to the prior estimates.

  5. A Bayesian Justification for Random Sampling in Sample Survey

    Directory of Open Access Journals (Sweden)

    Glen Meeden

    2012-07-01

    Full Text Available In the usual Bayesian approach to survey sampling the sampling design, plays a minimal role, at best. Although a close relationship between exchangeable prior distributions and simple random sampling has been noted; how to formally integrate simple random sampling into the Bayesian paradigm is not clear. Recently it has been argued that the sampling design can be thought of as part of a Bayesian's prior distribution. We will show here that under this scenario simple random sample can be given a Bayesian justification in survey sampling.

  6. Honest Importance Sampling with Multiple Markov Chains.

    Science.gov (United States)

    Tan, Aixin; Doss, Hani; Hobert, James P

    2015-01-01

    Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable

  7. ANALYTIC WORD RECOGNITION WITHOUT SEGMENTATION BASED ON MARKOV RANDOM FIELDS

    NARCIS (Netherlands)

    Coisy, C.; Belaid, A.

    2004-01-01

    In this paper, a method for analytic handwritten word recognition based on causal Markov random fields is described. The words models are HMMs where each state corresponds to a letter; each letter is modelled by a NSHP­HMM (Markov field). Global models are build dynamically, and used for recognition

  8. Development of reversible jump Markov Chain Monte Carlo algorithm in the Bayesian mixture modeling for microarray data in Indonesia

    Science.gov (United States)

    Astuti, Ani Budi; Iriawan, Nur; Irhamah, Kuswanto, Heri

    2017-12-01

    In the Bayesian mixture modeling requires stages the identification number of the most appropriate mixture components thus obtained mixture models fit the data through data driven concept. Reversible Jump Markov Chain Monte Carlo (RJMCMC) is a combination of the reversible jump (RJ) concept and the Markov Chain Monte Carlo (MCMC) concept used by some researchers to solve the problem of identifying the number of mixture components which are not known with certainty number. In its application, RJMCMC using the concept of the birth/death and the split-merge with six types of movement, that are w updating, θ updating, z updating, hyperparameter β updating, split-merge for components and birth/death from blank components. The development of the RJMCMC algorithm needs to be done according to the observed case. The purpose of this study is to know the performance of RJMCMC algorithm development in identifying the number of mixture components which are not known with certainty number in the Bayesian mixture modeling for microarray data in Indonesia. The results of this study represent that the concept RJMCMC algorithm development able to properly identify the number of mixture components in the Bayesian normal mixture model wherein the component mixture in the case of microarray data in Indonesia is not known for certain number.

  9. Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling

    Energy Technology Data Exchange (ETDEWEB)

    Vrugt, Jasper A [Los Alamos National Laboratory; Hyman, James M [Los Alamos National Laboratory; Robinson, Bruce A [Los Alamos National Laboratory; Higdon, Dave [Los Alamos National Laboratory; Ter Braak, Cajo J F [NETHERLANDS; Diks, Cees G H [UNIV OF AMSTERDAM

    2008-01-01

    Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled DiffeRential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, high-dimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems.

  10. Influence of Averaging Preprocessing on Image Analysis with a Markov Random Field Model

    Science.gov (United States)

    Sakamoto, Hirotaka; Nakanishi-Ohno, Yoshinori; Okada, Masato

    2018-02-01

    This paper describes our investigations into the influence of averaging preprocessing on the performance of image analysis. Averaging preprocessing involves a trade-off: image averaging is often undertaken to reduce noise while the number of image data available for image analysis is decreased. We formulated a process of generating image data by using a Markov random field (MRF) model to achieve image analysis tasks such as image restoration and hyper-parameter estimation by a Bayesian approach. According to the notions of Bayesian inference, posterior distributions were analyzed to evaluate the influence of averaging. There are three main results. First, we found that the performance of image restoration with a predetermined value for hyper-parameters is invariant regardless of whether averaging is conducted. We then found that the performance of hyper-parameter estimation deteriorates due to averaging. Our analysis of the negative logarithm of the posterior probability, which is called the free energy based on an analogy with statistical mechanics, indicated that the confidence of hyper-parameter estimation remains higher without averaging. Finally, we found that when the hyper-parameters are estimated from the data, the performance of image restoration worsens as averaging is undertaken. We conclude that averaging adversely influences the performance of image analysis through hyper-parameter estimation.

  11. Epigenetic change detection and pattern recognition via Bayesian hierarchical hidden Markov models.

    Science.gov (United States)

    Wang, Xinlei; Zang, Miao; Xiao, Guanghua

    2013-06-15

    Epigenetics is the study of changes to the genome that can switch genes on or off and determine which proteins are transcribed without altering the DNA sequence. Recently, epigenetic changes have been linked to the development and progression of disease such as psychiatric disorders. High-throughput epigenetic experiments have enabled researchers to measure genome-wide epigenetic profiles and yield data consisting of intensity ratios of immunoprecipitation versus reference samples. The intensity ratios can provide a view of genomic regions where protein binding occur under one experimental condition and further allow us to detect epigenetic alterations through comparison between two different conditions. However, such experiments can be expensive, with only a few replicates available. Moreover, epigenetic data are often spatially correlated with high noise levels. In this paper, we develop a Bayesian hierarchical model, combined with hidden Markov processes with four states for modeling spatial dependence, to detect genomic sites with epigenetic changes from two-sample experiments with paired internal control. One attractive feature of the proposed method is that the four states of the hidden Markov process have well-defined biological meanings and allow us to directly call the change patterns based on the corresponding posterior probabilities. In contrast, none of existing methods can offer this advantage. In addition, the proposed method offers great power in statistical inference by spatial smoothing (via hidden Markov modeling) and information pooling (via hierarchical modeling). Both simulation studies and real data analysis in a cocaine addiction study illustrate the reliability and success of this method. Copyright © 2012 John Wiley & Sons, Ltd.

  12. A sow replacement model using Bayesian updating in a three-level hierarchic Markov process. I. Biological model

    DEFF Research Database (Denmark)

    Kristensen, Anders Ringgaard; Søllested, Thomas Algot

    2004-01-01

    that really uses all these methodological improvements. In this paper, the biological model describing the performance and feed intake of sows is presented. In particular, estimation of herd specific parameters is emphasized. The optimization model is described in a subsequent paper......Several replacement models have been presented in literature. In other applicational areas like dairy cow replacement, various methodological improvements like hierarchical Markov processes and Bayesian updating have been implemented, but not in sow models. Furthermore, there are methodological...... improvements like multi-level hierarchical Markov processes with decisions on multiple time scales, efficient methods for parameter estimations at herd level and standard software that has been hardly implemented at all in any replacement model. The aim of this study is to present a sow replacement model...

  13. Markov processes

    CERN Document Server

    Kirkwood, James R

    2015-01-01

    Review of ProbabilityShort HistoryReview of Basic Probability DefinitionsSome Common Probability DistributionsProperties of a Probability DistributionProperties of the Expected ValueExpected Value of a Random Variable with Common DistributionsGenerating FunctionsMoment Generating FunctionsExercisesDiscrete-Time, Finite-State Markov ChainsIntroductionNotationTransition MatricesDirected Graphs: Examples of Markov ChainsRandom Walk with Reflecting BoundariesGambler’s RuinEhrenfest ModelCentral Problem of Markov ChainsCondition to Ensure a Unique Equilibrium StateFinding the Equilibrium StateTransient and Recurrent StatesIndicator FunctionsPerron-Frobenius TheoremAbsorbing Markov ChainsMean First Passage TimeMean Recurrence Time and the Equilibrium StateFundamental Matrix for Regular Markov ChainsDividing a Markov Chain into Equivalence ClassesPeriodic Markov ChainsReducible Markov ChainsSummaryExercisesDiscrete-Time, Infinite-State Markov ChainsRenewal ProcessesDelayed Renewal ProcessesEquilibrium State f...

  14. An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method

    International Nuclear Information System (INIS)

    Ma Xiang; Zabaras, Nicholas

    2009-01-01

    A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media

  15. Markov stochasticity coordinates

    International Nuclear Information System (INIS)

    Eliazar, Iddo

    2017-01-01

    Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

  16. Markov stochasticity coordinates

    Energy Technology Data Exchange (ETDEWEB)

    Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

    2017-01-15

    Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

  17. Bayesian Markov chain Monte Carlo Inversion of Time-Lapse Geophysical Data To Characterize the Vadose Zone

    DEFF Research Database (Denmark)

    Scholer, Marie; Irving, James; Zibar, Majken Caroline Looms

    Geophysical methods have the potential to provide valuable information on hydrological properties in the unsaturated zone. In particular, time-lapse geophysical data, when coupled with a hydrological model and inverted stochastically, may allow for the effective estimation of subsurface hydraulic...... parameters and their corresponding uncertainties. In this study, we use a Bayesian Markov-chain-Monte-Carlo (MCMC) inversion approach to investigate how much information regarding vadose zone hydraulic properties can be retrieved from time-lapse crosshole GPR data collected at the Arrenaes field site...

  18. Some Limit Properties of Random Transition Probability for Second-Order Nonhomogeneous Markov Chains Indexed by a Tree

    Directory of Open Access Journals (Sweden)

    Shi Zhiyan

    2009-01-01

    Full Text Available We study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain and a nonhomogeneous Markov chain indexed by a tree. As corollary, we obtain the property of the harmonic mean of random transition probability for a nonhomogeneous Markov chain.

  19. A sow replacement model using Bayesian updating in a three-level hierarchic Markov process. II. Optimization model

    DEFF Research Database (Denmark)

    Kristensen, Anders Ringgaard; Søllested, Thomas Algot

    2004-01-01

    improvements. The biological model of the replacement model is described in a previous paper and in this paper the optimization model is described. The model is developed as a prototype for use under practical conditions. The application of the model is demonstrated using data from two commercial Danish sow......Recent methodological improvements in replacement models comprising multi-level hierarchical Markov processes and Bayesian updating have hardly been implemented in any replacement model and the aim of this study is to present a sow replacement model that really uses these methodological...... herds. It is concluded that the Bayesian updating technique and the hierarchical structure decrease the size of the state space dramatically. Since parameter estimates vary considerably among herds it is concluded that decision support concerning sow replacement only makes sense with parameters...

  20. Bayesian Nonparametric Regression Analysis of Data with Random Effects Covariates from Longitudinal Measurements

    KAUST Repository

    Ryu, Duchwan

    2010-09-28

    We consider nonparametric regression analysis in a generalized linear model (GLM) framework for data with covariates that are the subject-specific random effects of longitudinal measurements. The usual assumption that the effects of the longitudinal covariate processes are linear in the GLM may be unrealistic and if this happens it can cast doubt on the inference of observed covariate effects. Allowing the regression functions to be unknown, we propose to apply Bayesian nonparametric methods including cubic smoothing splines or P-splines for the possible nonlinearity and use an additive model in this complex setting. To improve computational efficiency, we propose the use of data-augmentation schemes. The approach allows flexible covariance structures for the random effects and within-subject measurement errors of the longitudinal processes. The posterior model space is explored through a Markov chain Monte Carlo (MCMC) sampler. The proposed methods are illustrated and compared to other approaches, the "naive" approach and the regression calibration, via simulations and by an application that investigates the relationship between obesity in adulthood and childhood growth curves. © 2010, The International Biometric Society.

  1. A relation between non-Markov and Markov processes

    International Nuclear Information System (INIS)

    Hara, H.

    1980-01-01

    With the aid of a transformation technique, it is shown that some memory effects in the non-Markov processes can be eliminated. In other words, some non-Markov processes are rewritten in a form obtained by the random walk process; the Markov process. To this end, two model processes which have some memory or correlation in the random walk process are introduced. An explanation of the memory in the processes is given. (orig.)

  2. Bayesian methods for data analysis

    CERN Document Server

    Carlin, Bradley P.

    2009-01-01

    Approaches for statistical inference Introduction Motivating Vignettes Defining the Approaches The Bayes-Frequentist Controversy Some Basic Bayesian Models The Bayes approach Introduction Prior Distributions Bayesian Inference Hierarchical Modeling Model Assessment Nonparametric Methods Bayesian computation Introduction Asymptotic Methods Noniterative Monte Carlo Methods Markov Chain Monte Carlo Methods Model criticism and selection Bayesian Modeling Bayesian Robustness Model Assessment Bayes Factors via Marginal Density Estimation Bayes Factors

  3. Bayesian random-effect model for predicting outcome fraught with heterogeneity--an illustration with episodes of 44 patients with intractable epilepsy.

    Science.gov (United States)

    Yen, A M-F; Liou, H-H; Lin, H-L; Chen, T H-H

    2006-01-01

    The study aimed to develop a predictive model to deal with data fraught with heterogeneity that cannot be explained by sampling variation or measured covariates. The random-effect Poisson regression model was first proposed to deal with over-dispersion for data fraught with heterogeneity after making allowance for measured covariates. Bayesian acyclic graphic model in conjunction with Markov Chain Monte Carlo (MCMC) technique was then applied to estimate the parameters of both relevant covariates and random effect. Predictive distribution was then generated to compare the predicted with the observed for the Bayesian model with and without random effect. Data from repeated measurement of episodes among 44 patients with intractable epilepsy were used as an illustration. The application of Poisson regression without taking heterogeneity into account to epilepsy data yielded a large value of heterogeneity (heterogeneity factor = 17.90, deviance = 1485, degree of freedom (df) = 83). After taking the random effect into account, the value of heterogeneity factor was greatly reduced (heterogeneity factor = 0.52, deviance = 42.5, df = 81). The Pearson chi2 for the comparison between the expected seizure frequencies and the observed ones at two and three months of the model with and without random effect were 34.27 (p = 1.00) and 1799.90 (p dispersion attributed either to correlated property or to subject-to-subject variability.

  4. Ensemble bayesian model averaging using markov chain Monte Carlo sampling

    Energy Technology Data Exchange (ETDEWEB)

    Vrugt, Jasper A [Los Alamos National Laboratory; Diks, Cees G H [NON LANL; Clark, Martyn P [NON LANL

    2008-01-01

    Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery etal. Mon Weather Rev 133: 1155-1174, 2(05)) has recommended the Expectation-Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed Differential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model stream-flow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.

  5. Sub-seasonal-to-seasonal Reservoir Inflow Forecast using Bayesian Hierarchical Hidden Markov Model

    Science.gov (United States)

    Mukhopadhyay, S.; Arumugam, S.

    2017-12-01

    Sub-seasonal-to-seasonal (S2S) (15-90 days) streamflow forecasting is an emerging area of research that provides seamless information for reservoir operation from weather time scales to seasonal time scales. From an operational perspective, sub-seasonal inflow forecasts are highly valuable as these enable water managers to decide short-term releases (15-30 days), while holding water for seasonal needs (e.g., irrigation and municipal supply) and to meet end-of-the-season target storage at a desired level. We propose a Bayesian Hierarchical Hidden Markov Model (BHHMM) to develop S2S inflow forecasts for the Tennessee Valley Area (TVA) reservoir system. Here, the hidden states are predicted by relevant indices that influence the inflows at S2S time scale. The hidden Markov model also captures the both spatial and temporal hierarchy in predictors that operate at S2S time scale with model parameters being estimated as a posterior distribution using a Bayesian framework. We present our work in two steps, namely single site model and multi-site model. For proof of concept, we consider inflows to Douglas Dam, Tennessee, in the single site model. For multisite model we consider reservoirs in the upper Tennessee valley. Streamflow forecasts are issued and updated continuously every day at S2S time scale. We considered precipitation forecasts obtained from NOAA Climate Forecast System (CFSv2) GCM as predictors for developing S2S streamflow forecasts along with relevant indices for predicting hidden states. Spatial dependence of the inflow series of reservoirs are also preserved in the multi-site model. To circumvent the non-normality of the data, we consider the HMM in a Generalized Linear Model setting. Skill of the proposed approach is tested using split sample validation against a traditional multi-site canonical correlation model developed using the same set of predictors. From the posterior distribution of the inflow forecasts, we also highlight different system behavior

  6. An Active Lattice Model in a Bayesian Framework

    DEFF Research Database (Denmark)

    Carstensen, Jens Michael

    1996-01-01

    A Markov Random Field is used as a structural model of a deformable rectangular lattice. When used as a template prior in a Bayesian framework this model is powerful for making inferences about lattice structures in images. The model assigns maximum probability to the perfect regular lattice...... by penalizing deviations in alignment and lattice node distance. The Markov random field represents prior knowledge about the lattice structure, and through an observation model that incorporates the visual appearance of the nodes, we can simulate realizations from the posterior distribution. A maximum...... a posteriori (MAP) estimate, found by simulated annealing, is used as the reconstructed lattice. The model was developed as a central part of an algorithm for automatic analylsis of genetic experiments, positioned in a lattice structure by a robot. The algorithm has been successfully applied to many images...

  7. Bayesian Network Induction via Local Neighborhoods

    National Research Council Canada - National Science Library

    Margaritis, Dimitris

    1999-01-01

    .... We present an efficient algorithm for learning Bayesian networks from data. Our approach constructs Bayesian networks by first identifying each node's Markov blankets, then connecting nodes in a consistent way...

  8. Evaluating impacts using a BACI design, ratios, and a Bayesian approach with a focus on restoration

    OpenAIRE

    Conner, Mary M.; Saunders, W. Carl; Bouwes, Nicolaas; Jordan, Chris

    2016-01-01

    Before-after-control-impact (BACI) designs are an effective method to evaluate natural and human-induced perturbations on ecological variables when treatment sites cannot be randomly chosen. While effect sizes of interest can be tested with frequentist methods, using Bayesian Markov chain Monte Carlo (MCMC) sampling methods, probabilities of effect sizes, such as a ?20?% increase in density after restoration, can be directly estimated. Although BACI and Bayesian methods are used widely for as...

  9. Phasic Triplet Markov Chains.

    Science.gov (United States)

    El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar

    2014-11-01

    Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.

  10. A Bayesian Approach for Structural Learning with Hidden Markov Models

    Directory of Open Access Journals (Sweden)

    Cen Li

    2002-01-01

    Full Text Available Hidden Markov Models(HMM have proved to be a successful modeling paradigm for dynamic and spatial processes in many domains, such as speech recognition, genomics, and general sequence alignment. Typically, in these applications, the model structures are predefined by domain experts. Therefore, the HMM learning problem focuses on the learning of the parameter values of the model to fit the given data sequences. However, when one considers other domains, such as, economics and physiology, model structure capturing the system dynamic behavior is not available. In order to successfully apply the HMM methodology in these domains, it is important that a mechanism is available for automatically deriving the model structure from the data. This paper presents a HMM learning procedure that simultaneously learns the model structure and the maximum likelihood parameter values of a HMM from data. The HMM model structures are derived based on the Bayesian model selection methodology. In addition, we introduce a new initialization procedure for HMM parameter value estimation based on the K-means clustering method. Experimental results with artificially generated data show the effectiveness of the approach.

  11. Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

    International Nuclear Information System (INIS)

    Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Bao, Jie; Swiler, Laura

    2017-01-01

    In this paper we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.

  12. Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

    Science.gov (United States)

    Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Bao, Jie; Swiler, Laura

    2017-12-01

    In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated - reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.

  13. Subgeometric Ergodicity Analysis of Continuous-Time Markov Chains under Random-Time State-Dependent Lyapunov Drift Conditions

    Directory of Open Access Journals (Sweden)

    Mokaedi V. Lekgari

    2014-01-01

    Full Text Available We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs. We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.

  14. Random recurrence equations and ruin in a Markov-dependent stochastic economic environment

    DEFF Research Database (Denmark)

    Collamore, Jeffrey F.

    2009-01-01

    series models.  Our results build upon work of Goldie, who has developed tail asymptotics applicable for independent sequences of random variables subject to a random recurrence equation.  In contrast, we adopt a general approach based on the theory of Harris recurrent Markov chains and the associated...

  15. Shape Modelling Using Markov Random Field Restoration of Point Correspondences

    DEFF Research Database (Denmark)

    Paulsen, Rasmus Reinhold; Hilger, Klaus Baggesen

    2003-01-01

    A method for building statistical point distribution models is proposed. The novelty in this paper is the adaption of Markov random field regularization of the correspondence field over the set of shapes. The new approach leads to a generative model that produces highly homogeneous polygonized sh...

  16. Bayesian inference for Markov jump processes with informative observations.

    Science.gov (United States)

    Golightly, Andrew; Wilkinson, Darren J

    2015-04-01

    In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis.

  17. Calibration of environmental radionuclide transfer models using a Bayesian approach with Markov chain Monte Carlo simulations and model comparisons - Calibration of radionuclides transfer models in the environment using a Bayesian approach with Markov chain Monte Carlo simulation and comparison of models

    Energy Technology Data Exchange (ETDEWEB)

    Nicoulaud-Gouin, V.; Giacalone, M.; Gonze, M.A. [Institut de Radioprotection et de Surete Nucleaire-PRP-ENV/SERIS/LM2E (France); Martin-Garin, A.; Garcia-Sanchez, L. [IRSN-PRP-ENV/SERIS/L2BT (France)

    2014-07-01

    Calibration of transfer models according to observation data is a challenge, especially if parameters uncertainty is required, and if competing models should be decided between them. Generally two main calibration methods are used: The frequentist approach in which the unknown parameter of interest is supposed fixed and its estimation is based on the data only. In this category, least squared method has many restrictions in nonlinear models and competing models need to be nested in order to be compared. The bayesian inference in which the unknown parameter of interest is supposed random and its estimation is based on the data and on prior information. Compared to frequentist method, it provides probability density functions and therefore pointwise estimation with credible intervals. However, in practical cases, Bayesian inference is a complex problem of numerical integration, which explains its low use in operational modeling including radioecology. This study aims to illustrate the interest and feasibility of Bayesian approach in radioecology particularly in the case of ordinary differential equations with non-constant coefficients models, which cover most radiological risk assessment models, notably those implemented in the Symbiose platform (Gonze et al, 2010). Markov Chain Monte Carlo (MCMC) method (Metropolis et al., 1953) was used because the posterior expectations are intractable integrals. The invariant distribution of the parameters was performed by the metropolis-Hasting algorithm (Hastings, 1970). GNU-MCSim software (Bois and Maszle, 2011) a bayesian hierarchical framework, was used to deal with nonlinear differential models. Two case studies including this type of model were investigated: An Equilibrium Kinetic sorption model (EK) (e.g. van Genuchten et al, 1974), with experimental data concerning {sup 137}Cs and {sup 85}Sr sorption and desorption in different soils studied in stirred flow-through reactors. This model, generalizing the K{sub d} approach

  18. A Bayesian nonparametric approach to reconstruction and prediction of random dynamical systems

    Science.gov (United States)

    Merkatas, Christos; Kaloudis, Konstantinos; Hatjispyros, Spyridon J.

    2017-06-01

    We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods. Our results can be used by researchers in physical modeling interested in a fast and accurate estimation of low dimensional stochastic models when the size of the observed time series is small and the noise process (perhaps) is non-Gaussian. The inference procedure is demonstrated specifically in the case of polynomial maps of an arbitrary degree and when a Geometric Stick Breaking mixture process prior over the space of densities, is applied to the additive errors. Our method is parsimonious compared to Bayesian nonparametric techniques based on Dirichlet process mixtures, flexible and general. Simulations based on synthetic time series are presented.

  19. A Bayesian nonparametric approach to reconstruction and prediction of random dynamical systems.

    Science.gov (United States)

    Merkatas, Christos; Kaloudis, Konstantinos; Hatjispyros, Spyridon J

    2017-06-01

    We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods. Our results can be used by researchers in physical modeling interested in a fast and accurate estimation of low dimensional stochastic models when the size of the observed time series is small and the noise process (perhaps) is non-Gaussian. The inference procedure is demonstrated specifically in the case of polynomial maps of an arbitrary degree and when a Geometric Stick Breaking mixture process prior over the space of densities, is applied to the additive errors. Our method is parsimonious compared to Bayesian nonparametric techniques based on Dirichlet process mixtures, flexible and general. Simulations based on synthetic time series are presented.

  20. Bayesian statistics an introduction

    CERN Document Server

    Lee, Peter M

    2012-01-01

    Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as wel

  1. Bayesian structural inference for hidden processes

    Science.gov (United States)

    Strelioff, Christopher C.; Crutchfield, James P.

    2014-04-01

    We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ɛ-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ɛ-machines, irrespective of estimated transition probabilities. Properties of ɛ-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

  2. Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors

    International Nuclear Information System (INIS)

    Lucka, Felix

    2012-01-01

    Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in the prior distribution has attracted attention. Important questions about the relation between regularization theory and Bayesian inference still need to be addressed when using sparsity promoting inversion. A practical obstacle for these examinations is the lack of fast posterior sampling algorithms for sparse, high-dimensional Bayesian inversion. Accessing the full range of Bayesian inference methods requires being able to draw samples from the posterior probability distribution in a fast and efficient way. This is usually done using Markov chain Monte Carlo (MCMC) sampling algorithms. In this paper, we develop and examine a new implementation of a single component Gibbs MCMC sampler for sparse priors relying on L1-norms. We demonstrate that the efficiency of our Gibbs sampler increases when the level of sparsity or the dimension of the unknowns is increased. This property is contrary to the properties of the most commonly applied Metropolis–Hastings (MH) sampling schemes. We demonstrate that the efficiency of MH schemes for L1-type priors dramatically decreases when the level of sparsity or the dimension of the unknowns is increased. Practically, Bayesian inversion for L1-type priors using MH samplers is not feasible at all. As this is commonly believed to be an intrinsic feature of MCMC sampling, the performance of our Gibbs sampler also challenges common beliefs about the applicability of sample based Bayesian inference. (paper)

  3. Bayesian Parameter Estimation via Filtering and Functional Approximations

    KAUST Repository

    Matthies, Hermann G.

    2016-11-25

    The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.

  4. Bayesian Parameter Estimation via Filtering and Functional Approximations

    KAUST Repository

    Matthies, Hermann G.; Litvinenko, Alexander; Rosic, Bojana V.; Zander, Elmar

    2016-01-01

    The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.

  5. A Bayesian sequential design with adaptive randomization for 2-sided hypothesis test.

    Science.gov (United States)

    Yu, Qingzhao; Zhu, Lin; Zhu, Han

    2017-11-01

    Bayesian sequential and adaptive randomization designs are gaining popularity in clinical trials thanks to their potentials to reduce the number of required participants and save resources. We propose a Bayesian sequential design with adaptive randomization rates so as to more efficiently attribute newly recruited patients to different treatment arms. In this paper, we consider 2-arm clinical trials. Patients are allocated to the 2 arms with a randomization rate to achieve minimum variance for the test statistic. Algorithms are presented to calculate the optimal randomization rate, critical values, and power for the proposed design. Sensitivity analysis is implemented to check the influence on design by changing the prior distributions. Simulation studies are applied to compare the proposed method and traditional methods in terms of power and actual sample sizes. Simulations show that, when total sample size is fixed, the proposed design can obtain greater power and/or cost smaller actual sample size than the traditional Bayesian sequential design. Finally, we apply the proposed method to a real data set and compare the results with the Bayesian sequential design without adaptive randomization in terms of sample sizes. The proposed method can further reduce required sample size. Copyright © 2017 John Wiley & Sons, Ltd.

  6. Multivariate longitudinal data analysis with mixed effects hidden Markov models.

    Science.gov (United States)

    Raffa, Jesse D; Dubin, Joel A

    2015-09-01

    Multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest, which is often hidden and not directly measurable. We outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process. We propose a class of models which uses a hidden Markov model with separate but correlated random effects between multiple longitudinal responses. This approach was motivated by a smoking cessation clinical trial, where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior. A Bayesian method using Markov chain Monte Carlo is used. Comparison of separate univariate response models to the bivariate response models was undertaken. Our methods are demonstrated on the smoking cessation clinical trial dataset, and properties of our approach are examined through extensive simulation studies. © 2015, The International Biometric Society.

  7. Observation uncertainty in reversible Markov chains.

    Science.gov (United States)

    Metzner, Philipp; Weber, Marcus; Schütte, Christof

    2010-09-01

    In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .

  8. Efficient tests for equivalence of hidden Markov processes and quantum random walks

    NARCIS (Netherlands)

    U. Faigle; A. Schönhuth (Alexander)

    2011-01-01

    htmlabstractWhile two hidden Markov process (HMP) resp.~quantum random walk (QRW) parametrizations can differ from one another, the stochastic processes arising from them can be equivalent. Here a polynomial-time algorithm is presented which can determine equivalence of two HMP parametrizations

  9. Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

    Science.gov (United States)

    Lu, Dan; Ricciuto, Daniel; Walker, Anthony; Safta, Cosmin; Munger, William

    2017-09-01

    Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.

  10. Learning dynamic Bayesian networks with mixed variables

    DEFF Research Database (Denmark)

    Bøttcher, Susanne Gammelgaard

    This paper considers dynamic Bayesian networks for discrete and continuous variables. We only treat the case, where the distribution of the variables is conditional Gaussian. We show how to learn the parameters and structure of a dynamic Bayesian network and also how the Markov order can be learned...

  11. Stability of the Markov operator and synchronization of Markovian random products

    Science.gov (United States)

    Díaz, Lorenzo J.; Matias, Edgar

    2018-05-01

    We study Markovian random products on a large class of ‘m-dimensional’ connected compact metric spaces (including products of closed intervals and trees). We introduce a splitting condition, generalizing the classical one by Dubins and Freedman, and prove that this condition implies the asymptotic stability of the corresponding Markov operator and (exponentially fast) synchronization.

  12. Non-homogeneous dynamic Bayesian networks for continuous data

    NARCIS (Netherlands)

    Grzegorczyk, Marco; Husmeier, Dirk

    Classical dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption and cannot deal with non-homogeneous temporal processes. Various approaches to relax the homogeneity assumption have recently been proposed. The present paper presents a combination of a Bayesian network with

  13. Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts

    Science.gov (United States)

    Jia, Chen

    2017-09-01

    Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

  14. Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

    Science.gov (United States)

    Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

    2017-12-01

    Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

  15. Bayesian Nonparametric Hidden Markov Models with application to the analysis of copy-number-variation in mammalian genomes.

    Science.gov (United States)

    Yau, C; Papaspiliopoulos, O; Roberts, G O; Holmes, C

    2011-01-01

    We consider the development of Bayesian Nonparametric methods for product partition models such as Hidden Markov Models and change point models. Our approach uses a Mixture of Dirichlet Process (MDP) model for the unknown sampling distribution (likelihood) for the observations arising in each state and a computationally efficient data augmentation scheme to aid inference. The method uses novel MCMC methodology which combines recent retrospective sampling methods with the use of slice sampler variables. The methodology is computationally efficient, both in terms of MCMC mixing properties, and robustness to the length of the time series being investigated. Moreover, the method is easy to implement requiring little or no user-interaction. We apply our methodology to the analysis of genomic copy number variation.

  16. Bayesian methods to restore and re build images: application to gamma-graphy and to photofission tomography

    International Nuclear Information System (INIS)

    Stawinski, G.

    1998-01-01

    Bayesian algorithms are developed to solve inverse problems in gamma imaging and photofission tomography. The first part of this work is devoted to the modeling of our measurement systems. Two models have been found for both applications: the first one is a simple conventional model and the second one is a cascaded point process model. EM and MCMC Bayesian algorithms for image restoration and image reconstruction have been developed for these models and compared. The cascaded point process model does not improve significantly the results previously obtained by the classical model. To original approaches have been proposed, which increase the results previously obtained. The first approach uses an inhomogeneous Markov Random Field as a prior law, and makes the regularization parameter spatially vary. However, the problem of the estimation of hyper-parameters has not been solved. In the case of the deconvolution of point sources, a second approach has been proposed, which introduces a high level prior model. The picture is modeled as a list of objects, whose parameters and number are unknown. The results obtained with this method are more accurate than those obtained with the conventional Markov Random Field prior model and require less computational costs. (author)

  17. Rate estimation in partially observed Markov jump processes with measurement errors

    OpenAIRE

    Amrein, Michael; Kuensch, Hans R.

    2010-01-01

    We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data, we embed the Markov jump process into the framework of a general state space model. We do not use diffusion approximations. Markov chain Monte Carlo and particle filter type algorithms are introduced, which allow sampling from the posterior distribution of t...

  18. Bayesian models: A statistical primer for ecologists

    Science.gov (United States)

    Hobbs, N. Thompson; Hooten, Mevin B.

    2015-01-01

    Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach.Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian models

  19. Stability Analysis of Networked Control Systems with Random Time Delays and Packet Dropouts Modeled by Markov Chains

    Directory of Open Access Journals (Sweden)

    Li Qiu

    2013-01-01

    unified Markov jump model. The random time delays and packet dropouts existed in feedback communication link are modeled by two independent Markov chains; the resulting closed-loop system is described by a new Markovian jump linear system (MJLS with Markov delays. Sufficient conditions of the stochastic stability for NCSs is obtained by constructing a novel Lyapunov functional, and the mode-dependent output feedback controller design method is presented based on linear matrix inequality (LMI technique. A numerical example is given to illustrate the effectiveness of the proposed method.

  20. Bayesian modeling using WinBUGS

    CERN Document Server

    Ntzoufras, Ioannis

    2009-01-01

    A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all ...

  1. Exact Markov chains versus diffusion theory for haploid random mating.

    Science.gov (United States)

    Tyvand, Peder A; Thorvaldsen, Steinar

    2010-05-01

    Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck. 2010 Elsevier Inc. All rights reserved.

  2. Joint modeling of ChIP-seq data via a Markov random field model

    NARCIS (Netherlands)

    Bao, Yanchun; Vinciotti, Veronica; Wit, Ernst; 't Hoen, Peter A C

    Chromatin ImmunoPrecipitation-sequencing (ChIP-seq) experiments have now become routine in biology for the detection of protein-binding sites. In this paper, we present a Markov random field model for the joint analysis of multiple ChIP-seq experiments. The proposed model naturally accounts for

  3. Prestack inversion based on anisotropic Markov random field-maximum posterior probability inversion and its application to identify shale gas sweet spots

    Science.gov (United States)

    Wang, Kang-Ning; Sun, Zan-Dong; Dong, Ning

    2015-12-01

    Economic shale gas production requires hydraulic fracture stimulation to increase the formation permeability. Hydraulic fracturing strongly depends on geomechanical parameters such as Young's modulus and Poisson's ratio. Fracture-prone sweet spots can be predicted by prestack inversion, which is an ill-posed problem; thus, regularization is needed to obtain unique and stable solutions. To characterize gas-bearing shale sedimentary bodies, elastic parameter variations are regarded as an anisotropic Markov random field. Bayesian statistics are adopted for transforming prestack inversion to the maximum posterior probability. Two energy functions for the lateral and vertical directions are used to describe the distribution, and the expectation-maximization algorithm is used to estimate the hyperparameters of the prior probability of elastic parameters. Finally, the inversion yields clear geological boundaries, high vertical resolution, and reasonable lateral continuity using the conjugate gradient method to minimize the objective function. Antinoise and imaging ability of the method were tested using synthetic and real data.

  4. Bayesian prediction of future ice sheet volume using local approximation Markov chain Monte Carlo methods

    Science.gov (United States)

    Davis, A. D.; Heimbach, P.; Marzouk, Y.

    2017-12-01

    We develop a Bayesian inverse modeling framework for predicting future ice sheet volume with associated formal uncertainty estimates. Marine ice sheets are drained by fast-flowing ice streams, which we simulate using a flowline model. Flowline models depend on geometric parameters (e.g., basal topography), parameterized physical processes (e.g., calving laws and basal sliding), and climate parameters (e.g., surface mass balance), most of which are unknown or uncertain. Given observations of ice surface velocity and thickness, we define a Bayesian posterior distribution over static parameters, such as basal topography. We also define a parameterized distribution over variable parameters, such as future surface mass balance, which we assume are not informed by the data. Hyperparameters are used to represent climate change scenarios, and sampling their distributions mimics internal variation. For example, a warming climate corresponds to increasing mean surface mass balance but an individual sample may have periods of increasing or decreasing surface mass balance. We characterize the predictive distribution of ice volume by evaluating the flowline model given samples from the posterior distribution and the distribution over variable parameters. Finally, we determine the effect of climate change on future ice sheet volume by investigating how changing the hyperparameters affects the predictive distribution. We use state-of-the-art Bayesian computation to address computational feasibility. Characterizing the posterior distribution (using Markov chain Monte Carlo), sampling the full range of variable parameters and evaluating the predictive model is prohibitively expensive. Furthermore, the required resolution of the inferred basal topography may be very high, which is often challenging for sampling methods. Instead, we leverage regularity in the predictive distribution to build a computationally cheaper surrogate over the low dimensional quantity of interest (future ice

  5. Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates

    KAUST Repository

    Elsheikh, Ahmed H.

    2014-02-01

    An efficient Bayesian calibration method based on the nested sampling (NS) algorithm and non-intrusive polynomial chaos method is presented. Nested sampling is a Bayesian sampling algorithm that builds a discrete representation of the posterior distributions by iteratively re-focusing a set of samples to high likelihood regions. NS allows representing the posterior probability density function (PDF) with a smaller number of samples and reduces the curse of dimensionality effects. The main difficulty of the NS algorithm is in the constrained sampling step which is commonly performed using a random walk Markov Chain Monte-Carlo (MCMC) algorithm. In this work, we perform a two-stage sampling using a polynomial chaos response surface to filter out rejected samples in the Markov Chain Monte-Carlo method. The combined use of nested sampling and the two-stage MCMC based on approximate response surfaces provides significant computational gains in terms of the number of simulation runs. The proposed algorithm is applied for calibration and model selection of subsurface flow models. © 2013.

  6. Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images

    International Nuclear Information System (INIS)

    Mumcuglu, E.U.; Leahy, R.; Zhou, Z.; Cherry, S.R.

    1994-01-01

    The authors describe conjugate gradient algorithms for reconstruction of transmission and emission PET images. The reconstructions are based on a Bayesian formulation, where the data are modeled as a collection of independent Poisson random variables and the image is modeled using a Markov random field. A conjugate gradient algorithm is used to compute a maximum a posteriori (MAP) estimate of the image by maximizing over the posterior density. To ensure nonnegativity of the solution, a penalty function is used to convert the problem to one of unconstrained optimization. Preconditioners are used to enhance convergence rates. These methods generally achieve effective convergence in 15--25 iterations. Reconstructions are presented of an 18 FDG whole body scan from data collected using a Siemens/CTI ECAT931 whole body system. These results indicate significant improvements in emission image quality using the Bayesian approach, in comparison to filtered backprojection, particularly when reprojections of the MAP transmission image are used in place of the standard attenuation correction factors

  7. Hierarchical Bayesian Markov switching models with application to predicting spawning success of shovelnose sturgeon

    Science.gov (United States)

    Holan, S.H.; Davis, G.M.; Wildhaber, M.L.; DeLonay, A.J.; Papoulias, D.M.

    2009-01-01

    The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed. ?? Journal compilation 2009 Royal Statistical Society.

  8. Bayesian reconstruction of seafloor shape from side-scan sonar measurements using a Markov Random Field

    OpenAIRE

    Woock, P.; Pak, Alexey

    2014-01-01

    To explore the seafloor, a side-scan sonar emits a directed acoustic signal and then records the returning (reflected) signal intensity as a function of time. The inversion of that process is not unique: multiple shapes may lead to identical measured responses. In this work, we suggest a Bayesian approach to reconstructing the 3D shape of the seafloor from multiple sonar measurements, inspired by the state-of-the-art methods of inverse raytracing that originated in computer vision. The space ...

  9. Colour and rotation invariant textural features based on Markov random fields

    Czech Academy of Sciences Publication Activity Database

    Vácha, Pavel; Haindl, Michal; Suk, Tomáš

    2011-01-01

    Roč. 32, č. 6 (2011), s. 771-779 ISSN 0167-8655 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593 Grant - others:GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : Image modelling * colour texture * Illumination invariance * Markov random field * rotation invariance Subject RIV: BD - Theory of Information Impact factor: 1.034, year: 2011 http://library.utia.cas.cz/separaty/2011/RO/vacha-0357314.pdf

  10. Bayesian Modelling of fMRI Time Series

    DEFF Research Database (Denmark)

    Højen-Sørensen, Pedro; Hansen, Lars Kai; Rasmussen, Carl Edward

    2000-01-01

    We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte...... Carlo (MCMC) sampling techniques. The advantage of this method is that detection of short time learning effects between repeated trials is possible since inference is based only on single trial experiments....

  11. Bayesian target tracking based on particle filter

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    For being able to deal with the nonlinear or non-Gaussian problems, particle filters have been studied by many researchers. Based on particle filter, the extended Kalman filter (EKF) proposal function is applied to Bayesian target tracking. Markov chain Monte Carlo (MCMC) method, the resampling step, etc novel techniques are also introduced into Bayesian target tracking. And the simulation results confirm the improved particle filter with these techniques outperforms the basic one.

  12. A Correlated Random Effects Model for Non-homogeneous Markov Processes with Nonignorable Missingness.

    Science.gov (United States)

    Chen, Baojiang; Zhou, Xiao-Hua

    2013-05-01

    Life history data arising in clusters with prespecified assessment time points for patients often feature incomplete data since patients may choose to visit the clinic based on their needs. Markov process models provide a useful tool describing disease progression for life history data. The literature mainly focuses on time homogeneous process. In this paper we develop methods to deal with non-homogeneous Markov process with incomplete clustered life history data. A correlated random effects model is developed to deal with the nonignorable missingness, and a time transformation is employed to address the non-homogeneity in the transition model. Maximum likelihood estimate based on the Monte-Carlo EM algorithm is advocated for parameter estimation. Simulation studies demonstrate that the proposed method works well in many situations. We also apply this method to an Alzheimer's disease study.

  13. A Bayesian MCMC method for point process models with intractable normalising constants

    DEFF Research Database (Denmark)

    Berthelsen, Kasper Klitgaard; Møller, Jesper

    2004-01-01

    to simulate from the "unknown distribution", perfect simulation algorithms become useful. We illustrate the method in cases whre the likelihood is given by a Markov point process model. Particularly, we consider semi-parametric Bayesian inference in connection to both inhomogeneous Markov point process models...... and pairwise interaction point processes....

  14. A Markov random walk under constraint for discovering overlapping communities in complex networks

    International Nuclear Information System (INIS)

    Jin, Di; Yang, Bo; Liu, Dayou; He, Dongxiao; Liu, Jie; Baquero, Carlos

    2011-01-01

    The detection of overlapping communities in complex networks has motivated recent research in relevant fields. Aiming to address this problem, we propose a Markov-dynamics-based algorithm, called UEOC, which means 'unfold and extract overlapping communities'. In UEOC, when identifying each natural community that overlaps, a Markov random walk method combined with a constraint strategy, which is based on the corresponding annealed network (degree conserving random network), is performed to unfold the community. Then, a cutoff criterion with the aid of a local community function, called conductance, which can be thought of as the ratio between the number of edges inside the community and those leaving it, is presented to extract this emerged community from the entire network. The UEOC algorithm depends on only one parameter whose value can be easily set, and it requires no prior knowledge of the hidden community structures. The proposed UEOC has been evaluated both on synthetic benchmarks and on some real-world networks, and has been compared with a set of competing algorithms. The experimental result has shown that UEOC is highly effective and efficient for discovering overlapping communities

  15. Bayesian community detection

    DEFF Research Database (Denmark)

    Mørup, Morten; Schmidt, Mikkel N

    2012-01-01

    Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model...... for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities...... consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled....

  16. Markov Tail Chains

    OpenAIRE

    janssen, Anja; Segers, Johan

    2013-01-01

    The extremes of a univariate Markov chain with regularly varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper we extend this fact to Markov chains with multivariate regularly varying marginal distributions in Rd. We analyze both the forward and the backward tail process and show that they mutually determine each other through a kind of adjoint relation. In ...

  17. Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution

    Science.gov (United States)

    Saputro, D. R. S.; Amalia, F.; Widyaningsih, P.; Affan, R. C.

    2018-05-01

    Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

  18. Bayesian Inference and Online Learning in Poisson Neuronal Networks.

    Science.gov (United States)

    Huang, Yanping; Rao, Rajesh P N

    2016-08-01

    Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.

  19. MCMC for parameters estimation by bayesian approach

    International Nuclear Information System (INIS)

    Ait Saadi, H.; Ykhlef, F.; Guessoum, A.

    2011-01-01

    This article discusses the parameter estimation for dynamic system by a Bayesian approach associated with Markov Chain Monte Carlo methods (MCMC). The MCMC methods are powerful for approximating complex integrals, simulating joint distributions, and the estimation of marginal posterior distributions, or posterior means. The MetropolisHastings algorithm has been widely used in Bayesian inference to approximate posterior densities. Calibrating the proposal distribution is one of the main issues of MCMC simulation in order to accelerate the convergence.

  20. A nonparametric Bayesian approach for genetic evaluation in ...

    African Journals Online (AJOL)

    Unknown

    Finally, one can report the whole of the posterior probability distributions of the parameters in ... the Markov Chain Monte Carlo Methods, and more specific Gibbs Sampling, these ...... Bayesian Methods in Animal Breeding Theory. J. Anim. Sci.

  1. Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.

    Science.gov (United States)

    Chaubert-Pereira, Florence; Guédon, Yann; Lavergne, Christian; Trottier, Catherine

    2010-09-01

    Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates. © 2009, The International Biometric Society.

  2. Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

    Energy Technology Data Exchange (ETDEWEB)

    Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Bao, Jie; Swiler, Laura

    2017-12-01

    In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic amplitude versus angle (AVA) and controlled source electromagnetic (CSEM) data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo (MCMC) sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis (DREAM) and Adaptive Metropolis (AM) samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and CSEM data. The multi-chain MCMC is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic AVA and CSEM joint inversion provides better estimation of reservoir saturations than the seismic AVA-only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated – reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.

  3. Bayesian analysis of longitudinal Johne's disease diagnostic data without a gold standard test

    DEFF Research Database (Denmark)

    Wang, C.; Turnbull, B.W.; Nielsen, Søren Saxmose

    2011-01-01

    the posterior estimates of the model parameters that provide the basis for inference concerning the accuracy of the diagnostic procedure. Based on the Bayesian approach, the posterior probability distribution of the change-point onset time can be obtained and used as a criterion for infection diagnosis......-point process with a Weibull survival hazard function was used to model the progression of the hidden disease status. The model adjusted for the fixed effects of covariate variables and random effects of subject on the diagnostic testing procedure. Markov chain Monte Carlo methods were used to compute....... An application is presented to an analysis of ELISA and fecal culture test outcomes in the diagnostic testing of paratuberculosis (Johne's disease) for a Danish longitudinal study from January 2000 to March 2003. The posterior probability criterion based on the Bayesian model with 4 repeated observations has...

  4. Cover estimation and payload location using Markov random fields

    Science.gov (United States)

    Quach, Tu-Thach

    2014-02-01

    Payload location is an approach to find the message bits hidden in steganographic images, but not necessarily their logical order. Its success relies primarily on the accuracy of the underlying cover estimators and can be improved if more estimators are used. This paper presents an approach based on Markov random field to estimate the cover image given a stego image. It uses pairwise constraints to capture the natural two-dimensional statistics of cover images and forms a basis for more sophisticated models. Experimental results show that it is competitive against current state-of-the-art estimators and can locate payload embedded by simple LSB steganography and group-parity steganography. Furthermore, when combined with existing estimators, payload location accuracy improves significantly.

  5. Nonparametric Bayesian Modeling of Complex Networks

    DEFF Research Database (Denmark)

    Schmidt, Mikkel Nørgaard; Mørup, Morten

    2013-01-01

    an infinite mixture model as running example, we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model?s fit and predictive performance. We explain how advanced nonparametric models......Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...

  6. A Fuzzy-Logic Power Management Strategy Based on Markov Random Prediction for Hybrid Energy Storage Systems

    Directory of Open Access Journals (Sweden)

    Yanzi Wang

    2016-01-01

    Full Text Available Over the last few years; issues regarding the use of hybrid energy storage systems (HESSs in hybrid electric vehicles have been highlighted by the industry and in academic fields. This paper proposes a fuzzy-logic power management strategy based on Markov random prediction for an active parallel battery-UC HESS. The proposed power management strategy; the inputs for which are the vehicle speed; the current electric power demand and the predicted electric power demand; is used to distribute the electrical power between the battery bank and the UC bank. In this way; the battery bank power is limited to a certain range; and the peak and average charge/discharge power of the battery bank and overall loss incurred by the whole HESS are also reduced. Simulations and scaled-down experimental platforms are constructed to verify the proposed power management strategy. The simulations and experimental results demonstrate the advantages; feasibility and effectiveness of the fuzzy-logic power management strategy based on Markov random prediction.

  7. A Unified 3D Mesh Segmentation Framework Based on Markov Random Field

    OpenAIRE

    Z.F. Shi; L.Y. Lu; D. Le; X.M. Niu

    2012-01-01

    3D Mesh segmentation has become an important research field in computer graphics during the past decades. Many geometry based and semantic oriented approaches for 3D mesh segmentation has been presented. In this paper, we present a definition of mesh segmentation according to labeling problem. Inspired by the Markov Random Field (MRF) based image segmentation, we propose a new framework of 3D mesh segmentation based on MRF and use graph cuts to solve it. Any features of 3D mesh can be integra...

  8. On the application of Hidden Markov Model and Bayesian Belief Network to seismic noise at Las Canadas Caldera, Tenerife, Spain

    International Nuclear Information System (INIS)

    Quintero Oliveros, Anggi; Carniel, Roberto; Tarraga, Marta; Aspinall, Willy

    2008-01-01

    The Teide-Pico Viejo volcanic complex situated in Tenerife Island (Canary Islands, Spain) has recently shown signs of unrest, long after its last eruptive episode at Chinyero in 1909, and the last explosive episode which happened at Montana Blanca, 2000 years ago. In this paper we study the seismicity of the Teide-Pico Viejo complex recorded between May and December 2004, in order to show the applicability of tools such as Hidden Markov Models and Bayesian Belief Networks which can be used to build a structure for evaluating the probability of given eruptive or volcano-related scenarios. The results support the existence of a bidirectional relationship between volcano-tectonic events and the background seismic noise - in particular its frequency content. This in turn suggests that the two phenomena can be related to one unique process influencing their generation

  9. On the application of Hidden Markov Model and Bayesian Belief Network to seismic noise at Las Canadas Caldera, Tenerife, Spain

    Energy Technology Data Exchange (ETDEWEB)

    Quintero Oliveros, Anggi [Dipartimento di Georisorse e Territorio, Universita di Udine (Italy); Departamento de Ciencias de La Tierra, Universidad Simon Bolivar, Caracas (Venezuela); Carniel, Roberto [Dipartimento di Georisorse e Territorio, Universita di Udine (Italy)], E-mail: roberto.carniel@uniud.it; Tarraga, Marta [Departamento de Volcanologia, Museo Nacional de Ciencias Naturales, CSIC, Madrid (Spain); Aspinall, Willy [Aspinall and Associates, 5 Woodside Close, Beaconsfield, Bucks (United Kingdom)

    2008-08-15

    The Teide-Pico Viejo volcanic complex situated in Tenerife Island (Canary Islands, Spain) has recently shown signs of unrest, long after its last eruptive episode at Chinyero in 1909, and the last explosive episode which happened at Montana Blanca, 2000 years ago. In this paper we study the seismicity of the Teide-Pico Viejo complex recorded between May and December 2004, in order to show the applicability of tools such as Hidden Markov Models and Bayesian Belief Networks which can be used to build a structure for evaluating the probability of given eruptive or volcano-related scenarios. The results support the existence of a bidirectional relationship between volcano-tectonic events and the background seismic noise - in particular its frequency content. This in turn suggests that the two phenomena can be related to one unique process influencing their generation.

  10. Bayesian Markov-Chain-Monte-Carlo inversion of time-lapse crosshole GPR data to characterize the vadose zone at the Arrenaes Site, Denmark

    DEFF Research Database (Denmark)

    Scholer, Marie; Irving, James; Zibar, Majken Caroline Looms

    2012-01-01

    We examined to what extent time-lapse crosshole ground-penetrating radar traveltimes, measured during a forced infiltration experiment at the Arreneas field site in Denmark, could help to quantify vadose zone hydraulic properties and their corresponding uncertainties using a Bayesian Markov...... distributions compared with the corresponding priors, which in turn significantly improves knowledge of soil hydraulic properties. Overall, the results obtained clearly demonstrate the value of the information contained in time-lapse GPR data for characterizing vadose zone dynamics.......-chain-Monte-Carlo inversion approach with different priors. The ground-penetrating radar (GPR) geophysical method has the potential to provide valuable information on the hydraulic properties of the vadose zone because of its strong sensitivity to soil water content. In particular, recent evidence has suggested...

  11. Fast sampling from a Hidden Markov Model posterior for large data

    DEFF Research Database (Denmark)

    Bonnevie, Rasmus; Hansen, Lars Kai

    2014-01-01

    Hidden Markov Models are of interest in a broad set of applications including modern data driven systems involving very large data sets. However, approximate inference methods based on Bayesian averaging are precluded in such applications as each sampling step requires a full sweep over the data...

  12. A Markov random field approach for microstructure synthesis

    International Nuclear Information System (INIS)

    Kumar, A; Nguyen, L; DeGraef, M; Sundararaghavan, V

    2016-01-01

    We test the notion that many microstructures have an underlying stationary probability distribution. The stationary probability distribution is ubiquitous: we know that different windows taken from a polycrystalline microstructure are generally ‘statistically similar’. To enable computation of such a probability distribution, microstructures are represented in the form of undirected probabilistic graphs called Markov Random Fields (MRFs). In the model, pixels take up integer or vector states and interact with multiple neighbors over a window. Using this lattice structure, algorithms are developed to sample the conditional probability density for the state of each pixel given the known states of its neighboring pixels. The sampling is performed using reference experimental images. 2D microstructures are artificially synthesized using the sampled probabilities. Statistical features such as grain size distribution and autocorrelation functions closely match with those of the experimental images. The mechanical properties of the synthesized microstructures were computed using the finite element method and were also found to match the experimental values. (paper)

  13. Introduction to Bayesian statistics

    CERN Document Server

    Bolstad, William M

    2017-01-01

    There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this Third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression. In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference with unknown mean and variance; Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computati...

  14. Entropy and long-range memory in random symbolic additive Markov chains.

    Science.gov (United States)

    Melnik, S S; Usatenko, O V

    2016-06-01

    The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory.

  15. A default Bayesian hypothesis test for mediation.

    Science.gov (United States)

    Nuijten, Michèle B; Wetzels, Ruud; Matzke, Dora; Dolan, Conor V; Wagenmakers, Eric-Jan

    2015-03-01

    In order to quantify the relationship between multiple variables, researchers often carry out a mediation analysis. In such an analysis, a mediator (e.g., knowledge of a healthy diet) transmits the effect from an independent variable (e.g., classroom instruction on a healthy diet) to a dependent variable (e.g., consumption of fruits and vegetables). Almost all mediation analyses in psychology use frequentist estimation and hypothesis-testing techniques. A recent exception is Yuan and MacKinnon (Psychological Methods, 14, 301-322, 2009), who outlined a Bayesian parameter estimation procedure for mediation analysis. Here we complete the Bayesian alternative to frequentist mediation analysis by specifying a default Bayesian hypothesis test based on the Jeffreys-Zellner-Siow approach. We further extend this default Bayesian test by allowing a comparison to directional or one-sided alternatives, using Markov chain Monte Carlo techniques implemented in JAGS. All Bayesian tests are implemented in the R package BayesMed (Nuijten, Wetzels, Matzke, Dolan, & Wagenmakers, 2014).

  16. On Bayesian shared component disease mapping and ecological regression with errors in covariates.

    Science.gov (United States)

    MacNab, Ying C

    2010-05-20

    Recent literature on Bayesian disease mapping presents shared component models (SCMs) for joint spatial modeling of two or more diseases with common risk factors. In this study, Bayesian hierarchical formulations of shared component disease mapping and ecological models are explored and developed in the context of ecological regression, taking into consideration errors in covariates. A review of multivariate disease mapping models (MultiVMs) such as the multivariate conditional autoregressive models that are also part of the more recent Bayesian disease mapping literature is presented. Some insights into the connections and distinctions between the SCM and MultiVM procedures are communicated. Important issues surrounding (appropriate) formulation of shared- and disease-specific components, consideration/choice of spatial or non-spatial random effects priors, and identification of model parameters in SCMs are explored and discussed in the context of spatial and ecological analysis of small area multivariate disease or health outcome rates and associated ecological risk factors. The methods are illustrated through an in-depth analysis of four-variate road traffic accident injury (RTAI) data: gender-specific fatal and non-fatal RTAI rates in 84 local health areas in British Columbia (Canada). Fully Bayesian inference via Markov chain Monte Carlo simulations is presented. Copyright 2010 John Wiley & Sons, Ltd.

  17. Bayesian theory and applications

    CERN Document Server

    Dellaportas, Petros; Polson, Nicholas G; Stephens, David A

    2013-01-01

    The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book has a unique format. There is an explanatory chapter devoted to each conceptual advance followed by journal-style chapters that provide applications or further advances on the concept. Thus, the volume is both a textbook and a compendium of papers covering a vast range of topics. It is appropriate for a well-informed novice interested in understanding the basic approach, methods and recent applications. Because of its advanced chapters and recent work, it is also appropriate for a more mature reader interested in recent applications and devel...

  18. Bayesian network learning for natural hazard assessments

    Science.gov (United States)

    Vogel, Kristin

    2016-04-01

    Even though quite different in occurrence and consequences, from a modelling perspective many natural hazards share similar properties and challenges. Their complex nature as well as lacking knowledge about their driving forces and potential effects make their analysis demanding. On top of the uncertainty about the modelling framework, inaccurate or incomplete event observations and the intrinsic randomness of the natural phenomenon add up to different interacting layers of uncertainty, which require a careful handling. Thus, for reliable natural hazard assessments it is crucial not only to capture and quantify involved uncertainties, but also to express and communicate uncertainties in an intuitive way. Decision-makers, who often find it difficult to deal with uncertainties, might otherwise return to familiar (mostly deterministic) proceedings. In the scope of the DFG research training group „NatRiskChange" we apply the probabilistic framework of Bayesian networks for diverse natural hazard and vulnerability studies. The great potential of Bayesian networks was already shown in previous natural hazard assessments. Treating each model component as random variable, Bayesian networks aim at capturing the joint distribution of all considered variables. Hence, each conditional distribution of interest (e.g. the effect of precautionary measures on damage reduction) can be inferred. The (in-)dependencies between the considered variables can be learned purely data driven or be given by experts. Even a combination of both is possible. By translating the (in-)dependences into a graph structure, Bayesian networks provide direct insights into the workings of the system and allow to learn about the underlying processes. Besides numerous studies on the topic, learning Bayesian networks from real-world data remains challenging. In previous studies, e.g. on earthquake induced ground motion and flood damage assessments, we tackled the problems arising with continuous variables

  19. Modeling and Bayesian parameter estimation for shape memory alloy bending actuators

    Science.gov (United States)

    Crews, John H.; Smith, Ralph C.

    2012-04-01

    In this paper, we employ a homogenized energy model (HEM) for shape memory alloy (SMA) bending actuators. Additionally, we utilize a Bayesian method for quantifying parameter uncertainty. The system consists of a SMA wire attached to a flexible beam. As the actuator is heated, the beam bends, providing endoscopic motion. The model parameters are fit to experimental data using an ordinary least-squares approach. The uncertainty in the fit model parameters is then quantified using Markov Chain Monte Carlo (MCMC) methods. The MCMC algorithm provides bounds on the parameters, which will ultimately be used in robust control algorithms. One purpose of the paper is to test the feasibility of the Random Walk Metropolis algorithm, the MCMC method used here.

  20. Bayesian spatiotemporal model of fMRI data using transfer functions.

    Science.gov (United States)

    Quirós, Alicia; Diez, Raquel Montes; Wilson, Simon P

    2010-09-01

    This research describes a new Bayesian spatiotemporal model to analyse BOLD fMRI studies. In the temporal dimension, we describe the shape of the hemodynamic response function (HRF) with a transfer function model. The spatial continuity and local homogeneity of the evoked responses are modelled by a Gaussian Markov random field prior on the parameter indicating activations. The proposal constitutes an extension of the spatiotemporal model presented in a previous approach [Quirós, A., Montes Diez, R. and Gamerman, D., 2010. Bayesian spatiotemporal model of fMRI data, Neuroimage, 49: 442-456], offering more flexibility in the estimation of the HRF and computational advantages in the resulting MCMC algorithm. Simulations from the model are performed in order to ascertain the performance of the sampling scheme and the ability of the posterior to estimate model parameters, as well as to check the model sensitivity to signal to noise ratio. Results are shown on synthetic data and on a real data set from a block-design fMRI experiment. Copyright (c) 2010 Elsevier Inc. All rights reserved.

  1. Bayesian Estimation and Inference using Stochastic Hardware

    Directory of Open Access Journals (Sweden)

    Chetan Singh Thakur

    2016-03-01

    Full Text Available In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker, demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND, we show how inference can be performed in a Directed Acyclic Graph (DAG using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

  2. Bayesian Estimation and Inference Using Stochastic Electronics.

    Science.gov (United States)

    Thakur, Chetan Singh; Afshar, Saeed; Wang, Runchun M; Hamilton, Tara J; Tapson, Jonathan; van Schaik, André

    2016-01-01

    In this paper, we present the implementation of two types of Bayesian inference problems to demonstrate the potential of building probabilistic algorithms in hardware using single set of building blocks with the ability to perform these computations in real time. The first implementation, referred to as the BEAST (Bayesian Estimation and Stochastic Tracker), demonstrates a simple problem where an observer uses an underlying Hidden Markov Model (HMM) to track a target in one dimension. In this implementation, sensors make noisy observations of the target position at discrete time steps. The tracker learns the transition model for target movement, and the observation model for the noisy sensors, and uses these to estimate the target position by solving the Bayesian recursive equation online. We show the tracking performance of the system and demonstrate how it can learn the observation model, the transition model, and the external distractor (noise) probability interfering with the observations. In the second implementation, referred to as the Bayesian INference in DAG (BIND), we show how inference can be performed in a Directed Acyclic Graph (DAG) using stochastic circuits. We show how these building blocks can be easily implemented using simple digital logic gates. An advantage of the stochastic electronic implementation is that it is robust to certain types of noise, which may become an issue in integrated circuit (IC) technology with feature sizes in the order of tens of nanometers due to their low noise margin, the effect of high-energy cosmic rays and the low supply voltage. In our framework, the flipping of random individual bits would not affect the system performance because information is encoded in a bit stream.

  3. Flux through a Markov chain

    International Nuclear Information System (INIS)

    Floriani, Elena; Lima, Ricardo; Ourrad, Ouerdia; Spinelli, Lionel

    2016-01-01

    Highlights: • The flux through a Markov chain of a conserved quantity (mass) is studied. • Mass is supplied by an external source and ends in the absorbing states of the chain. • Meaningful for modeling open systems whose dynamics has a Markov property. • The analytical expression of mass distribution is given for a constant source. • The expression of mass distribution is given for periodic or random sources. - Abstract: In this paper we study the flux through a finite Markov chain of a quantity, that we will call mass, which moves through the states of the chain according to the Markov transition probabilities. Mass is supplied by an external source and accumulates in the absorbing states of the chain. We believe that studying how this conserved quantity evolves through the transient (non-absorbing) states of the chain could be useful for the modelization of open systems whose dynamics has a Markov property.

  4. Estimating safety effects of pavement management factors utilizing Bayesian random effect models.

    Science.gov (United States)

    Jiang, Ximiao; Huang, Baoshan; Zaretzki, Russell L; Richards, Stephen; Yan, Xuedong

    2013-01-01

    Previous studies of pavement management factors that relate to the occurrence of traffic-related crashes are rare. Traditional research has mostly employed summary statistics of bidirectional pavement quality measurements in extended longitudinal road segments over a long time period, which may cause a loss of important information and result in biased parameter estimates. The research presented in this article focuses on crash risk of roadways with overall fair to good pavement quality. Real-time and location-specific data were employed to estimate the effects of pavement management factors on the occurrence of crashes. This research is based on the crash data and corresponding pavement quality data for the Tennessee state route highways from 2004 to 2009. The potential temporal and spatial correlations among observations caused by unobserved factors were considered. Overall 6 models were built accounting for no correlation, temporal correlation only, and both the temporal and spatial correlations. These models included Poisson, negative binomial (NB), one random effect Poisson and negative binomial (OREP, ORENB), and two random effect Poisson and negative binomial (TREP, TRENB) models. The Bayesian method was employed to construct these models. The inference is based on the posterior distribution from the Markov chain Monte Carlo (MCMC) simulation. These models were compared using the deviance information criterion. Analysis of the posterior distribution of parameter coefficients indicates that the pavement management factors indexed by Present Serviceability Index (PSI) and Pavement Distress Index (PDI) had significant impacts on the occurrence of crashes, whereas the variable rutting depth was not significant. Among other factors, lane width, median width, type of terrain, and posted speed limit were significant in affecting crash frequency. The findings of this study indicate that a reduction in pavement roughness would reduce the likelihood of traffic

  5. Probability distributions for Markov chain based quantum walks

    Science.gov (United States)

    Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.

    2018-01-01

    We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.

  6. A Bayesian Approach to Person Fit Analysis in Item Response Theory Models. Research Report.

    Science.gov (United States)

    Glas, Cees A. W.; Meijer, Rob R.

    A Bayesian approach to the evaluation of person fit in item response theory (IRT) models is presented. In a posterior predictive check, the observed value on a discrepancy variable is positioned in its posterior distribution. In a Bayesian framework, a Markov Chain Monte Carlo procedure can be used to generate samples of the posterior distribution…

  7. Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas behind the Algorithm

    Science.gov (United States)

    Stewart, Wayne; Stewart, Sepideh

    2014-01-01

    For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

  8. Predicting protein subcellular locations using hierarchical ensemble of Bayesian classifiers based on Markov chains

    Directory of Open Access Journals (Sweden)

    Eils Roland

    2006-06-01

    Full Text Available Abstract Background The subcellular location of a protein is closely related to its function. It would be worthwhile to develop a method to predict the subcellular location for a given protein when only the amino acid sequence of the protein is known. Although many efforts have been made to predict subcellular location from sequence information only, there is the need for further research to improve the accuracy of prediction. Results A novel method called HensBC is introduced to predict protein subcellular location. HensBC is a recursive algorithm which constructs a hierarchical ensemble of classifiers. The classifiers used are Bayesian classifiers based on Markov chain models. We tested our method on six various datasets; among them are Gram-negative bacteria dataset, data for discriminating outer membrane proteins and apoptosis proteins dataset. We observed that our method can predict the subcellular location with high accuracy. Another advantage of the proposed method is that it can improve the accuracy of the prediction of some classes with few sequences in training and is therefore useful for datasets with imbalanced distribution of classes. Conclusion This study introduces an algorithm which uses only the primary sequence of a protein to predict its subcellular location. The proposed recursive scheme represents an interesting methodology for learning and combining classifiers. The method is computationally efficient and competitive with the previously reported approaches in terms of prediction accuracies as empirical results indicate. The code for the software is available upon request.

  9. Bayesian linkage and segregation analysis: factoring the problem.

    Science.gov (United States)

    Matthysse, S

    2000-01-01

    Complex segregation analysis and linkage methods are mathematical techniques for the genetic dissection of complex diseases. They are used to delineate complex modes of familial transmission and to localize putative disease susceptibility loci to specific chromosomal locations. The computational problem of Bayesian linkage and segregation analysis is one of integration in high-dimensional spaces. In this paper, three available techniques for Bayesian linkage and segregation analysis are discussed: Markov Chain Monte Carlo (MCMC), importance sampling, and exact calculation. The contribution of each to the overall integration will be explicitly discussed.

  10. Bayesian and maximum likelihood estimation of genetic maps

    DEFF Research Database (Denmark)

    York, Thomas L.; Durrett, Richard T.; Tanksley, Steven

    2005-01-01

    There has recently been increased interest in the use of Markov Chain Monte Carlo (MCMC)-based Bayesian methods for estimating genetic maps. The advantage of these methods is that they can deal accurately with missing data and genotyping errors. Here we present an extension of the previous methods...... of genotyping errors. A similar advantage of the Bayesian method was not observed for missing data. We also re-analyse a recently published set of data from the eggplant and show that the use of the MCMC-based method leads to smaller estimates of genetic distances....

  11. Bayesian modeling of ChIP-chip data using latent variables.

    KAUST Repository

    Wu, Mingqi; Liang, Faming; Tian, Yanan

    2009-01-01

    and plants. Various methods have been proposed in the literature for analyzing the ChIP-chip data, such as the sliding window methods, the hidden Markov model-based methods, and Bayesian methods. Although, due to the integrated consideration of uncertainty

  12. Bayesian modeling of ChIP-chip data using latent variables.

    KAUST Repository

    Wu, Mingqi

    2009-10-26

    BACKGROUND: The ChIP-chip technology has been used in a wide range of biomedical studies, such as identification of human transcription factor binding sites, investigation of DNA methylation, and investigation of histone modifications in animals and plants. Various methods have been proposed in the literature for analyzing the ChIP-chip data, such as the sliding window methods, the hidden Markov model-based methods, and Bayesian methods. Although, due to the integrated consideration of uncertainty of the models and model parameters, Bayesian methods can potentially work better than the other two classes of methods, the existing Bayesian methods do not perform satisfactorily. They usually require multiple replicates or some extra experimental information to parametrize the model, and long CPU time due to involving of MCMC simulations. RESULTS: In this paper, we propose a Bayesian latent model for the ChIP-chip data. The new model mainly differs from the existing Bayesian models, such as the joint deconvolution model, the hierarchical gamma mixture model, and the Bayesian hierarchical model, in two respects. Firstly, it works on the difference between the averaged treatment and control samples. This enables the use of a simple model for the data, which avoids the probe-specific effect and the sample (control/treatment) effect. As a consequence, this enables an efficient MCMC simulation of the posterior distribution of the model, and also makes the model more robust to the outliers. Secondly, it models the neighboring dependence of probes by introducing a latent indicator vector. A truncated Poisson prior distribution is assumed for the latent indicator variable, with the rationale being justified at length. CONCLUSION: The Bayesian latent method is successfully applied to real and ten simulated datasets, with comparisons with some of the existing Bayesian methods, hidden Markov model methods, and sliding window methods. The numerical results indicate that the

  13. Reconstruction of Exposure to m-Xylene from Human Biomonitoring Data Using PBPK Modelling, Bayesian Inference, and Markov Chain Monte Carlo Simulation

    Science.gov (United States)

    McNally, Kevin; Cotton, Richard; Cocker, John; Jones, Kate; Bartels, Mike; Rick, David; Price, Paul; Loizou, George

    2012-01-01

    There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure. PMID:22719759

  14. Reconstruction of Exposure to m-Xylene from Human Biomonitoring Data Using PBPK Modelling, Bayesian Inference, and Markov Chain Monte Carlo Simulation

    Directory of Open Access Journals (Sweden)

    Kevin McNally

    2012-01-01

    Full Text Available There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure.

  15. Risk-based design of process systems using discrete-time Bayesian networks

    International Nuclear Information System (INIS)

    Khakzad, Nima; Khan, Faisal; Amyotte, Paul

    2013-01-01

    Temporal Bayesian networks have gained popularity as a robust technique to model dynamic systems in which the components' sequential dependency, as well as their functional dependency, cannot be ignored. In this regard, discrete-time Bayesian networks have been proposed as a viable alternative to solve dynamic fault trees without resort to Markov chains. This approach overcomes the drawbacks of Markov chains such as the state-space explosion and the error-prone conversion procedure from dynamic fault tree. It also benefits from the inherent advantages of Bayesian networks such as probability updating. However, effective mapping of the dynamic gates of dynamic fault trees into Bayesian networks while avoiding the consequent huge multi-dimensional probability tables has always been a matter of concern. In this paper, a new general formalism has been developed to model two important elements of dynamic fault tree, i.e., cold spare gate and sequential enforcing gate, with any arbitrary probability distribution functions. Also, an innovative Neutral Dependency algorithm has been introduced to model dynamic gates such as priority-AND gate, thus reducing the dimension of conditional probability tables by an order of magnitude. The second part of the paper is devoted to the application of discrete-time Bayesian networks in the risk assessment and safety analysis of complex process systems. It has been shown how dynamic techniques can effectively be applied for optimal allocation of safety systems to obtain maximum risk reduction.

  16. Statistical Shape Modelling and Markov Random Field Restoration (invited tutorial and exercise)

    DEFF Research Database (Denmark)

    Hilger, Klaus Baggesen

    This tutorial focuses on statistical shape analysis using point distribution models (PDM) which is widely used in modelling biological shape variability over a set of annotated training data. Furthermore, Active Shape Models (ASM) and Active Appearance Models (AAM) are based on PDMs and have proven...... deformation field between shapes. The tutorial demonstrates both generative active shape and appearance models, and MRF restoration on 3D polygonized surfaces. ''Exercise: Spectral-Spatial classification of multivariate images'' From annotated training data this exercise applies spatial image restoration...... using Markov random field relaxation of a spectral classifier. Keywords: the Ising model, the Potts model, stochastic sampling, discriminant analysis, expectation maximization....

  17. Exploring the Influence of Neighborhood Characteristics on Burglary Risks: A Bayesian Random Effects Modeling Approach

    Directory of Open Access Journals (Sweden)

    Hongqiang Liu

    2016-06-01

    Full Text Available A Bayesian random effects modeling approach was used to examine the influence of neighborhood characteristics on burglary risks in Jianghan District, Wuhan, China. This random effects model is essentially spatial; a spatially structured random effects term and an unstructured random effects term are added to the traditional non-spatial Poisson regression model. Based on social disorganization and routine activity theories, five covariates extracted from the available data at the neighborhood level were used in the modeling. Three regression models were fitted and compared by the deviance information criterion to identify which model best fit our data. A comparison of the results from the three models indicates that the Bayesian random effects model is superior to the non-spatial models in fitting the data and estimating regression coefficients. Our results also show that neighborhoods with above average bar density and department store density have higher burglary risks. Neighborhood-specific burglary risks and posterior probabilities of neighborhoods having a burglary risk greater than 1.0 were mapped, indicating the neighborhoods that should warrant more attention and be prioritized for crime intervention and reduction. Implications and limitations of the study are discussed in our concluding section.

  18. A Bayesian spatio-temporal geostatistical model with an auxiliary lattice for large datasets

    KAUST Repository

    Xu, Ganggang

    2015-01-01

    When spatio-temporal datasets are large, the computational burden can lead to failures in the implementation of traditional geostatistical tools. In this paper, we propose a computationally efficient Bayesian hierarchical spatio-temporal model in which the spatial dependence is approximated by a Gaussian Markov random field (GMRF) while the temporal correlation is described using a vector autoregressive model. By introducing an auxiliary lattice on the spatial region of interest, the proposed method is not only able to handle irregularly spaced observations in the spatial domain, but it is also able to bypass the missing data problem in a spatio-temporal process. Because the computational complexity of the proposed Markov chain Monte Carlo algorithm is of the order O(n) with n the total number of observations in space and time, our method can be used to handle very large spatio-temporal datasets with reasonable CPU times. The performance of the proposed model is illustrated using simulation studies and a dataset of precipitation data from the coterminous United States.

  19. Bayesian methods to restore and re build images: application to gamma-graphy and to photofission tomography; Methodes bayesiennes pour la restauration et la reconstruction d`images application a la gammagraphie et a la tomographie par photofissions

    Energy Technology Data Exchange (ETDEWEB)

    Stawinski, G

    1998-10-26

    Bayesian algorithms are developed to solve inverse problems in gamma imaging and photofission tomography. The first part of this work is devoted to the modeling of our measurement systems. Two models have been found for both applications: the first one is a simple conventional model and the second one is a cascaded point process model. EM and MCMC Bayesian algorithms for image restoration and image reconstruction have been developed for these models and compared. The cascaded point process model does not improve significantly the results previously obtained by the classical model. To original approaches have been proposed, which increase the results previously obtained. The first approach uses an inhomogeneous Markov Random Field as a prior law, and makes the regularization parameter spatially vary. However, the problem of the estimation of hyper-parameters has not been solved. In the case of the deconvolution of point sources, a second approach has been proposed, which introduces a high level prior model. The picture is modeled as a list of objects, whose parameters and number are unknown. The results obtained with this method are more accurate than those obtained with the conventional Markov Random Field prior model and require less computational costs. (author)

  20. Bayesian inference in probabilistic risk assessment-The current state of the art

    International Nuclear Information System (INIS)

    Kelly, Dana L.; Smith, Curtis L.

    2009-01-01

    Markov chain Monte Carlo (MCMC) approaches to sampling directly from the joint posterior distribution of aleatory model parameters have led to tremendous advances in Bayesian inference capability in a wide variety of fields, including probabilistic risk analysis. The advent of freely available software coupled with inexpensive computing power has catalyzed this advance. This paper examines where the risk assessment community is with respect to implementing modern computational-based Bayesian approaches to inference. Through a series of examples in different topical areas, it introduces salient concepts and illustrates the practical application of Bayesian inference via MCMC sampling to a variety of important problems

  1. A multi-level hierarchic Markov process with Bayesian updating for herd optimization and simulation in dairy cattle.

    Science.gov (United States)

    Demeter, R M; Kristensen, A R; Dijkstra, J; Oude Lansink, A G J M; Meuwissen, M P M; van Arendonk, J A M

    2011-12-01

    Herd optimization models that determine economically optimal insemination and replacement decisions are valuable research tools to study various aspects of farming systems. The aim of this study was to develop a herd optimization and simulation model for dairy cattle. The model determines economically optimal insemination and replacement decisions for individual cows and simulates whole-herd results that follow from optimal decisions. The optimization problem was formulated as a multi-level hierarchic Markov process, and a state space model with Bayesian updating was applied to model variation in milk yield. Methodological developments were incorporated in 2 main aspects. First, we introduced an additional level to the model hierarchy to obtain a more tractable and efficient structure. Second, we included a recently developed cattle feed intake model. In addition to methodological developments, new parameters were used in the state space model and other biological functions. Results were generated for Dutch farming conditions, and outcomes were in line with actual herd performance in the Netherlands. Optimal culling decisions were sensitive to variation in milk yield but insensitive to energy requirements for maintenance and feed intake capacity. We anticipate that the model will be applied in research and extension. Copyright © 2011 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

  2. Prediction of small molecule binding property of protein domains with Bayesian classifiers based on Markov chains.

    Science.gov (United States)

    Bulashevska, Alla; Stein, Martin; Jackson, David; Eils, Roland

    2009-12-01

    Accurate computational methods that can help to predict biological function of a protein from its sequence are of great interest to research biologists and pharmaceutical companies. One approach to assume the function of proteins is to predict the interactions between proteins and other molecules. In this work, we propose a machine learning method that uses a primary sequence of a domain to predict its propensity for interaction with small molecules. By curating the Pfam database with respect to the small molecule binding ability of its component domains, we have constructed a dataset of small molecule binding and non-binding domains. This dataset was then used as training set to learn a Bayesian classifier, which should distinguish members of each class. The domain sequences of both classes are modelled with Markov chains. In a Jack-knife test, our classification procedure achieved the predictive accuracies of 77.2% and 66.7% for binding and non-binding classes respectively. We demonstrate the applicability of our classifier by using it to identify previously unknown small molecule binding domains. Our predictions are available as supplementary material and can provide very useful information to drug discovery specialists. Given the ubiquitous and essential role small molecules play in biological processes, our method is important for identifying pharmaceutically relevant components of complete proteomes. The software is available from the author upon request.

  3. Bayesian Estimation of the Logistic Positive Exponent IRT Model

    Science.gov (United States)

    Bolfarine, Heleno; Bazan, Jorge Luis

    2010-01-01

    A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric…

  4. Bayesian Statistics: Concepts and Applications in Animal Breeding – A Review

    Directory of Open Access Journals (Sweden)

    Lsxmikant-Sambhaji Kokate

    2011-07-01

    Full Text Available Statistics uses two major approaches- conventional (or frequentist and Bayesian approach. Bayesian approach provides a complete paradigm for both statistical inference and decision making under uncertainty. Bayesian methods solve many of the difficulties faced by conventional statistical methods, and extend the applicability of statistical methods. It exploits the use of probabilistic models to formulate scientific problems. To use Bayesian statistics, there is computational difficulty and secondly, Bayesian methods require specifying prior probability distributions. Markov Chain Monte-Carlo (MCMC methods were applied to overcome the computational difficulty, and interest in Bayesian methods was renewed. In Bayesian statistics, Bayesian structural equation model (SEM is used. It provides a powerful and flexible approach for studying quantitative traits for wide spectrum problems and thus it has no operational difficulties, with the exception of some complex cases. In this method, the problems are solved at ease, and the statisticians feel it comfortable with the particular way of expressing the results and employing the software available to analyze a large variety of problems.

  5. A Bayesian test for periodic signals in red noise

    Science.gov (United States)

    Vaughan, S.

    2010-02-01

    Many astrophysical sources, especially compact accreting sources, show strong, random brightness fluctuations with broad power spectra in addition to periodic or quasi-periodic oscillations (QPOs) that have narrower spectra. The random nature of the dominant source of variance greatly complicates the process of searching for possible weak periodic signals. We have addressed this problem using the tools of Bayesian statistics; in particular, using Markov Chain Monte Carlo techniques to approximate the posterior distribution of model parameters, and posterior predictive model checking to assess model fits and search for periodogram outliers that may represent periodic signals. The methods developed are applied to two example data sets, both long XMM-Newton observations of highly variable Seyfert 1 galaxies: RE J1034 + 396 and Mrk 766. In both cases, a bend (or break) in the power spectrum is evident. In the case of RE J1034 + 396, the previously reported QPO is found but with somewhat weaker statistical significance than reported in previous analyses. The difference is due partly to the improved continuum modelling, better treatment of nuisance parameters and partly to different data selection methods.

  6. Caveats on Bayesian and hidden-Markov models (v2.8)

    OpenAIRE

    Schomaker, Lambert

    2016-01-01

    This paper describes a number of fundamental and practical problems in the application of hidden-Markov models and Bayes when applied to cursive-script recognition. Several problems, however, will have an effect in other application areas. The most fundamental problem is the propagation of error in the product of probabilities. This is a common and pervasive problem which deserves more attention. On the basis of Monte Carlo modeling, tables for the expected relative error are given. It seems ...

  7. Bayesian prediction of spatial count data using generalized linear mixed models

    DEFF Research Database (Denmark)

    Christensen, Ole Fredslund; Waagepetersen, Rasmus Plenge

    2002-01-01

    Spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a Bayesian approach and Markov chain Monte Carlo. Informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling. Furthermore, ...

  8. Markov Chains and Markov Processes

    OpenAIRE

    Ogunbayo, Segun

    2016-01-01

    Markov chain, which was named after Andrew Markov is a mathematical system that transfers a state to another state. Many real world systems contain uncertainty. This study helps us to understand the basic idea of a Markov chain and how is been useful in our daily lives. For some times there had been suspense on distinct predictions and future existences. Also in different games there had been different expectations or results involved. That is the reason why we need Markov chains to predict o...

  9. Bayesian clustering of DNA sequences using Markov chains and a stochastic partition model.

    Science.gov (United States)

    Jääskinen, Väinö; Parkkinen, Ville; Cheng, Lu; Corander, Jukka

    2014-02-01

    In many biological applications it is necessary to cluster DNA sequences into groups that represent underlying organismal units, such as named species or genera. In metagenomics this grouping needs typically to be achieved on the basis of relatively short sequences which contain different types of errors, making the use of a statistical modeling approach desirable. Here we introduce a novel method for this purpose by developing a stochastic partition model that clusters Markov chains of a given order. The model is based on a Dirichlet process prior and we use conjugate priors for the Markov chain parameters which enables an analytical expression for comparing the marginal likelihoods of any two partitions. To find a good candidate for the posterior mode in the partition space, we use a hybrid computational approach which combines the EM-algorithm with a greedy search. This is demonstrated to be faster and yield highly accurate results compared to earlier suggested clustering methods for the metagenomics application. Our model is fairly generic and could also be used for clustering of other types of sequence data for which Markov chains provide a reasonable way to compress information, as illustrated by experiments on shotgun sequence type data from an Escherichia coli strain.

  10. Markov processes and controlled Markov chains

    CERN Document Server

    Filar, Jerzy; Chen, Anyue

    2002-01-01

    The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South Ameri...

  11. Recursive estimation of high-order Markov chains: Approximation by finite mixtures

    Czech Academy of Sciences Publication Activity Database

    Kárný, Miroslav

    2016-01-01

    Roč. 326, č. 1 (2016), s. 188-201 ISSN 0020-0255 R&D Projects : GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Markov chain * Approximate parameter estimation * Bayesian recursive estimation * Adaptive systems * Kullback–Leibler divergence * Forgetting Subject RIV: BC - Control Systems Theory Impact factor: 4.832, year: 2016 http://library.utia.cas.cz/separaty/2015/AS/karny-0447119.pdf

  12. Bayesian log-periodic model for financial crashes

    DEFF Research Database (Denmark)

    Rodríguez-Caballero, Carlos Vladimir; Knapik, Oskar

    2014-01-01

    This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions...... cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student’s t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical...... part of the study, we analyze a well-known example of financial bubble – the S&P 500 1987 crash – to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian...

  13. The Bayesian group lasso for confounded spatial data

    Science.gov (United States)

    Hefley, Trevor J.; Hooten, Mevin B.; Hanks, Ephraim M.; Russell, Robin E.; Walsh, Daniel P.

    2017-01-01

    Generalized linear mixed models for spatial processes are widely used in applied statistics. In many applications of the spatial generalized linear mixed model (SGLMM), the goal is to obtain inference about regression coefficients while achieving optimal predictive ability. When implementing the SGLMM, multicollinearity among covariates and the spatial random effects can make computation challenging and influence inference. We present a Bayesian group lasso prior with a single tuning parameter that can be chosen to optimize predictive ability of the SGLMM and jointly regularize the regression coefficients and spatial random effect. We implement the group lasso SGLMM using efficient Markov chain Monte Carlo (MCMC) algorithms and demonstrate how multicollinearity among covariates and the spatial random effect can be monitored as a derived quantity. To test our method, we compared several parameterizations of the SGLMM using simulated data and two examples from plant ecology and disease ecology. In all examples, problematic levels multicollinearity occurred and influenced sampling efficiency and inference. We found that the group lasso prior resulted in roughly twice the effective sample size for MCMC samples of regression coefficients and can have higher and less variable predictive accuracy based on out-of-sample data when compared to the standard SGLMM.

  14. Detection of bursts in extracellular spike trains using hidden semi-Markov point process models.

    Science.gov (United States)

    Tokdar, Surya; Xi, Peiyi; Kelly, Ryan C; Kass, Robert E

    2010-08-01

    Neurons in vitro and in vivo have epochs of bursting or "up state" activity during which firing rates are dramatically elevated. Various methods of detecting bursts in extracellular spike trains have appeared in the literature, the most widely used apparently being Poisson Surprise (PS). A natural description of the phenomenon assumes (1) there are two hidden states, which we label "burst" and "non-burst," (2) the neuron evolves stochastically, switching at random between these two states, and (3) within each state the spike train follows a time-homogeneous point process. If in (2) the transitions from non-burst to burst and burst to non-burst states are memoryless, this becomes a hidden Markov model (HMM). For HMMs, the state transitions follow exponential distributions, and are highly irregular. Because observed bursting may in some cases be fairly regular-exhibiting inter-burst intervals with small variation-we relaxed this assumption. When more general probability distributions are used to describe the state transitions the two-state point process model becomes a hidden semi-Markov model (HSMM). We developed an efficient Bayesian computational scheme to fit HSMMs to spike train data. Numerical simulations indicate the method can perform well, sometimes yielding very different results than those based on PS.

  15. Multilayer Markov Random Field models for change detection in optical remote sensing images

    Science.gov (United States)

    Benedek, Csaba; Shadaydeh, Maha; Kato, Zoltan; Szirányi, Tamás; Zerubia, Josiane

    2015-09-01

    In this paper, we give a comparative study on three Multilayer Markov Random Field (MRF) based solutions proposed for change detection in optical remote sensing images, called Multicue MRF, Conditional Mixed Markov model, and Fusion MRF. Our purposes are twofold. On one hand, we highlight the significance of the focused model family and we set them against various state-of-the-art approaches through a thematic analysis and quantitative tests. We discuss the advantages and drawbacks of class comparison vs. direct approaches, usage of training data, various targeted application fields and different ways of Ground Truth generation, meantime informing the Reader in which roles the Multilayer MRFs can be efficiently applied. On the other hand we also emphasize the differences between the three focused models at various levels, considering the model structures, feature extraction, layer interpretation, change concept definition, parameter tuning and performance. We provide qualitative and quantitative comparison results using principally a publicly available change detection database which contains aerial image pairs and Ground Truth change masks. We conclude that the discussed models are competitive against alternative state-of-the-art solutions, if one uses them as pre-processing filters in multitemporal optical image analysis. In addition, they cover together a large range of applications, considering the different usage options of the three approaches.

  16. Bayesian Reliability Analysis of Non-Stationarity in Multi-agent Systems

    Directory of Open Access Journals (Sweden)

    TONT Gabriela

    2013-05-01

    Full Text Available The Bayesian methods provide information about the meaningful parameters in a statistical analysis obtained by combining the prior and sampling distributions to form the posterior distribution of theparameters. The desired inferences are obtained from this joint posterior. An estimation strategy for hierarchical models, where the resulting joint distribution of the associated model parameters cannotbe evaluated analytically, is to use sampling algorithms, known as Markov Chain Monte Carlo (MCMC methods, from which approximate solutions can be obtained. Both serial and parallel configurations of subcomponents are permitted. The capability of time-dependent method to describe a multi-state system is based on a case study, assessingthe operatial situation of studied system. The rationality and validity of the presented model are demonstrated via a case of study. The effect of randomness of the structural parameters is alsoexamined.

  17. bNEAT: a Bayesian network method for detecting epistatic interactions in genome-wide association studies

    Directory of Open Access Journals (Sweden)

    Chen Xue-wen

    2011-07-01

    Full Text Available Abstract Background Detecting epistatic interactions plays a significant role in improving pathogenesis, prevention, diagnosis and treatment of complex human diseases. A recent study in automatic detection of epistatic interactions shows that Markov Blanket-based methods are capable of finding genetic variants strongly associated with common diseases and reducing false positives when the number of instances is large. Unfortunately, a typical dataset from genome-wide association studies consists of very limited number of examples, where current methods including Markov Blanket-based method may perform poorly. Results To address small sample problems, we propose a Bayesian network-based approach (bNEAT to detect epistatic interactions. The proposed method also employs a Branch-and-Bound technique for learning. We apply the proposed method to simulated datasets based on four disease models and a real dataset. Experimental results show that our method outperforms Markov Blanket-based methods and other commonly-used methods, especially when the number of samples is small. Conclusions Our results show bNEAT can obtain a strong power regardless of the number of samples and is especially suitable for detecting epistatic interactions with slight or no marginal effects. The merits of the proposed approach lie in two aspects: a suitable score for Bayesian network structure learning that can reflect higher-order epistatic interactions and a heuristic Bayesian network structure learning method.

  18. Quality guaranteed and reliability

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Tae Hun

    2012-12-15

    This book deals with analysis of Bayesian like conditional probability and independence, total probability law and Bayes formula, analysis of Bayesian, simulation including summary and examples, random number generation and occurrence of probability variable, Markov chain such as property of Markovian, market share problem, Markov chain and safe state probability, transition matrix, and absorption of Markov chain, and queueing model like M/M/1/3, PASTA and Little's law and independent trial and poisson process and Balance equation of CTMC.

  19. Quality guaranteed and reliability

    International Nuclear Information System (INIS)

    Lee, Tae Hun

    2012-12-01

    This book deals with analysis of Bayesian like conditional probability and independence, total probability law and Bayes formula, analysis of Bayesian, simulation including summary and examples, random number generation and occurrence of probability variable, Markov chain such as property of Markovian, market share problem, Markov chain and safe state probability, transition matrix, and absorption of Markov chain, and queueing model like M/M/1/3, PASTA and Little's law and independent trial and poisson process and Balance equation of CTMC.

  20. Assessing fit in Bayesian models for spatial processes

    KAUST Repository

    Jun, M.; Katzfuss, M.; Hu, J.; Johnson, V. E.

    2014-01-01

    © 2014 John Wiley & Sons, Ltd. Gaussian random fields are frequently used to model spatial and spatial-temporal data, particularly in geostatistical settings. As much of the attention of the statistics community has been focused on defining and estimating the mean and covariance functions of these processes, little effort has been devoted to developing goodness-of-fit tests to allow users to assess the models' adequacy. We describe a general goodness-of-fit test and related graphical diagnostics for assessing the fit of Bayesian Gaussian process models using pivotal discrepancy measures. Our method is applicable for both regularly and irregularly spaced observation locations on planar and spherical domains. The essential idea behind our method is to evaluate pivotal quantities defined for a realization of a Gaussian random field at parameter values drawn from the posterior distribution. Because the nominal distribution of the resulting pivotal discrepancy measures is known, it is possible to quantitatively assess model fit directly from the output of Markov chain Monte Carlo algorithms used to sample from the posterior distribution on the parameter space. We illustrate our method in a simulation study and in two applications.

  1. Assessing fit in Bayesian models for spatial processes

    KAUST Repository

    Jun, M.

    2014-09-16

    © 2014 John Wiley & Sons, Ltd. Gaussian random fields are frequently used to model spatial and spatial-temporal data, particularly in geostatistical settings. As much of the attention of the statistics community has been focused on defining and estimating the mean and covariance functions of these processes, little effort has been devoted to developing goodness-of-fit tests to allow users to assess the models\\' adequacy. We describe a general goodness-of-fit test and related graphical diagnostics for assessing the fit of Bayesian Gaussian process models using pivotal discrepancy measures. Our method is applicable for both regularly and irregularly spaced observation locations on planar and spherical domains. The essential idea behind our method is to evaluate pivotal quantities defined for a realization of a Gaussian random field at parameter values drawn from the posterior distribution. Because the nominal distribution of the resulting pivotal discrepancy measures is known, it is possible to quantitatively assess model fit directly from the output of Markov chain Monte Carlo algorithms used to sample from the posterior distribution on the parameter space. We illustrate our method in a simulation study and in two applications.

  2. A Bayesian method for inferring transmission chains in a partially observed epidemic.

    Energy Technology Data Exchange (ETDEWEB)

    Marzouk, Youssef M.; Ray, Jaideep

    2008-10-01

    We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historical data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.

  3. Markov chain analysis of single spin flip Ising simulations

    International Nuclear Information System (INIS)

    Hennecke, M.

    1997-01-01

    The Markov processes defined by random and loop-based schemes for single spin flip attempts in Monte Carlo simulations of the 2D Ising model are investigated, by explicitly constructing their transition matrices. Their analysis reveals that loops over all lattice sites using a Metropolis-type single spin flip probability often do not define ergodic Markov chains, and have distorted dynamical properties even if they are ergodic. The transition matrices also enable a comparison of the dynamics of random versus loop spin selection and Glauber versus Metropolis probabilities

  4. Bayesian image restoration, using configurations

    OpenAIRE

    Thorarinsdottir, Thordis

    2006-01-01

    In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the re...

  5. Bayesian statistic methods and theri application in probabilistic simulation models

    Directory of Open Access Journals (Sweden)

    Sergio Iannazzo

    2007-03-01

    Full Text Available Bayesian statistic methods are facing a rapidly growing level of interest and acceptance in the field of health economics. The reasons of this success are probably to be found on the theoretical fundaments of the discipline that make these techniques more appealing to decision analysis. To this point should be added the modern IT progress that has developed different flexible and powerful statistical software framework. Among them probably one of the most noticeably is the BUGS language project and its standalone application for MS Windows WinBUGS. Scope of this paper is to introduce the subject and to show some interesting applications of WinBUGS in developing complex economical models based on Markov chains. The advantages of this approach reside on the elegance of the code produced and in its capability to easily develop probabilistic simulations. Moreover an example of the integration of bayesian inference models in a Markov model is shown. This last feature let the analyst conduce statistical analyses on the available sources of evidence and exploit them directly as inputs in the economic model.

  6. GPU implementation of Bayesian neural network construction for data-intensive applications

    International Nuclear Information System (INIS)

    Perry, Michelle; Meyer-Baese, Anke; Prosper, Harrison B

    2014-01-01

    We describe a graphical processing unit (GPU) implementation of the Hybrid Markov Chain Monte Carlo (HMC) method for training Bayesian Neural Networks (BNN). Our implementation uses NVIDIA's parallel computing architecture, CUDA. We briefly review BNNs and the HMC method and we describe our implementations and give preliminary results.

  7. Adaptive Markov Random Fields for Example-Based Super-resolution of Faces

    Directory of Open Access Journals (Sweden)

    Stephenson Todd A

    2006-01-01

    Full Text Available Image enhancement of low-resolution images can be done through methods such as interpolation, super-resolution using multiple video frames, and example-based super-resolution. Example-based super-resolution, in particular, is suited to images that have a strong prior (for those frameworks that work on only a single image, it is more like image restoration than traditional, multiframe super-resolution. For example, hallucination and Markov random field (MRF methods use examples drawn from the same domain as the image being enhanced to determine what the missing high-frequency information is likely to be. We propose to use even stronger prior information by extending MRF-based super-resolution to use adaptive observation and transition functions, that is, to make these functions region-dependent. We show with face images how we can adapt the modeling for each image patch so as to improve the resolution.

  8. Adaptive Markov Random Fields for Example-Based Super-resolution of Faces

    Science.gov (United States)

    Stephenson, Todd A.; Chen, Tsuhan

    2006-12-01

    Image enhancement of low-resolution images can be done through methods such as interpolation, super-resolution using multiple video frames, and example-based super-resolution. Example-based super-resolution, in particular, is suited to images that have a strong prior (for those frameworks that work on only a single image, it is more like image restoration than traditional, multiframe super-resolution). For example, hallucination and Markov random field (MRF) methods use examples drawn from the same domain as the image being enhanced to determine what the missing high-frequency information is likely to be. We propose to use even stronger prior information by extending MRF-based super-resolution to use adaptive observation and transition functions, that is, to make these functions region-dependent. We show with face images how we can adapt the modeling for each image patch so as to improve the resolution.

  9. Bayesian inference for Hawkes processes

    DEFF Research Database (Denmark)

    Rasmussen, Jakob Gulddahl

    The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....

  10. Bayesian inference for Hawkes processes

    DEFF Research Database (Denmark)

    Rasmussen, Jakob Gulddahl

    2013-01-01

    The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....

  11. A Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions

    KAUST Repository

    Ruggeri, Fabrizio

    2016-05-12

    In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.

  12. Assessment of myocardial metabolic rate of glucose by means of Bayesian ICA and Markov Chain Monte Carlo methods in small animal PET imaging

    Science.gov (United States)

    Berradja, Khadidja; Boughanmi, Nabil

    2016-09-01

    In dynamic cardiac PET FDG studies the assessment of myocardial metabolic rate of glucose (MMRG) requires the knowledge of the blood input function (IF). IF can be obtained by manual or automatic blood sampling and cross calibrated with PET. These procedures are cumbersome, invasive and generate uncertainties. The IF is contaminated by spillover of radioactivity from the adjacent myocardium and this could cause important error in the estimated MMRG. In this study, we show that the IF can be extracted from the images in a rat heart study with 18F-fluorodeoxyglucose (18F-FDG) by means of Independent Component Analysis (ICA) based on Bayesian theory and Markov Chain Monte Carlo (MCMC) sampling method (BICA). Images of the heart from rats were acquired with the Sherbrooke small animal PET scanner. A region of interest (ROI) was drawn around the rat image and decomposed into blood and tissue using BICA. The Statistical study showed that there is a significant difference (p corrupted with spillover.

  13. Bayesian estimation of parameters in a regional hydrological model

    Directory of Open Access Journals (Sweden)

    K. Engeland

    2002-01-01

    Full Text Available This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1 process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis

  14. Image reconstruction using three-dimensional compound Gauss-Markov random field in emission computed tomography

    International Nuclear Information System (INIS)

    Watanabe, Shuichi; Kudo, Hiroyuki; Saito, Tsuneo

    1993-01-01

    In this paper, we propose a new reconstruction algorithm based on MAP (maximum a posteriori probability) estimation principle for emission tomography. To improve noise suppression properties of the conventional ML-EM (maximum likelihood expectation maximization) algorithm, direct three-dimensional reconstruction that utilizes intensity correlations between adjacent transaxial slices is introduced. Moreover, to avoid oversmoothing of edges, a priori knowledge of RI (radioisotope) distribution is represented by using a doubly-stochastic image model called the compound Gauss-Markov random field. The a posteriori probability is maximized by using the iterative GEM (generalized EM) algorithm. Computer simulation results are shown to demonstrate validity of the proposed algorithm. (author)

  15. Micronutrients in HIV: a Bayesian meta-analysis.

    Directory of Open Access Journals (Sweden)

    George M Carter

    Full Text Available Approximately 28.5 million people living with HIV are eligible for treatment (CD4<500, but currently have no access to antiretroviral therapy. Reduced serum level of micronutrients is common in HIV disease. Micronutrient supplementation (MNS may mitigate disease progression and mortality.We synthesized evidence on the effect of micronutrient supplementation on mortality and rate of disease progression in HIV disease.We searched MEDLINE, EMBASE, the Cochrane Central, AMED and CINAHL databases through December 2014, without language restriction, for studies of greater than 3 micronutrients versus any or no comparator. We built a hierarchical Bayesian random effects model to synthesize results. Inferences are based on the posterior distribution of the population effects; posterior distributions were approximated by Markov chain Monte Carlo in OpenBugs.From 2166 initial references, we selected 49 studies for full review and identified eight reporting on disease progression and/or mortality. Bayesian synthesis of data from 2,249 adults in three studies estimated the relative risk of disease progression in subjects on MNS vs. control as 0.62 (95% credible interval, 0.37, 0.96. Median number needed to treat is 8.4 (4.8, 29.9 and the Bayes Factor 53.4. Based on data reporting on 4,095 adults reporting mortality in 7 randomized controlled studies, the RR was 0.84 (0.38, 1.85, NNT is 25 (4.3, ∞.MNS significantly and substantially slows disease progression in HIV+ adults not on ARV, and possibly reduces mortality. Micronutrient supplements are effective in reducing progression with a posterior probability of 97.9%. Considering MNS low cost and lack of adverse effects, MNS should be standard of care for HIV+ adults not yet on ARV.

  16. Bayesian conditional-independence modeling of the AIDS epidemic in England and Wales

    Science.gov (United States)

    Gilks, Walter R.; De Angelis, Daniela; Day, Nicholas E.

    We describe the use of conditional-independence modeling, Bayesian inference and Markov chain Monte Carlo, to model and project the HIV-AIDS epidemic in homosexual/bisexual males in England and Wales. Complexity in this analysis arises through selectively missing data, indirectly observed underlying processes, and measurement error. Our emphasis is on presentation and discussion of the concepts, not on the technicalities of this analysis, which can be found elsewhere [D. De Angelis, W.R. Gilks, N.E. Day, Bayesian projection of the the acquired immune deficiency syndrome epidemic (with discussion), Applied Statistics, in press].

  17. Process Modeling for Energy Usage in “Smart House” System with a Help of Markov Discrete Chain

    Directory of Open Access Journals (Sweden)

    Victor Kravets

    2016-05-01

    Full Text Available Method for evaluating economic efficiency of technical systems using discrete Markov chains modelling illustrated by the system of “Smart house”, consisting, for example, of the three independently functioning elements. Dynamic model of a random power consumption process in the form of a symmetrical state graph of heterogeneous discrete Markov chain is built. The corresponding mathematical model of a random Markov process of power consumption in the “smart house” system in recurrent matrix form is being developed. Technique of statistical determination of probability of random transition elements of the system and the corresponding to the transition probability matrix of the discrete inhomogeneous Markov chain are developed. Statistically determined random transitions of system elements power consumption and the corresponding distribution laws are introduced. The matrix of transition prices, expectations for the possible states of a system price transition and, eventually, the cost of Markov process of power consumption throughout the day.

  18. Complexity analysis of accelerated MCMC methods for Bayesian inversion

    International Nuclear Information System (INIS)

    Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M

    2013-01-01

    The Bayesian approach to inverse problems, in which the posterior probability distribution on an unknown field is sampled for the purposes of computing posterior expectations of quantities of interest, is starting to become computationally feasible for partial differential equation (PDE) inverse problems. Balancing the sources of error arising from finite-dimensional approximation of the unknown field, the PDE forward solution map and the sampling of the probability space under the posterior distribution are essential for the design of efficient computational Bayesian methods for PDE inverse problems. We study Bayesian inversion for a model elliptic PDE with an unknown diffusion coefficient. We provide complexity analyses of several Markov chain Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data δ. Particular attention is given to bounds on the overall work required to achieve a prescribed error level ε. Specifically, we first bound the computational complexity of ‘plain’ MCMC, based on combining MCMC sampling with linear complexity multi-level solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) ‘surrogate’ representation of the forward response map of the PDE over the entire parameter space, and, second, a novel multi-level Markov chain Monte Carlo strategy which utilizes sampling from a multi-level discretization of the posterior and the forward PDE. For both of these strategies, we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular, we provide sufficient conditions on the regularity of the unknown coefficients of the PDE and on the

  19. A sufficiency property arising from the characterization of extremes of Markov chains

    OpenAIRE

    Bortot, Paola; Coles, Stuart

    2000-01-01

    At extreme levels, it is known that for a particular choice of marginal distribution, transitions of a Markov chain behave like a random walk. For a broad class of Markov chains, we give a characterization for the step length density of the limiting random walk, which leads to an interesting sufficiency property. This representation also leads us to propose a new technique for kernel density estimation for this class of models.

  20. Markov chain Monte Carlo with the Integrated Nested Laplace Approximation

    KAUST Repository

    Gómez-Rubio, Virgilio

    2017-10-06

    The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with

  1. Markov chain Monte Carlo with the Integrated Nested Laplace Approximation

    KAUST Repository

    Gó mez-Rubio, Virgilio; Rue, Haavard

    2017-01-01

    The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with

  2. Markov chain aggregation for agent-based models

    CERN Document Server

    Banisch, Sven

    2016-01-01

    This self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting “micro-chain” including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the upd...

  3. A trans-dimensional Bayesian Markov chain Monte Carlo algorithm for model assessment using frequency-domain electromagnetic data

    Science.gov (United States)

    Minsley, Burke J.

    2011-01-01

    A meaningful interpretation of geophysical measurements requires an assessment of the space of models that are consistent with the data, rather than just a single, ‘best’ model which does not convey information about parameter uncertainty. For this purpose, a trans-dimensional Bayesian Markov chain Monte Carlo (MCMC) algorithm is developed for assessing frequencydomain electromagnetic (FDEM) data acquired from airborne or ground-based systems. By sampling the distribution of models that are consistent with measured data and any prior knowledge, valuable inferences can be made about parameter values such as the likely depth to an interface, the distribution of possible resistivity values as a function of depth and non-unique relationships between parameters. The trans-dimensional aspect of the algorithm allows the number of layers to be a free parameter that is controlled by the data, where models with fewer layers are inherently favoured, which provides a natural measure of parsimony and a significant degree of flexibility in parametrization. The MCMC algorithm is used with synthetic examples to illustrate how the distribution of acceptable models is affected by the choice of prior information, the system geometry and configuration and the uncertainty in the measured system elevation. An airborne FDEM data set that was acquired for the purpose of hydrogeological characterization is also studied. The results compare favorably with traditional least-squares analysis, borehole resistivity and lithology logs from the site, and also provide new information about parameter uncertainty necessary for model assessment.

  4. Bayesian Probability Theory

    Science.gov (United States)

    von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

    2014-06-01

    Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

  5. Discovering Alzheimer Genetic Biomarkers Using Bayesian Networks

    Directory of Open Access Journals (Sweden)

    Fayroz F. Sherif

    2015-01-01

    Full Text Available Single nucleotide polymorphisms (SNPs contribute most of the genetic variation to the human genome. SNPs associate with many complex and common diseases like Alzheimer’s disease (AD. Discovering SNP biomarkers at different loci can improve early diagnosis and treatment of these diseases. Bayesian network provides a comprehensible and modular framework for representing interactions between genes or single SNPs. Here, different Bayesian network structure learning algorithms have been applied in whole genome sequencing (WGS data for detecting the causal AD SNPs and gene-SNP interactions. We focused on polymorphisms in the top ten genes associated with AD and identified by genome-wide association (GWA studies. New SNP biomarkers were observed to be significantly associated with Alzheimer’s disease. These SNPs are rs7530069, rs113464261, rs114506298, rs73504429, rs7929589, rs76306710, and rs668134. The obtained results demonstrated the effectiveness of using BN for identifying AD causal SNPs with acceptable accuracy. The results guarantee that the SNP set detected by Markov blanket based methods has a strong association with AD disease and achieves better performance than both naïve Bayes and tree augmented naïve Bayes. Minimal augmented Markov blanket reaches accuracy of 66.13% and sensitivity of 88.87% versus 61.58% and 59.43% in naïve Bayes, respectively.

  6. Bayesian interpolation in a dynamic sinusoidal model with application to packet-loss concealment

    DEFF Research Database (Denmark)

    Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Cemgil, Ali Taylan

    2010-01-01

    a Bayesian inference scheme for the missing observations, hidden states and model parameters of the dynamic model. The inference scheme is based on a Markov chain Monte Carlo method known as Gibbs sampler. We illustrate the performance of the inference scheme to the application of packet-loss concealment...

  7. Road maintenance optimization through a discrete-time semi-Markov decision process

    International Nuclear Information System (INIS)

    Zhang Xueqing; Gao Hui

    2012-01-01

    Optimization models are necessary for efficient and cost-effective maintenance of a road network. In this regard, road deterioration is commonly modeled as a discrete-time Markov process such that an optimal maintenance policy can be obtained based on the Markov decision process, or as a renewal process such that an optimal maintenance policy can be obtained based on the renewal theory. However, the discrete-time Markov process cannot capture the real time at which the state transits while the renewal process considers only one state and one maintenance action. In this paper, road deterioration is modeled as a semi-Markov process in which the state transition has the Markov property and the holding time in each state is assumed to follow a discrete Weibull distribution. Based on this semi-Markov process, linear programming models are formulated for both infinite and finite planning horizons in order to derive optimal maintenance policies to minimize the life-cycle cost of a road network. A hypothetical road network is used to illustrate the application of the proposed optimization models. The results indicate that these linear programming models are practical for the maintenance of a road network having a large number of road segments and that they are convenient to incorporate various constraints on the decision process, for example, performance requirements and available budgets. Although the optimal maintenance policies obtained for the road network are randomized stationary policies, the extent of this randomness in decision making is limited. The maintenance actions are deterministic for most states and the randomness in selecting actions occurs only for a few states.

  8. Apples and oranges: avoiding different priors in Bayesian DNA sequence analysis

    Directory of Open Access Journals (Sweden)

    Posch Stefan

    2010-03-01

    Full Text Available Abstract Background One of the challenges of bioinformatics remains the recognition of short signal sequences in genomic DNA such as donor or acceptor splice sites, splicing enhancers or silencers, translation initiation sites, transcription start sites, transcription factor binding sites, nucleosome binding sites, miRNA binding sites, or insulator binding sites. During the last decade, a wealth of algorithms for the recognition of such DNA sequences has been developed and compared with the goal of improving their performance and to deepen our understanding of the underlying cellular processes. Most of these algorithms are based on statistical models belonging to the family of Markov random fields such as position weight matrix models, weight array matrix models, Markov models of higher order, or moral Bayesian networks. While in many comparative studies different learning principles or different statistical models have been compared, the influence of choosing different prior distributions for the model parameters when using different learning principles has been overlooked, and possibly lead to questionable conclusions. Results With the goal of allowing direct comparisons of different learning principles for models from the family of Markov random fields based on the same a-priori information, we derive a generalization of the commonly-used product-Dirichlet prior. We find that the derived prior behaves like a Gaussian prior close to the maximum and like a Laplace prior in the far tails. In two case studies, we illustrate the utility of the derived prior for a direct comparison of different learning principles with different models for the recognition of binding sites of the transcription factor Sp1 and human donor splice sites. Conclusions We find that comparisons of different learning principles using the same a-priori information can lead to conclusions different from those of previous studies in which the effect resulting from different

  9. Classification of Active Microwave and Passive Optical Data Based on Bayesian Theory and Mrf

    Science.gov (United States)

    Yu, F.; Li, H. T.; Han, Y. S.; Gu, H. Y.

    2012-08-01

    A classifier based on Bayesian theory and Markov random field (MRF) is presented to classify the active microwave and passive optical remote sensing data, which have demonstrated their respective advantages in inversion of surface soil moisture content. In the method, the VV, VH polarization of ASAR and all the 7 TM bands are taken as the input of the classifier to get the class labels of each pixel of the images. And the model is validated for the necessities of integration of TM and ASAR, it shows that, the total precision of classification in this paper is 89.4%. Comparing with the classification with single TM, the accuracy increase 11.5%, illustrating that synthesis of active and passive optical remote sensing data is efficient and potential in classification.

  10. CLASSIFICATION OF ACTIVE MICROWAVE AND PASSIVE OPTICAL DATA BASED ON BAYESIAN THEORY AND MRF

    Directory of Open Access Journals (Sweden)

    F. Yu

    2012-08-01

    Full Text Available A classifier based on Bayesian theory and Markov random field (MRF is presented to classify the active microwave and passive optical remote sensing data, which have demonstrated their respective advantages in inversion of surface soil moisture content. In the method, the VV, VH polarization of ASAR and all the 7 TM bands are taken as the input of the classifier to get the class labels of each pixel of the images. And the model is validated for the necessities of integration of TM and ASAR, it shows that, the total precision of classification in this paper is 89.4%. Comparing with the classification with single TM, the accuracy increase 11.5%, illustrating that synthesis of active and passive optical remote sensing data is efficient and potential in classification.

  11. On the entropy of a hidden Markov process.

    Science.gov (United States)

    Jacquet, Philippe; Seroussi, Gadiel; Szpankowski, Wojciech

    2008-05-01

    We study the entropy rate of a hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a first-order binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem. By presenting the probability of a sequence under the model as a product of random matrices, one can see that the entropy rate sought is equal to a top Lyapunov exponent of the product. This offers an explanation for the elusiveness of explicit expressions for the HMP entropy rate, as Lyapunov exponents are notoriously difficult to compute. Consequently, we focus on asymptotic estimates, and apply the same product of random matrices to derive an explicit expression for a Taylor approximation of the entropy rate with respect to the parameter of the binary symmetric channel. The accuracy of the approximation is validated against empirical simulation results. We also extend our results to higher-order Markov processes and to Rényi entropies of any order.

  12. Recovery of Graded Response Model Parameters: A Comparison of Marginal Maximum Likelihood and Markov Chain Monte Carlo Estimation

    Science.gov (United States)

    Kieftenbeld, Vincent; Natesan, Prathiba

    2012-01-01

    Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

  13. A Bayesian framework to estimate diversification rates and their variation through time and space

    Directory of Open Access Journals (Sweden)

    Silvestro Daniele

    2011-10-01

    Full Text Available Abstract Background Patterns of species diversity are the result of speciation and extinction processes, and molecular phylogenetic data can provide valuable information to derive their variability through time and across clades. Bayesian Markov chain Monte Carlo methods offer a promising framework to incorporate phylogenetic uncertainty when estimating rates of diversification. Results We introduce a new approach to estimate diversification rates in a Bayesian framework over a distribution of trees under various constant and variable rate birth-death and pure-birth models, and test it on simulated phylogenies. Furthermore, speciation and extinction rates and their posterior credibility intervals can be estimated while accounting for non-random taxon sampling. The framework is particularly suitable for hypothesis testing using Bayes factors, as we demonstrate analyzing dated phylogenies of Chondrostoma (Cyprinidae and Lupinus (Fabaceae. In addition, we develop a model that extends the rate estimation to a meta-analysis framework in which different data sets are combined in a single analysis to detect general temporal and spatial trends in diversification. Conclusions Our approach provides a flexible framework for the estimation of diversification parameters and hypothesis testing while simultaneously accounting for uncertainties in the divergence times and incomplete taxon sampling.

  14. Markov processes an introduction for physical scientists

    CERN Document Server

    Gillespie, Daniel T

    1991-01-01

    Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.Key Features* A self-contained, prgamatic exposition of the needed elements of random variable theory* Logically integrated derviations of the Chapman-Kolmogorov e

  15. A Nonparametric Bayesian Approach For Emission Tomography Reconstruction

    International Nuclear Information System (INIS)

    Barat, Eric; Dautremer, Thomas

    2007-01-01

    We introduce a PET reconstruction algorithm following a nonparametric Bayesian (NPB) approach. In contrast with Expectation Maximization (EM), the proposed technique does not rely on any space discretization. Namely, the activity distribution--normalized emission intensity of the spatial poisson process--is considered as a spatial probability density and observations are the projections of random emissions whose distribution has to be estimated. This approach is nonparametric in the sense that the quantity of interest belongs to the set of probability measures on R k (for reconstruction in k-dimensions) and it is Bayesian in the sense that we define a prior directly on this spatial measure. In this context, we propose to model the nonparametric probability density as an infinite mixture of multivariate normal distributions. As a prior for this mixture we consider a Dirichlet Process Mixture (DPM) with a Normal-Inverse Wishart (NIW) model as base distribution of the Dirichlet Process. As in EM-family reconstruction, we use a data augmentation scheme where the set of hidden variables are the emission locations for each observed line of response in the continuous object space. Thanks to the data augmentation, we propose a Markov Chain Monte Carlo (MCMC) algorithm (Gibbs sampler) which is able to generate draws from the posterior distribution of the spatial intensity. A difference with EM is that one step of the Gibbs sampler corresponds to the generation of emission locations while only the expected number of emissions per pixel/voxel is used in EM. Another key difference is that the estimated spatial intensity is a continuous function such that there is no need to compute a projection matrix. Finally, draws from the intensity posterior distribution allow the estimation of posterior functionnals like the variance or confidence intervals. Results are presented for simulated data based on a 2D brain phantom and compared to Bayesian MAP-EM

  16. Pose-invariant face recognition using Markov random fields.

    Science.gov (United States)

    Ho, Huy Tho; Chellappa, Rama

    2013-04-01

    One of the key challenges for current face recognition techniques is how to handle pose variations between the probe and gallery face images. In this paper, we present a method for reconstructing the virtual frontal view from a given nonfrontal face image using Markov random fields (MRFs) and an efficient variant of the belief propagation algorithm. In the proposed approach, the input face image is divided into a grid of overlapping patches, and a globally optimal set of local warps is estimated to synthesize the patches at the frontal view. A set of possible warps for each patch is obtained by aligning it with images from a training database of frontal faces. The alignments are performed efficiently in the Fourier domain using an extension of the Lucas-Kanade algorithm that can handle illumination variations. The problem of finding the optimal warps is then formulated as a discrete labeling problem using an MRF. The reconstructed frontal face image can then be used with any face recognition technique. The two main advantages of our method are that it does not require manually selected facial landmarks or head pose estimation. In order to improve the performance of our pose normalization method in face recognition, we also present an algorithm for classifying whether a given face image is at a frontal or nonfrontal pose. Experimental results on different datasets are presented to demonstrate the effectiveness of the proposed approach.

  17. Markov analysis of alpha-helical, beta-sheet and random coil regions of proteins

    International Nuclear Information System (INIS)

    Macchiato, M.; Tramontano, A.

    1983-01-01

    The rules up to now used to predict the spatial configuration of proteins from their primary structure are mostly based on the recurrence analysis of some doublets, triplets and so on of contiguous amino acids, but they do not take into account the correlation characteristics of the whole amino acid sequence. A statistical analysis of amino acid sequences for the alpha-helical, beta-sheet and random coil regions of about twenty proteins with known secondary structure by considering correlations effects has been carried out. The obtained results demonstrate that these sequences are at least a second-order Markov chain, i.e. they appear as if they were generated by a source that remembers at least the two aminoacids before the one being generated and that these two previous symbols influence the present choice

  18. Approximate Bayesian evaluations of measurement uncertainty

    Science.gov (United States)

    Possolo, Antonio; Bodnar, Olha

    2018-04-01

    The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

  19. Mixture estimation with state-space components and Markov model of switching

    Czech Academy of Sciences Publication Activity Database

    Nagy, Ivan; Suzdaleva, Evgenia

    2013-01-01

    Roč. 37, č. 24 (2013), s. 9970-9984 ISSN 0307-904X R&D Projects: GA TA ČR TA01030123 Institutional support: RVO:67985556 Keywords : probabilistic dynamic mixtures, * probability density function * state-space models * recursive mixture estimation * Bayesian dynamic decision making under uncertainty * Kerridge inaccuracy Subject RIV: BC - Control Systems Theory Impact factor: 2.158, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/nagy-mixture estimation with state-space components and markov model of switching.pdf

  20. A Multilayer Hidden Markov Models-Based Method for Human-Robot Interaction

    Directory of Open Access Journals (Sweden)

    Chongben Tao

    2013-01-01

    Full Text Available To achieve Human-Robot Interaction (HRI by using gestures, a continuous gesture recognition approach based on Multilayer Hidden Markov Models (MHMMs is proposed, which consists of two parts. One part is gesture spotting and segment module, the other part is continuous gesture recognition module. Firstly, a Kinect sensor is used to capture 3D acceleration and 3D angular velocity data of hand gestures. And then, a Feed-forward Neural Networks (FNNs and a threshold criterion are used for gesture spotting and segment, respectively. Afterwards, the segmented gesture signals are respectively preprocessed and vector symbolized by a sliding window and a K-means clustering method. Finally, symbolized data are sent into Lower Hidden Markov Models (LHMMs to identify individual gestures, and then, a Bayesian filter with sequential constraints among gestures in Upper Hidden Markov Models (UHMMs is used to correct recognition errors created in LHMMs. Five predefined gestures are used to interact with a Kinect mobile robot in experiments. The experimental results show that the proposed method not only has good effectiveness and accuracy, but also has favorable real-time performance.

  1. A spatio-temporal nonparametric Bayesian variable selection model of fMRI data for clustering correlated time courses.

    Science.gov (United States)

    Zhang, Linlin; Guindani, Michele; Versace, Francesco; Vannucci, Marina

    2014-07-15

    In this paper we present a novel wavelet-based Bayesian nonparametric regression model for the analysis of functional magnetic resonance imaging (fMRI) data. Our goal is to provide a joint analytical framework that allows to detect regions of the brain which exhibit neuronal activity in response to a stimulus and, simultaneously, infer the association, or clustering, of spatially remote voxels that exhibit fMRI time series with similar characteristics. We start by modeling the data with a hemodynamic response function (HRF) with a voxel-dependent shape parameter. We detect regions of the brain activated in response to a given stimulus by using mixture priors with a spike at zero on the coefficients of the regression model. We account for the complex spatial correlation structure of the brain by using a Markov random field (MRF) prior on the parameters guiding the selection of the activated voxels, therefore capturing correlation among nearby voxels. In order to infer association of the voxel time courses, we assume correlated errors, in particular long memory, and exploit the whitening properties of discrete wavelet transforms. Furthermore, we achieve clustering of the voxels by imposing a Dirichlet process (DP) prior on the parameters of the long memory process. For inference, we use Markov Chain Monte Carlo (MCMC) sampling techniques that combine Metropolis-Hastings schemes employed in Bayesian variable selection with sampling algorithms for nonparametric DP models. We explore the performance of the proposed model on simulated data, with both block- and event-related design, and on real fMRI data. Copyright © 2014 Elsevier Inc. All rights reserved.

  2. The explicit form of the rate function for semi-Markov processes and its contractions

    Science.gov (United States)

    Sughiyama, Yuki; Kobayashi, Testuya J.

    2018-03-01

    We derive the explicit form of the rate function for semi-Markov processes. Here, the ‘random time change trick’ plays an essential role. Also, by exploiting the contraction principle of large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the level 2.5 rate function for Markov processes to semi-Markov cases.

  3. Studying stellar binary systems with the Laser Interferometer Space Antenna using delayed rejection Markov chain Monte Carlo methods

    International Nuclear Information System (INIS)

    Trias, Miquel; Vecchio, Alberto; Veitch, John

    2009-01-01

    Bayesian analysis of Laser Interferometer Space Antenna (LISA) data sets based on Markov chain Monte Carlo methods has been shown to be a challenging problem, in part due to the complicated structure of the likelihood function consisting of several isolated local maxima that dramatically reduces the efficiency of the sampling techniques. Here we introduce a new fully Markovian algorithm, a delayed rejection Metropolis-Hastings Markov chain Monte Carlo method, to efficiently explore these kind of structures and we demonstrate its performance on selected LISA data sets containing a known number of stellar-mass binary signals embedded in Gaussian stationary noise.

  4. Bayesian variable selection for multistate Markov models with interval-censored data in an ecological momentary assessment study of smoking cessation.

    Science.gov (United States)

    Koslovsky, Matthew D; Swartz, Michael D; Chan, Wenyaw; Leon-Novelo, Luis; Wilkinson, Anna V; Kendzor, Darla E; Businelle, Michael S

    2017-10-11

    The application of sophisticated analytical methods to intensive longitudinal data, collected with ecological momentary assessments (EMA), has helped researchers better understand smoking behaviors after a quit attempt. Unfortunately, the wealth of information captured with EMAs is typically underutilized in practice. Thus, novel methods are needed to extract this information in exploratory research studies. One of the main objectives of intensive longitudinal data analysis is identifying relations between risk factors and outcomes of interest. Our goal is to develop and apply expectation maximization variable selection for Bayesian multistate Markov models with interval-censored data to generate new insights into the relation between potential risk factors and transitions between smoking states. Through simulation, we demonstrate the effectiveness of our method in identifying associated risk factors and its ability to outperform the LASSO in a special case. Additionally, we use the expectation conditional-maximization algorithm to simplify estimation, a deterministic annealing variant to reduce the algorithm's dependence on starting values, and Louis's method to estimate unknown parameter uncertainty. We then apply our method to intensive longitudinal data collected with EMA to identify risk factors associated with transitions between smoking states after a quit attempt in a cohort of socioeconomically disadvantaged smokers who were interested in quitting. © 2017, The International Biometric Society.

  5. Adiabatic condition and the quantum hitting time of Markov chains

    International Nuclear Information System (INIS)

    Krovi, Hari; Ozols, Maris; Roland, Jeremie

    2010-01-01

    We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P ' where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP ' and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.

  6. Multi-dimensional quasitoeplitz Markov chains

    Directory of Open Access Journals (Sweden)

    Alexander N. Dudin

    1999-01-01

    Full Text Available This paper deals with multi-dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector-generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP-input, which operate in synchronous random environment.

  7. On a full Bayesian inference for force reconstruction problems

    Science.gov (United States)

    Aucejo, M.; De Smet, O.

    2018-05-01

    In a previous paper, the authors introduced a flexible methodology for reconstructing mechanical sources in the frequency domain from prior local information on both their nature and location over a linear and time invariant structure. The proposed approach was derived from Bayesian statistics, because of its ability in mathematically accounting for experimenter's prior knowledge. However, since only the Maximum a Posteriori estimate was computed, the posterior uncertainty about the regularized solution given the measured vibration field, the mechanical model and the regularization parameter was not assessed. To answer this legitimate question, this paper fully exploits the Bayesian framework to provide, from a Markov Chain Monte Carlo algorithm, credible intervals and other statistical measures (mean, median, mode) for all the parameters of the force reconstruction problem.

  8. Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

    Science.gov (United States)

    Li, Zhiqiang; Xu, Tingxue; Gu, Junyuan; Dong, Qi; Fu, Linyu

    2018-04-01

    This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables, can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit.

  9. A Bayesian approach to probabilistic sensitivity analysis in structured benefit-risk assessment.

    Science.gov (United States)

    Waddingham, Ed; Mt-Isa, Shahrul; Nixon, Richard; Ashby, Deborah

    2016-01-01

    Quantitative decision models such as multiple criteria decision analysis (MCDA) can be used in benefit-risk assessment to formalize trade-offs between benefits and risks, providing transparency to the assessment process. There is however no well-established method for propagating uncertainty of treatment effects data through such models to provide a sense of the variability of the benefit-risk balance. Here, we present a Bayesian statistical method that directly models the outcomes observed in randomized placebo-controlled trials and uses this to infer indirect comparisons between competing active treatments. The resulting treatment effects estimates are suitable for use within the MCDA setting, and it is possible to derive the distribution of the overall benefit-risk balance through Markov Chain Monte Carlo simulation. The method is illustrated using a case study of natalizumab for relapsing-remitting multiple sclerosis. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  10. Bayesian Markov Chain Monte Carlo inversion for weak anisotropy parameters and fracture weaknesses using azimuthal elastic impedance

    Science.gov (United States)

    Chen, Huaizhen; Pan, Xinpeng; Ji, Yuxin; Zhang, Guangzhi

    2017-08-01

    A system of aligned vertical fractures and fine horizontal shale layers combine to form equivalent orthorhombic media. Weak anisotropy parameters and fracture weaknesses play an important role in the description of orthorhombic anisotropy (OA). We propose a novel approach of utilizing seismic reflection amplitudes to estimate weak anisotropy parameters and fracture weaknesses from observed seismic data, based on azimuthal elastic impedance (EI). We first propose perturbation in stiffness matrix in terms of weak anisotropy parameters and fracture weaknesses, and using the perturbation and scattering function, we derive PP-wave reflection coefficient and azimuthal EI for the case of an interface separating two OA media. Then we demonstrate an approach to first use a model constrained damped least-squares algorithm to estimate azimuthal EI from partially incidence-phase-angle-stack seismic reflection data at different azimuths, and then extract weak anisotropy parameters and fracture weaknesses from the estimated azimuthal EI using a Bayesian Markov Chain Monte Carlo inversion method. In addition, a new procedure to construct rock physics effective model is presented to estimate weak anisotropy parameters and fracture weaknesses from well log interpretation results (minerals and their volumes, porosity, saturation, fracture density, etc.). Tests on synthetic and real data indicate that unknown parameters including elastic properties (P- and S-wave impedances and density), weak anisotropy parameters and fracture weaknesses can be estimated stably in the case of seismic data containing a moderate noise, and our approach can make a reasonable estimation of anisotropy in a fractured shale reservoir.

  11. Inferring animal densities from tracking data using Markov chains.

    Science.gov (United States)

    Whitehead, Hal; Jonsen, Ian D

    2013-01-01

    The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.

  12. Inferring animal densities from tracking data using Markov chains.

    Directory of Open Access Journals (Sweden)

    Hal Whitehead

    Full Text Available The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.

  13. Bayesian inference of chemical kinetic models from proposed reactions

    KAUST Repository

    Galagali, Nikhil

    2015-02-01

    © 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure-such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.

  14. Decomposition of conditional probability for high-order symbolic Markov chains

    Science.gov (United States)

    Melnik, S. S.; Usatenko, O. V.

    2017-07-01

    The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

  15. A Bayesian Analysis of a Random Effects Small Business Loan Credit Scoring Model

    Directory of Open Access Journals (Sweden)

    Patrick J. Farrell

    2011-09-01

    Full Text Available One of the most important aspects of credit scoring is constructing a model that has low misclassification rates and is also flexible enough to allow for random variation. It is also well known that, when there are a large number of highly correlated variables as is typical in studies involving questionnaire data, a method must be found to reduce the number of variables to those that have high predictive power. Here we propose a Bayesian multivariate logistic regression model with both fixed and random effects for small business loan credit scoring and a variable reduction method using Bayes factors. The method is illustrated on an interesting data set based on questionnaires sent to loan officers in Canadian banks and venture capital companies

  16. Evaluating impacts using a BACI design, ratios, and a Bayesian approach with a focus on restoration.

    Science.gov (United States)

    Conner, Mary M; Saunders, W Carl; Bouwes, Nicolaas; Jordan, Chris

    2015-10-01

    Before-after-control-impact (BACI) designs are an effective method to evaluate natural and human-induced perturbations on ecological variables when treatment sites cannot be randomly chosen. While effect sizes of interest can be tested with frequentist methods, using Bayesian Markov chain Monte Carlo (MCMC) sampling methods, probabilities of effect sizes, such as a ≥20 % increase in density after restoration, can be directly estimated. Although BACI and Bayesian methods are used widely for assessing natural and human-induced impacts for field experiments, the application of hierarchal Bayesian modeling with MCMC sampling to BACI designs is less common. Here, we combine these approaches and extend the typical presentation of results with an easy to interpret ratio, which provides an answer to the main study question-"How much impact did a management action or natural perturbation have?" As an example of this approach, we evaluate the impact of a restoration project, which implemented beaver dam analogs, on survival and density of juvenile steelhead. Results indicated the probabilities of a ≥30 % increase were high for survival and density after the dams were installed, 0.88 and 0.99, respectively, while probabilities for a higher increase of ≥50 % were variable, 0.17 and 0.82, respectively. This approach demonstrates a useful extension of Bayesian methods that can easily be generalized to other study designs from simple (e.g., single factor ANOVA, paired t test) to more complicated block designs (e.g., crossover, split-plot). This approach is valuable for estimating the probabilities of restoration impacts or other management actions.

  17. Bayesian Estimation and Selection of Nonlinear Vector Error Correction Models: The Case of the Sugar-Ethanol-Oil Nexus in Brazil

    OpenAIRE

    Kelvin Balcombe; George Rapsomanikis

    2008-01-01

    Nonlinear adjustment toward long-run price equilibrium relationships in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalized bivariate error correction models that allow for cointegration between sugar, ethanol, and oil prices, where dynamic adjustments are potentially nonlinear functions of the disequilibrium errors. A range of models are estimated using Bayesian Monte Carlo Markov Chain algorithms and compared using Bayesian model selection methods. The results suggest ...

  18. Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method.

    Science.gov (United States)

    Zhang, Guanglei; Liu, Fei; Liu, Jie; Luo, Jianwen; Xie, Yaoqin; Bai, Jing; Xing, Lei

    2017-01-01

    X-ray luminescence computed tomography (XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. Combining the principles of X-ray excitation of luminescence-based probes and optical signal detection, XLCT naturally fuses functional and anatomical images and provides complementary information for a wide range of applications in biomedical research. In order to improve the data acquisition efficiency of previously developed narrow-beam XLCT, a cone beam XLCT (CB-XLCT) mode is adopted here to take advantage of the useful geometric features of cone beam excitation. Practically, a major hurdle in using cone beam X-ray for XLCT is that the inverse problem here is seriously ill-conditioned, hindering us to achieve good image quality. In this paper, we propose a novel Bayesian method to tackle the bottleneck in CB-XLCT reconstruction. The method utilizes a local regularization strategy based on Gaussian Markov random field to mitigate the ill-conditioness of CB-XLCT. An alternating optimization scheme is then used to automatically calculate all the unknown hyperparameters while an iterative coordinate descent algorithm is adopted to reconstruct the image with a voxel-based closed-form solution. Results of numerical simulations and mouse experiments show that the self-adaptive Bayesian method significantly improves the CB-XLCT image quality as compared with conventional methods.

  19. Bayesian Inference of a Multivariate Regression Model

    Directory of Open Access Journals (Sweden)

    Marick S. Sinay

    2014-01-01

    Full Text Available We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for the covariance matrix. Here we depart from this approach and propose a novel Bayesian estimator for the covariance. A multivariate normal prior for the unique elements of the matrix logarithm of the covariance matrix is considered. Such structure allows for a richer class of prior distributions for the covariance, with respect to strength of beliefs in prior location hyperparameters, as well as the added ability, to model potential correlation amongst the covariance structure. The posterior moments of all relevant parameters of interest are calculated based upon numerical results via a Markov chain Monte Carlo procedure. The Metropolis-Hastings-within-Gibbs algorithm is invoked to account for the construction of a proposal density that closely matches the shape of the target posterior distribution. As an application of the proposed technique, we investigate a multiple regression based upon the 1980 High School and Beyond Survey.

  20. Bayesian phylogeny analysis via stochastic approximation Monte Carlo

    KAUST Repository

    Cheon, Sooyoung

    2009-11-01

    Monte Carlo methods have received much attention in the recent literature of phylogeny analysis. However, the conventional Markov chain Monte Carlo algorithms, such as the Metropolis-Hastings algorithm, tend to get trapped in a local mode in simulating from the posterior distribution of phylogenetic trees, rendering the inference ineffective. In this paper, we apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm, to Bayesian phylogeny analysis. Our method is compared with two popular Bayesian phylogeny software, BAMBE and MrBayes, on simulated and real datasets. The numerical results indicate that our method outperforms BAMBE and MrBayes. Among the three methods, SAMC produces the consensus trees which have the highest similarity to the true trees, and the model parameter estimates which have the smallest mean square errors, but costs the least CPU time. © 2009 Elsevier Inc. All rights reserved.

  1. The generalization ability of online SVM classification based on Markov sampling.

    Science.gov (United States)

    Xu, Jie; Yan Tang, Yuan; Zou, Bin; Xu, Zongben; Li, Luoqing; Lu, Yang

    2015-03-01

    In this paper, we consider online support vector machine (SVM) classification learning algorithms with uniformly ergodic Markov chain (u.e.M.c.) samples. We establish the bound on the misclassification error of an online SVM classification algorithm with u.e.M.c. samples based on reproducing kernel Hilbert spaces and obtain a satisfactory convergence rate. We also introduce a novel online SVM classification algorithm based on Markov sampling, and present the numerical studies on the learning ability of online SVM classification based on Markov sampling for benchmark repository. The numerical studies show that the learning performance of the online SVM classification algorithm based on Markov sampling is better than that of classical online SVM classification based on random sampling as the size of training samples is larger.

  2. Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants

    KAUST Repository

    Jin, Ick Hoon

    2014-03-01

    Statistical inference for the models with intractable normalizing constants has attracted much attention. During the past two decades, various approximation- or simulation-based methods have been proposed for the problem, such as the Monte Carlo maximum likelihood method and the auxiliary variable Markov chain Monte Carlo methods. The Bayesian stochastic approximation Monte Carlo algorithm specifically addresses this problem: It works by sampling from a sequence of approximate distributions with their average converging to the target posterior distribution, where the approximate distributions can be achieved using the stochastic approximation Monte Carlo algorithm. A strong law of large numbers is established for the Bayesian stochastic approximation Monte Carlo estimator under mild conditions. Compared to the Monte Carlo maximum likelihood method, the Bayesian stochastic approximation Monte Carlo algorithm is more robust to the initial guess of model parameters. Compared to the auxiliary variable MCMC methods, the Bayesian stochastic approximation Monte Carlo algorithm avoids the requirement for perfect samples, and thus can be applied to many models for which perfect sampling is not available or very expensive. The Bayesian stochastic approximation Monte Carlo algorithm also provides a general framework for approximate Bayesian analysis. © 2012 Elsevier B.V. All rights reserved.

  3. Markov counting and reward processes for analysing the performance of a complex system subject to random inspections

    International Nuclear Information System (INIS)

    Ruiz-Castro, Juan Eloy

    2016-01-01

    In this paper, a discrete complex reliability system subject to internal failures and external shocks, is modelled algorithmically. Two types of internal failure are considered: repairable and non-repairable. When a repairable failure occurs, the unit goes to corrective repair. In addition, the unit is subject to external shocks that may produce an aggravation of the internal degradation level, cumulative damage or extreme failure. When a damage threshold is reached, the unit must be removed. When a non-repairable failure occurs, the device is replaced by a new, identical one. The internal performance and the external damage are partitioned in performance levels. Random inspections are carried out. When an inspection takes place, the internal performance of the system and the damage caused by external shocks are observed and if necessary the unit is sent to preventive maintenance. If the inspection observes minor state for the internal performance and/or external damage, then these states remain in memory when the unit goes to corrective or preventive maintenance. Transient and stationary analyses are performed. Markov counting and reward processes are developed in computational form to analyse the performance and profitability of the system with and without preventive maintenance. These aspects are implemented computationally with Matlab. - Highlights: • A multi-state device is modelled in an algorithmic and computational form. • The performance is partitioned in multi-states and degradation levels. • Several types of failures with repair times according to degradation levels. • Preventive maintenance as response to random inspection is introduced. • The performance-profitable is analysed through Markov counting and reward processes.

  4. Bayesian inference in processing experimental data: principles and basic applications

    International Nuclear Information System (INIS)

    D'Agostini, G

    2003-01-01

    This paper introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as the following: model comparison (including the automatic Ockham's Razor filter provided by the Bayesian approach); parametric inference; quantification of the uncertainty about the value of physical quantities, also taking into account systematic effects; role of marginalization; posterior characterization; predictive distributions; hierarchical modelling and hyperparameters; Gaussian approximation of the posterior and recovery of conventional methods, especially maximum likelihood and chi-square fits under well-defined conditions; conjugate priors, transformation invariance and maximum entropy motivated priors; and Monte Carlo (MC) estimates of expectation, including a short introduction to Markov Chain MC methods

  5. The mean field theory in EM procedures for blind Markov random field image restoration.

    Science.gov (United States)

    Zhang, J

    1993-01-01

    A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing.

  6. A Markov Random Field Groupwise Registration Framework for Face Recognition.

    Science.gov (United States)

    Liao, Shu; Shen, Dinggang; Chung, Albert C S

    2014-04-01

    In this paper, we propose a new framework for tackling face recognition problem. The face recognition problem is formulated as groupwise deformable image registration and feature matching problem. The main contributions of the proposed method lie in the following aspects: (1) Each pixel in a facial image is represented by an anatomical signature obtained from its corresponding most salient scale local region determined by the survival exponential entropy (SEE) information theoretic measure. (2) Based on the anatomical signature calculated from each pixel, a novel Markov random field based groupwise registration framework is proposed to formulate the face recognition problem as a feature guided deformable image registration problem. The similarity between different facial images are measured on the nonlinear Riemannian manifold based on the deformable transformations. (3) The proposed method does not suffer from the generalizability problem which exists commonly in learning based algorithms. The proposed method has been extensively evaluated on four publicly available databases: FERET, CAS-PEAL-R1, FRGC ver 2.0, and the LFW. It is also compared with several state-of-the-art face recognition approaches, and experimental results demonstrate that the proposed method consistently achieves the highest recognition rates among all the methods under comparison.

  7. IMAGE SEGMENTATION BASED ON MARKOV RANDOM FIELD AND WATERSHED TECHNIQUES

    Institute of Scientific and Technical Information of China (English)

    纳瑟; 刘重庆

    2002-01-01

    This paper presented a method that incorporates Markov Random Field(MRF), watershed segmentation and merging techniques for performing image segmentation and edge detection tasks. MRF is used to obtain an initial estimate of x regions in the image under process where in MRF model, gray level x, at pixel location i, in an image X, depends on the gray levels of neighboring pixels. The process needs an initial segmented result. An initial segmentation is got based on K-means clustering technique and the minimum distance, then the region process in modeled by MRF to obtain an image contains different intensity regions. Starting from this we calculate the gradient values of that image and then employ a watershed technique. When using MRF method it obtains an image that has different intensity regions and has all the edge and region information, then it improves the segmentation result by superimpose closed and an accurate boundary of each region using watershed algorithm. After all pixels of the segmented regions have been processed, a map of primitive region with edges is generated. Finally, a merge process based on averaged mean values is employed. The final segmentation and edge detection result is one closed boundary per actual region in the image.

  8. Decisive Markov Chains

    OpenAIRE

    Abdulla, Parosh Aziz; Henda, Noomene Ben; Mayr, Richard

    2007-01-01

    We consider qualitative and quantitative verification problems for infinite-state Markov chains. We call a Markov chain decisive w.r.t. a given set of target states F if it almost certainly eventually reaches either F or a state from which F can no longer be reached. While all finite Markov chains are trivially decisive (for every set F), this also holds for many classes of infinite Markov chains. Infinite Markov chains which contain a finite attractor are decisive w.r.t. every set F. In part...

  9. Driving Style Analysis Using Primitive Driving Patterns With Bayesian Nonparametric Approaches

    OpenAIRE

    Wang, Wenshuo; Xi, Junqiang; Zhao, Ding

    2017-01-01

    Analysis and recognition of driving styles are profoundly important to intelligent transportation and vehicle calibration. This paper presents a novel driving style analysis framework using the primitive driving patterns learned from naturalistic driving data. In order to achieve this, first, a Bayesian nonparametric learning method based on a hidden semi-Markov model (HSMM) is introduced to extract primitive driving patterns from time series driving data without prior knowledge of the number...

  10. Properly quantized history-dependent Parrondo games, Markov processes, and multiplexing circuits

    Energy Technology Data Exchange (ETDEWEB)

    Bleiler, Steven A. [Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, PO Box 751, Portland, OR 97207 (United States); Khan, Faisal Shah, E-mail: faisal.khan@kustar.ac.a [Khalifa University of Science, Technology and Research, PO Box 127788, Abu Dhabi (United Arab Emirates)

    2011-05-09

    Highlights: History-dependent Parrondo games are viewed as Markov processes. Quantum mechanical analogues of these Markov processes are constructed. These quantum analogues restrict to the original process on measurement. Relationship between these analogues and a quantum circuits is exhibited. - Abstract: In the context of quantum information theory, 'quantization' of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of probability distribution with higher order randomization notions from quantum mechanics such as quantum superposition with measurement. For this to be done 'properly', a faithful copy of the original construction is required to exist within the new quantum one, just as is required when a function is extended to a larger domain. Here procedures for extending history-dependent Parrondo games, Markov processes and multiplexing circuits to their quantum versions are analyzed from a game theoretic viewpoint, and from this viewpoint, proper quantizations developed.

  11. Featuring Multiple Local Optima to Assist the User in the Interpretation of Induced Bayesian Network Models

    DEFF Research Database (Denmark)

    Dalgaard, Jens; Pena, Jose; Kocka, Tomas

    2004-01-01

    We propose a method to assist the user in the interpretation of the best Bayesian network model indu- ced from data. The method consists in extracting relevant features from the model (e.g. edges, directed paths and Markov blankets) and, then, assessing the con¯dence in them by studying multiple...

  12. Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives

    NARCIS (Netherlands)

    Durbin, J.; Koopman, S.J.M.

    1998-01-01

    The analysis of non-Gaussian time series using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Monte Carlo Markov chain methods are not employed. Non-Gaussian

  13. BAYESIAN IMAGE RESTORATION, USING CONFIGURATIONS

    Directory of Open Access Journals (Sweden)

    Thordis Linda Thorarinsdottir

    2011-05-01

    Full Text Available In this paper, we develop a Bayesian procedure for removing noise from images that can be viewed as noisy realisations of random sets in the plane. The procedure utilises recent advances in configuration theory for noise free random sets, where the probabilities of observing the different boundary configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed in detail for 3 X 3 and 5 X 5 configurations and examples of the performance of the procedure are given.

  14. Fast and accurate Bayesian model criticism and conflict diagnostics using R-INLA

    KAUST Repository

    Ferkingstad, Egil

    2017-10-16

    Bayesian hierarchical models are increasingly popular for realistic modelling and analysis of complex data. This trend is accompanied by the need for flexible, general and computationally efficient methods for model criticism and conflict detection. Usually, a Bayesian hierarchical model incorporates a grouping of the individual data points, as, for example, with individuals in repeated measurement data. In such cases, the following question arises: Are any of the groups “outliers,” or in conflict with the remaining groups? Existing general approaches aiming to answer such questions tend to be extremely computationally demanding when model fitting is based on Markov chain Monte Carlo. We show how group-level model criticism and conflict detection can be carried out quickly and accurately through integrated nested Laplace approximations (INLA). The new method is implemented as a part of the open-source R-INLA package for Bayesian computing (http://r-inla.org).

  15. Hamiltonian Markov Chain Monte Carlo Methods for the CUORE Neutrinoless Double Beta Decay Sensitivity

    Science.gov (United States)

    Graham, Eleanor; Cuore Collaboration

    2017-09-01

    The CUORE experiment is a large-scale bolometric detector seeking to observe the never-before-seen process of neutrinoless double beta decay. Predictions for CUORE's sensitivity to neutrinoless double beta decay allow for an understanding of the half-life ranges that the detector can probe, and also to evaluate the relative importance of different detector parameters. Currently, CUORE uses a Bayesian analysis based in BAT, which uses Metropolis-Hastings Markov Chain Monte Carlo, for its sensitivity studies. My work evaluates the viability and potential improvements of switching the Bayesian analysis to Hamiltonian Monte Carlo, realized through the program Stan and its Morpho interface. I demonstrate that the BAT study can be successfully recreated in Stan, and perform a detailed comparison between the results and computation times of the two methods.

  16. Fracture Mechanical Markov Chain Crack Growth Model

    DEFF Research Database (Denmark)

    Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard

    1991-01-01

    propagation process can be described by a discrete space Markov theory. The model is applicable to deterministic as well as to random loading. Once the model parameters for a given material have been determined, the results can be used for any structure as soon as the geometrical function is known....

  17. Bayesian inference method for stochastic damage accumulation modeling

    International Nuclear Information System (INIS)

    Jiang, Xiaomo; Yuan, Yong; Liu, Xian

    2013-01-01

    Damage accumulation based reliability model plays an increasingly important role in successful realization of condition based maintenance for complicated engineering systems. This paper developed a Bayesian framework to establish stochastic damage accumulation model from historical inspection data, considering data uncertainty. Proportional hazards modeling technique is developed to model the nonlinear effect of multiple influencing factors on system reliability. Different from other hazard modeling techniques such as normal linear regression model, the approach does not require any distribution assumption for the hazard model, and can be applied for a wide variety of distribution models. A Bayesian network is created to represent the nonlinear proportional hazards models and to estimate model parameters by Bayesian inference with Markov Chain Monte Carlo simulation. Both qualitative and quantitative approaches are developed to assess the validity of the established damage accumulation model. Anderson–Darling goodness-of-fit test is employed to perform the normality test, and Box–Cox transformation approach is utilized to convert the non-normality data into normal distribution for hypothesis testing in quantitative model validation. The methodology is illustrated with the seepage data collected from real-world subway tunnels.

  18. Bayesian Peptide Peak Detection for High Resolution TOF Mass Spectrometry.

    Science.gov (United States)

    Zhang, Jianqiu; Zhou, Xiaobo; Wang, Honghui; Suffredini, Anthony; Zhang, Lin; Huang, Yufei; Wong, Stephen

    2010-11-01

    In this paper, we address the issue of peptide ion peak detection for high resolution time-of-flight (TOF) mass spectrometry (MS) data. A novel Bayesian peptide ion peak detection method is proposed for TOF data with resolution of 10 000-15 000 full width at half-maximum (FWHW). MS spectra exhibit distinct characteristics at this resolution, which are captured in a novel parametric model. Based on the proposed parametric model, a Bayesian peak detection algorithm based on Markov chain Monte Carlo (MCMC) sampling is developed. The proposed algorithm is tested on both simulated and real datasets. The results show a significant improvement in detection performance over a commonly employed method. The results also agree with expert's visual inspection. Moreover, better detection consistency is achieved across MS datasets from patients with identical pathological condition.

  19. MODIS 250m burned area mapping based on an algorithm using change point detection and Markov random fields.

    Science.gov (United States)

    Mota, Bernardo; Pereira, Jose; Campagnolo, Manuel; Killick, Rebeca

    2013-04-01

    Area burned in tropical savannas of Brazil was mapped using MODIS-AQUA daily 250m resolution imagery by adapting one of the European Space Agency fire_CCI project burned area algorithms, based on change point detection and Markov random fields. The study area covers 1,44 Mkm2 and was performed with data from 2005. The daily 1000 m image quality layer was used for cloud and cloud shadow screening. The algorithm addresses each pixel as a time series and detects changes in the statistical properties of NIR reflectance values, to identify potential burning dates. The first step of the algorithm is robust filtering, to exclude outlier observations, followed by application of the Pruned Exact Linear Time (PELT) change point detection technique. Near-infrared (NIR) spectral reflectance changes between time segments, and post change NIR reflectance values are combined into a fire likelihood score. Change points corresponding to an increase in reflectance are dismissed as potential burn events, as are those occurring outside of a pre-defined fire season. In the last step of the algorithm, monthly burned area probability maps and detection date maps are converted to dichotomous (burned-unburned maps) using Markov random fields, which take into account both spatial and temporal relations in the potential burned area maps. A preliminary assessment of our results is performed by comparison with data from the MODIS 1km active fires and the 500m burned area products, taking into account differences in spatial resolution between the two sensors.

  20. New Product Development in an Emerging Economy: Analysing the Role of Supplier Involvement Practices by Using Bayesian Markov Chain Monte Carlo Technique

    Directory of Open Access Journals (Sweden)

    Kanagi Kanapathy

    2014-01-01

    Full Text Available The research question is whether the positive relationship found between supplier involvement practices and new product development performances in developed economies also holds in emerging economies. The role of supplier involvement practices in new product development performance is yet to be substantially investigated in the emerging economies (other than China. This premise was examined by distributing a survey instrument (Jayaram’s (2008 published survey instrument that has been utilised in developed economies to Malaysian manufacturing companies. To gauge the relationship between the supplier involvement practices and new product development (NPD project performance of 146 companies, structural equation modelling was adopted. Our findings prove that supplier involvement practices have a significant positive impact on NPD project performance in an emerging economy with respect to quality objectives, design objectives, cost objectives, and “time-to-market” objectives. Further analysis using the Bayesian Markov Chain Monte Carlo algorithm, yielding a more credible and feasible differentiation, confirmed these results (even in the case of an emerging economy and indicated that these practices have a 28% impact on variance of NPD project performance. This considerable effect implies that supplier involvement is a must have, although further research is needed to identify the contingencies for its practices.

  1. Bayesian tomographic reconstruction of microsystems

    International Nuclear Information System (INIS)

    Salem, Sofia Fekih; Vabre, Alexandre; Mohammad-Djafari, Ali

    2007-01-01

    The microtomography by X ray transmission plays an increasingly dominating role in the study and the understanding of microsystems. Within this framework, an experimental setup of high resolution X ray microtomography was developed at CEA-List to quantify the physical parameters related to the fluids flow in microsystems. Several difficulties rise from the nature of experimental data collected on this setup: enhanced error measurements due to various physical phenomena occurring during the image formation (diffusion, beam hardening), and specificities of the setup (limited angle, partial view of the object, weak contrast).To reconstruct the object we must solve an inverse problem. This inverse problem is known to be ill-posed. It therefore needs to be regularized by introducing prior information. The main prior information we account for is that the object is composed of a finite known number of different materials distributed in compact regions. This a priori information is introduced via a Gauss-Markov field for the contrast distributions with a hidden Potts-Markov field for the class materials in the Bayesian estimation framework. The computations are done by using an appropriate Markov Chain Monte Carlo (MCMC) technique.In this paper, we present first the basic steps of the proposed algorithms. Then we focus on one of the main steps in any iterative reconstruction method which is the computation of forward and adjoint operators (projection and backprojection). A fast implementation of these two operators is crucial for the real application of the method. We give some details on the fast computation of these steps and show some preliminary results of simulations

  2. A nonparametric Bayesian approach for genetic evaluation in ...

    African Journals Online (AJOL)

    South African Journal of Animal Science ... the Bayesian and Classical models, a Bayesian procedure is provided which allows these random ... data from the Elsenburg Dormer sheep stud and data from a simulation experiment are utilized. >

  3. Musical Markov Chains

    Science.gov (United States)

    Volchenkov, Dima; Dawin, Jean René

    A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.

  4. Markov random field and Gaussian mixture for segmented MRI-based partial volume correction in PET

    International Nuclear Information System (INIS)

    Bousse, Alexandre; Thomas, Benjamin A; Erlandsson, Kjell; Hutton, Brian F; Pedemonte, Stefano; Ourselin, Sébastien; Arridge, Simon

    2012-01-01

    In this paper we propose a segmented magnetic resonance imaging (MRI) prior-based maximum penalized likelihood deconvolution technique for positron emission tomography (PET) images. The model assumes the existence of activity classes that behave like a hidden Markov random field (MRF) driven by the segmented MRI. We utilize a mean field approximation to compute the likelihood of the MRF. We tested our method on both simulated and clinical data (brain PET) and compared our results with PET images corrected with the re-blurred Van Cittert (VC) algorithm, the simplified Guven (SG) algorithm and the region-based voxel-wise (RBV) technique. We demonstrated our algorithm outperforms the VC algorithm and outperforms SG and RBV corrections when the segmented MRI is inconsistent (e.g. mis-segmentation, lesions, etc) with the PET image. (paper)

  5. The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective.

    Science.gov (United States)

    Kruschke, John K; Liddell, Torrin M

    2018-02-01

    In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from hypothesis testing to estimation has been dubbed "the New Statistics" (Cumming 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to hypothesis testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.

  6. A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

    Science.gov (United States)

    Karabatsos, George

    2017-02-01

    Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected

  7. Maximum Kolmogorov-Sinai Entropy Versus Minimum Mixing Time in Markov Chains

    Science.gov (United States)

    Mihelich, M.; Dubrulle, B.; Paillard, D.; Kral, Q.; Faranda, D.

    2018-01-01

    We establish a link between the maximization of Kolmogorov Sinai entropy (KSE) and the minimization of the mixing time for general Markov chains. Since the maximisation of KSE is analytical and easier to compute in general than mixing time, this link provides a new faster method to approximate the minimum mixing time dynamics. It could be interesting in computer sciences and statistical physics, for computations that use random walks on graphs that can be represented as Markov chains.

  8. Random resampling masks: a non-Bayesian one-shot strategy for noise reduction in digital holography.

    Science.gov (United States)

    Bianco, V; Paturzo, M; Memmolo, P; Finizio, A; Ferraro, P; Javidi, B

    2013-03-01

    Holographic imaging may become severely degraded by a mixture of speckle and incoherent additive noise. Bayesian approaches reduce the incoherent noise, but prior information is needed on the noise statistics. With no prior knowledge, one-shot reduction of noise is a highly desirable goal, as the recording process is simplified and made faster. Indeed, neither multiple acquisitions nor a complex setup are needed. So far, this result has been achieved at the cost of a deterministic resolution loss. Here we propose a fast non-Bayesian denoising method that avoids this trade-off by means of a numerical synthesis of a moving diffuser. In this way, only one single hologram is required as multiple uncorrelated reconstructions are provided by random complementary resampling masks. Experiments show a significant incoherent noise reduction, close to the theoretical improvement bound, resulting in image-contrast improvement. At the same time, we preserve the resolution of the unprocessed image.

  9. Semi-Markov processes

    CERN Document Server

    Grabski

    2014-01-01

    Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. Clearly defines the properties and

  10. A MARKOV RANDOM FIELD-BASED APPROACH TO CHARACTERIZING HUMAN BRAIN DEVELOPMENT USING SPATIAL-TEMPORAL TRANSCRIPTOME DATA.

    Science.gov (United States)

    Lin, Zhixiang; Sanders, Stephan J; Li, Mingfeng; Sestan, Nenad; State, Matthew W; Zhao, Hongyu

    2015-03-01

    Human neurodevelopment is a highly regulated biological process. In this article, we study the dynamic changes of neurodevelopment through the analysis of human brain microarray data, sampled from 16 brain regions in 15 time periods of neurodevelopment. We develop a two-step inferential procedure to identify expressed and unexpressed genes and to detect differentially expressed genes between adjacent time periods. Markov Random Field (MRF) models are used to efficiently utilize the information embedded in brain region similarity and temporal dependency in our approach. We develop and implement a Monte Carlo expectation-maximization (MCEM) algorithm to estimate the model parameters. Simulation studies suggest that our approach achieves lower misclassification error and potential gain in power compared with models not incorporating spatial similarity and temporal dependency.

  11. Applying Markov Chains for NDVI Time Series Forecasting of Latvian Regions

    Directory of Open Access Journals (Sweden)

    Stepchenko Arthur

    2015-12-01

    Full Text Available Time series of earth observation based estimates of vegetation inform about variations in vegetation at the scale of Latvia. A vegetation index is an indicator that describes the amount of chlorophyll (the green mass and shows the relative density and health of vegetation. NDVI index is an important variable for vegetation forecasting and management of various problems, such as climate change monitoring, energy usage monitoring, managing the consumption of natural resources, agricultural productivity monitoring, drought monitoring and forest fire detection. In this paper, we make a one-step-ahead prediction of 7-daily time series of NDVI index using Markov chains. The choice of a Markov chain is due to the fact that a Markov chain is a sequence of random variables where each variable is located in some state. And a Markov chain contains probabilities of moving from one state to other.

  12. A Bayesian Analysis of a Randomized Clinical Trial Comparing Antimetabolite Therapies for Non-Infectious Uveitis.

    Science.gov (United States)

    Browne, Erica N; Rathinam, Sivakumar R; Kanakath, Anuradha; Thundikandy, Radhika; Babu, Manohar; Lietman, Thomas M; Acharya, Nisha R

    2017-02-01

    To conduct a Bayesian analysis of a randomized clinical trial (RCT) for non-infectious uveitis using expert opinion as a subjective prior belief. A RCT was conducted to determine which antimetabolite, methotrexate or mycophenolate mofetil, is more effective as an initial corticosteroid-sparing agent for the treatment of intermediate, posterior, and pan-uveitis. Before the release of trial results, expert opinion on the relative effectiveness of these two medications was collected via online survey. Members of the American Uveitis Society executive committee were invited to provide an estimate for the relative decrease in efficacy with a 95% credible interval (CrI). A prior probability distribution was created from experts' estimates. A Bayesian analysis was performed using the constructed expert prior probability distribution and the trial's primary outcome. A total of 11 of the 12 invited uveitis specialists provided estimates. Eight of 11 experts (73%) believed mycophenolate mofetil is more effective. The group prior belief was that the odds of treatment success for patients taking mycophenolate mofetil were 1.4-fold the odds of those taking methotrexate (95% CrI 0.03-45.0). The odds of treatment success with mycophenolate mofetil compared to methotrexate was 0.4 from the RCT (95% confidence interval 0.1-1.2) and 0.7 (95% CrI 0.2-1.7) from the Bayesian analysis. A Bayesian analysis combining expert belief with the trial's result did not indicate preference for one drug. However, the wide credible interval leaves open the possibility of a substantial treatment effect. This suggests clinical equipoise necessary to allow a larger, more definitive RCT.

  13. Hidden Markov models for zero-inflated Poisson counts with an application to substance use.

    Science.gov (United States)

    DeSantis, Stacia M; Bandyopadhyay, Dipankar

    2011-06-30

    Paradigms for substance abuse cue-reactivity research involve pharmacological or stressful stimulation designed to elicit stress and craving responses in cocaine-dependent subjects. It is unclear as to whether stress induced from participation in such studies increases drug-seeking behavior. We propose a 2-state Hidden Markov model to model the number of cocaine abuses per week before and after participation in a stress-and cue-reactivity study. The hypothesized latent state corresponds to 'high' or 'low' use. To account for a preponderance of zeros, we assume a zero-inflated Poisson model for the count data. Transition probabilities depend on the prior week's state, fixed demographic variables, and time-varying covariates. We adopt a Bayesian approach to model fitting, and use the conditional predictive ordinate statistic to demonstrate that the zero-inflated Poisson hidden Markov model outperforms other models for longitudinal count data. Copyright © 2011 John Wiley & Sons, Ltd.

  14. A Bayesian alternative for multi-objective ecohydrological model specification

    Science.gov (United States)

    Tang, Yating; Marshall, Lucy; Sharma, Ashish; Ajami, Hoori

    2018-01-01

    Recent studies have identified the importance of vegetation processes in terrestrial hydrologic systems. Process-based ecohydrological models combine hydrological, physical, biochemical and ecological processes of the catchments, and as such are generally more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov chain Monte Carlo (MCMC) techniques. The Bayesian approach offers an appealing alternative to traditional multi-objective hydrologic model calibrations by defining proper prior distributions that can be considered analogous to the ad-hoc weighting often prescribed in multi-objective calibration. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological modeling framework based on a traditional Pareto-based model calibration technique. In our study, a Pareto-based multi-objective optimization and a formal Bayesian framework are implemented in a conceptual ecohydrological model that combines a hydrological model (HYMOD) and a modified Bucket Grassland Model (BGM). Simulations focused on one objective (streamflow/LAI) and multiple objectives (streamflow and LAI) with different emphasis defined via the prior distribution of the model error parameters. Results show more reliable outputs for both predicted streamflow and LAI using Bayesian multi-objective calibration with specified prior distributions for error parameters based on results from the Pareto front in the ecohydrological modeling. The methodology implemented here provides insight into the usefulness of multiobjective Bayesian calibration for ecohydrologic systems and the importance of appropriate prior

  15. Identification and Simulation of Subsurface Soil patterns using hidden Markov random fields and remote sensing and geophysical EMI data sets

    Science.gov (United States)

    Wang, Hui; Wellmann, Florian; Verweij, Elizabeth; von Hebel, Christian; van der Kruk, Jan

    2017-04-01

    Lateral and vertical spatial heterogeneity of subsurface properties such as soil texture and structure influences the available water and resource supply for crop growth. High-resolution mapping of subsurface structures using non-invasive geo-referenced geophysical measurements, like electromagnetic induction (EMI), enables a characterization of 3D soil structures, which have shown correlations to remote sensing information of the crop states. The benefit of EMI is that it can return 3D subsurface information, however the spatial dimensions are limited due to the labor intensive measurement procedure. Although active and passive sensors mounted on air- or space-borne platforms return 2D images, they have much larger spatial dimensions. Combining both approaches provides us with a potential pathway to extend the detailed 3D geophysical information to a larger area by using remote sensing information. In this study, we aim at extracting and providing insights into the spatial and statistical correlation of the geophysical and remote sensing observations of the soil/vegetation continuum system. To this end, two key points need to be addressed: 1) how to detect and recognize the geometric patterns (i.e., spatial heterogeneity) from multiple data sets, and 2) how to quantitatively describe the statistical correlation between remote sensing information and geophysical measurements. In the current study, the spatial domain is restricted to shallow depths up to 3 meters, and the geostatistical database contains normalized difference vegetation index (NDVI) derived from RapidEye satellite images and apparent electrical conductivities (ECa) measured from multi-receiver EMI sensors for nine depths of exploration ranging from 0-2.7 m. The integrated data sets are mapped into both the physical space (i.e. the spatial domain) and feature space (i.e. a two-dimensional space framed by the NDVI and the ECa data). Hidden Markov Random Fields (HMRF) are employed to model the

  16. Master equation for She-Leveque scaling and its classification in terms of other Markov models of developed turbulence

    Science.gov (United States)

    Nickelsen, Daniel

    2017-07-01

    The statistics of velocity increments in homogeneous and isotropic turbulence exhibit universal features in the limit of infinite Reynolds numbers. After Kolmogorov’s scaling law from 1941, many turbulence models aim for capturing these universal features, some are known to have an equivalent formulation in terms of Markov processes. We derive the Markov process equivalent to the particularly successful scaling law postulated by She and Leveque. The Markov process is a jump process for velocity increments u(r) in scale r in which the jumps occur randomly but with deterministic width in u. From its master equation we establish a prescription to simulate the She-Leveque process and compare it with Kolmogorov scaling. To put the She-Leveque process into the context of other established turbulence models on the Markov level, we derive a diffusion process for u(r) using two properties of the Navier-Stokes equation. This diffusion process already includes Kolmogorov scaling, extended self-similarity and a class of random cascade models. The fluctuation theorem of this Markov process implies a ‘second law’ that puts a loose bound on the multipliers of the random cascade models. This bound explicitly allows for instances of inverse cascades, which are necessary to satisfy the fluctuation theorem. By adding a jump process to the diffusion process, we go beyond Kolmogorov scaling and formulate the most general scaling law for the class of Markov processes having both diffusion and jump parts. This Markov scaling law includes She-Leveque scaling and a scaling law derived by Yakhot.

  17. Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

    Science.gov (United States)

    Warner, James E.; Hochhalter, Jacob D.

    2016-01-01

    This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

  18. Discrete probability models and methods probability on graphs and trees, Markov chains and random fields, entropy and coding

    CERN Document Server

    Brémaud, Pierre

    2017-01-01

    The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book. .

  19. Numerical Methods for Bayesian Inverse Problems

    KAUST Repository

    Ernst, Oliver

    2014-01-06

    We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.

  20. Numerical Methods for Bayesian Inverse Problems

    KAUST Repository

    Ernst, Oliver; Sprungk, Bjorn; Cliffe, K. Andrew; Starkloff, Hans-Jorg

    2014-01-01

    We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.

  1. Bayesian model discrimination for glucose-insulin homeostasis

    DEFF Research Database (Denmark)

    Andersen, Kim Emil; Brooks, Stephen P.; Højbjerre, Malene

    In this paper we analyse a set of experimental data on a number of healthy and diabetic patients and discuss a variety of models for describing the physiological processes involved in glucose absorption and insulin secretion within the human body. We adopt a Bayesian approach which facilitates...... as parameter uncertainty. Markov chain Monte Carlo methods are used, combining Metropolis Hastings, reversible jump and simulated tempering updates to provide rapidly mixing chains so as to provide robust inference. We demonstrate the methodology for both healthy and type II diabetic populations concluding...... that whilst both populations are well modelled by a common insulin model, their glucose dynamics differ considerably....

  2. A Coupled Hidden Markov Random Field Model for Simultaneous Face Clustering and Tracking in Videos

    KAUST Repository

    Wu, Baoyuan

    2016-10-25

    Face clustering and face tracking are two areas of active research in automatic facial video processing. They, however, have long been studied separately, despite the inherent link between them. In this paper, we propose to perform simultaneous face clustering and face tracking from real world videos. The motivation for the proposed research is that face clustering and face tracking can provide useful information and constraints to each other, thus can bootstrap and improve the performances of each other. To this end, we introduce a Coupled Hidden Markov Random Field (CHMRF) to simultaneously model face clustering, face tracking, and their interactions. We provide an effective algorithm based on constrained clustering and optimal tracking for the joint optimization of cluster labels and face tracking. We demonstrate significant improvements over state-of-the-art results in face clustering and tracking on several videos.

  3. A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.

    Science.gov (United States)

    Houseman, E Andres; Virji, M Abbas

    2017-08-01

    Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates

  4. Markov random field based automatic image alignment for electron tomography.

    Science.gov (United States)

    Amat, Fernando; Moussavi, Farshid; Comolli, Luis R; Elidan, Gal; Downing, Kenneth H; Horowitz, Mark

    2008-03-01

    We present a method for automatic full-precision alignment of the images in a tomographic tilt series. Full-precision automatic alignment of cryo electron microscopy images has remained a difficult challenge to date, due to the limited electron dose and low image contrast. These facts lead to poor signal to noise ratio (SNR) in the images, which causes automatic feature trackers to generate errors, even with high contrast gold particles as fiducial features. To enable fully automatic alignment for full-precision reconstructions, we frame the problem probabilistically as finding the most likely particle tracks given a set of noisy images, using contextual information to make the solution more robust to the noise in each image. To solve this maximum likelihood problem, we use Markov Random Fields (MRF) to establish the correspondence of features in alignment and robust optimization for projection model estimation. The resulting algorithm, called Robust Alignment and Projection Estimation for Tomographic Reconstruction, or RAPTOR, has not needed any manual intervention for the difficult datasets we have tried, and has provided sub-pixel alignment that is as good as the manual approach by an expert user. We are able to automatically map complete and partial marker trajectories and thus obtain highly accurate image alignment. Our method has been applied to challenging cryo electron tomographic datasets with low SNR from intact bacterial cells, as well as several plastic section and X-ray datasets.

  5. Revisiting Boltzmann learning: parameter estimation in Markov random fields

    DEFF Research Database (Denmark)

    Hansen, Lars Kai; Andersen, Lars Nonboe; Kjems, Ulrik

    1996-01-01

    This article presents a generalization of the Boltzmann machine that allows us to use the learning rule for a much wider class of maximum likelihood and maximum a posteriori problems, including both supervised and unsupervised learning. Furthermore, the approach allows us to discuss regularization...... and generalization in the context of Boltzmann machines. We provide an illustrative example concerning parameter estimation in an inhomogeneous Markov field. The regularized adaptation produces a parameter set that closely resembles the “teacher” parameters, hence, will produce segmentations that closely reproduce...

  6. Bayesian site selection for fast Gaussian process regression

    KAUST Repository

    Pourhabib, Arash; Liang, Faming; Ding, Yu

    2014-01-01

    Gaussian Process (GP) regression is a popular method in the field of machine learning and computer experiment designs; however, its ability to handle large data sets is hindered by the computational difficulty in inverting a large covariance matrix. Likelihood approximation methods were developed as a fast GP approximation, thereby reducing the computation cost of GP regression by utilizing a much smaller set of unobserved latent variables called pseudo points. This article reports a further improvement to the likelihood approximation methods by simultaneously deciding both the number and locations of the pseudo points. The proposed approach is a Bayesian site selection method where both the number and locations of the pseudo inputs are parameters in the model, and the Bayesian model is solved using a reversible jump Markov chain Monte Carlo technique. Through a number of simulated and real data sets, it is demonstrated that with appropriate priors chosen, the Bayesian site selection method can produce a good balance between computation time and prediction accuracy: it is fast enough to handle large data sets that a full GP is unable to handle, and it improves, quite often remarkably, the prediction accuracy, compared with the existing likelihood approximations. © 2014 Taylor and Francis Group, LLC.

  7. Bayesian site selection for fast Gaussian process regression

    KAUST Repository

    Pourhabib, Arash

    2014-02-05

    Gaussian Process (GP) regression is a popular method in the field of machine learning and computer experiment designs; however, its ability to handle large data sets is hindered by the computational difficulty in inverting a large covariance matrix. Likelihood approximation methods were developed as a fast GP approximation, thereby reducing the computation cost of GP regression by utilizing a much smaller set of unobserved latent variables called pseudo points. This article reports a further improvement to the likelihood approximation methods by simultaneously deciding both the number and locations of the pseudo points. The proposed approach is a Bayesian site selection method where both the number and locations of the pseudo inputs are parameters in the model, and the Bayesian model is solved using a reversible jump Markov chain Monte Carlo technique. Through a number of simulated and real data sets, it is demonstrated that with appropriate priors chosen, the Bayesian site selection method can produce a good balance between computation time and prediction accuracy: it is fast enough to handle large data sets that a full GP is unable to handle, and it improves, quite often remarkably, the prediction accuracy, compared with the existing likelihood approximations. © 2014 Taylor and Francis Group, LLC.

  8. Bayesian phylogeography finds its roots.

    Directory of Open Access Journals (Sweden)

    Philippe Lemey

    2009-09-01

    Full Text Available As a key factor in endemic and epidemic dynamics, the geographical distribution of viruses has been frequently interpreted in the light of their genetic histories. Unfortunately, inference of historical dispersal or migration patterns of viruses has mainly been restricted to model-free heuristic approaches that provide little insight into the temporal setting of the spatial dynamics. The introduction of probabilistic models of evolution, however, offers unique opportunities to engage in this statistical endeavor. Here we introduce a Bayesian framework for inference, visualization and hypothesis testing of phylogeographic history. By implementing character mapping in a Bayesian software that samples time-scaled phylogenies, we enable the reconstruction of timed viral dispersal patterns while accommodating phylogenetic uncertainty. Standard Markov model inference is extended with a stochastic search variable selection procedure that identifies the parsimonious descriptions of the diffusion process. In addition, we propose priors that can incorporate geographical sampling distributions or characterize alternative hypotheses about the spatial dynamics. To visualize the spatial and temporal information, we summarize inferences using virtual globe software. We describe how Bayesian phylogeography compares with previous parsimony analysis in the investigation of the influenza A H5N1 origin and H5N1 epidemiological linkage among sampling localities. Analysis of rabies in West African dog populations reveals how virus diffusion may enable endemic maintenance through continuous epidemic cycles. From these analyses, we conclude that our phylogeographic framework will make an important asset in molecular epidemiology that can be easily generalized to infer biogeogeography from genetic data for many organisms.

  9. Nuclear security assessment with Markov model approach

    International Nuclear Information System (INIS)

    Suzuki, Mitsutoshi; Terao, Norichika

    2013-01-01

    Nuclear security risk assessment with the Markov model based on random event is performed to explore evaluation methodology for physical protection in nuclear facilities. Because the security incidences are initiated by malicious and intentional acts, expert judgment and Bayes updating are used to estimate scenario and initiation likelihood, and it is assumed that the Markov model derived from stochastic process can be applied to incidence sequence. Both an unauthorized intrusion as Design Based Threat (DBT) and a stand-off attack as beyond-DBT are assumed to hypothetical facilities, and performance of physical protection and mitigation and minimization of consequence are investigated to develop the assessment methodology in a semi-quantitative manner. It is shown that cooperation between facility operator and security authority is important to respond to the beyond-DBT incidence. (author)

  10. The Bacterial Sequential Markov Coalescent.

    Science.gov (United States)

    De Maio, Nicola; Wilson, Daniel J

    2017-05-01

    Bacteria can exchange and acquire new genetic material from other organisms directly and via the environment. This process, known as bacterial recombination, has a strong impact on the evolution of bacteria, for example, leading to the spread of antibiotic resistance across clades and species, and to the avoidance of clonal interference. Recombination hinders phylogenetic and transmission inference because it creates patterns of substitutions (homoplasies) inconsistent with the hypothesis of a single evolutionary tree. Bacterial recombination is typically modeled as statistically akin to gene conversion in eukaryotes, i.e. , using the coalescent with gene conversion (CGC). However, this model can be very computationally demanding as it needs to account for the correlations of evolutionary histories of even distant loci. So, with the increasing popularity of whole genome sequencing, the need has emerged for a faster approach to model and simulate bacterial genome evolution. We present a new model that approximates the coalescent with gene conversion: the bacterial sequential Markov coalescent (BSMC). Our approach is based on a similar idea to the sequential Markov coalescent (SMC)-an approximation of the coalescent with crossover recombination. However, bacterial recombination poses hurdles to a sequential Markov approximation, as it leads to strong correlations and linkage disequilibrium across very distant sites in the genome. Our BSMC overcomes these difficulties, and shows a considerable reduction in computational demand compared to the exact CGC, and very similar patterns in simulated data. We implemented our BSMC model within new simulation software FastSimBac. In addition to the decreased computational demand compared to previous bacterial genome evolution simulators, FastSimBac provides more general options for evolutionary scenarios, allowing population structure with migration, speciation, population size changes, and recombination hotspots. FastSimBac is

  11. conting : an R package for Bayesian analysis of complete and incomplete contingency tables

    OpenAIRE

    Overstall, Antony; King, Ruth

    2014-01-01

    The aim of this paper is to demonstrate the R package conting for the Bayesian analysis of complete and incomplete contingency tables using hierarchical log-linear models. This package allows a user to identify interactions between categorical factors (via complete contingency tables) and to estimate closed population sizes using capture-recapture studies (via incomplete contingency tables). The models are fitted using Markov chain Monte Carlo methods. In particular, implementations of the Me...

  12. Bayesian inference and decision theory - A framework for decision making in natural resource management

    Science.gov (United States)

    Dorazio, R.M.; Johnson, F.A.

    2003-01-01

    Bayesian inference and decision theory may be used in the solution of relatively complex problems of natural resource management, owing to recent advances in statistical theory and computing. In particular, Markov chain Monte Carlo algorithms provide a computational framework for fitting models of adequate complexity and for evaluating the expected consequences of alternative management actions. We illustrate these features using an example based on management of waterfowl habitat.

  13. Markov chain beam randomization: a study of the impact of PLANCK beam measurement errors on cosmological parameter estimation

    Science.gov (United States)

    Rocha, G.; Pagano, L.; Górski, K. M.; Huffenberger, K. M.; Lawrence, C. R.; Lange, A. E.

    2010-04-01

    We introduce a new method to propagate uncertainties in the beam shapes used to measure the cosmic microwave background to cosmological parameters determined from those measurements. The method, called markov chain beam randomization (MCBR), randomly samples from a set of templates or functions that describe the beam uncertainties. The method is much faster than direct numerical integration over systematic “nuisance” parameters, and is not restricted to simple, idealized cases as is analytic marginalization. It does not assume the data are normally distributed, and does not require Gaussian priors on the specific systematic uncertainties. We show that MCBR properly accounts for and provides the marginalized errors of the parameters. The method can be generalized and used to propagate any systematic uncertainties for which a set of templates is available. We apply the method to the Planck satellite, and consider future experiments. Beam measurement errors should have a small effect on cosmological parameters as long as the beam fitting is performed after removal of 1/f noise.

  14. Markov chain Monte Carlo techniques applied to parton distribution functions determination: Proof of concept

    Science.gov (United States)

    Gbedo, Yémalin Gabin; Mangin-Brinet, Mariane

    2017-07-01

    We present a new procedure to determine parton distribution functions (PDFs), based on Markov chain Monte Carlo (MCMC) methods. The aim of this paper is to show that we can replace the standard χ2 minimization by procedures grounded on statistical methods, and on Bayesian inference in particular, thus offering additional insight into the rich field of PDFs determination. After a basic introduction to these techniques, we introduce the algorithm we have chosen to implement—namely Hybrid (or Hamiltonian) Monte Carlo. This algorithm, initially developed for Lattice QCD, turns out to be very interesting when applied to PDFs determination by global analyses; we show that it allows us to circumvent the difficulties due to the high dimensionality of the problem, in particular concerning the acceptance. A first feasibility study is performed and presented, which indicates that Markov chain Monte Carlo can successfully be applied to the extraction of PDFs and of their uncertainties.

  15. Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures

    Science.gov (United States)

    Larmier, Coline; Zoia, Andrea; Malvagi, Fausto; Dumonteil, Eric; Mazzolo, Alain

    2018-02-01

    Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of Monte Carlo algorithms taking into account the effects of stochastic media on particle propagation by generating on-the-fly the material interfaces crossed by the random walkers during their trajectories. Such methods enable a significant reduction of computational resources as opposed to reference solutions obtained by solving the Boltzmann equation for a large number of realizations of random media. CLS solutions, which neglect correlations induced by the spatial disorder, are faster albeit approximate, and might thus show discrepancies with respect to reference solutions. In this work we propose a new family of algorithms (called 'Poisson Box Sampling', PBS) aimed at improving the accuracy of the CLS approach for transport in d-dimensional binary Markov mixtures. In order to probe the features of PBS methods, we will focus on three-dimensional Markov media and revisit the benchmark problem originally proposed by Adams, Larsen and Pomraning [1] and extended by Brantley [2]: for these configurations we will compare reference solutions, standard CLS solutions and the new PBS solutions for scalar particle flux, transmission and reflection coefficients. PBS will be shown to perform better than CLS at the expense of a reasonable increase in computational time.

  16. Entropy, complexity, and Markov diagrams for random walk cancer models.

    Science.gov (United States)

    Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

    2014-12-19

    The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

  17. Nonpoint source solute transport normal to aquifer bedding in heterogeneous, Markov chain random fields

    Science.gov (United States)

    Zhang, Hua; Harter, Thomas; Sivakumar, Bellie

    2006-06-01

    Facies-based geostatistical models have become important tools for analyzing flow and mass transport processes in heterogeneous aquifers. Yet little is known about the relationship between these latter processes and the parameters of facies-based geostatistical models. In this study, we examine the transport of a nonpoint source solute normal (perpendicular) to the major bedding plane of an alluvial aquifer medium that contains multiple geologic facies, including interconnected, high-conductivity (coarse textured) facies. We also evaluate the dependence of the transport behavior on the parameters of the constitutive facies model. A facies-based Markov chain geostatistical model is used to quantify the spatial variability of the aquifer system's hydrostratigraphy. It is integrated with a groundwater flow model and a random walk particle transport model to estimate the solute traveltime probability density function (pdf) for solute flux from the water table to the bottom boundary (the production horizon) of the aquifer. The cases examined include two-, three-, and four-facies models, with mean length anisotropy ratios for horizontal to vertical facies, ek, from 25:1 to 300:1 and with a wide range of facies volume proportions (e.g., from 5 to 95% coarse-textured facies). Predictions of traveltime pdfs are found to be significantly affected by the number of hydrostratigraphic facies identified in the aquifer. Those predictions of traveltime pdfs also are affected by the proportions of coarse-textured sediments, the mean length of the facies (particularly the ratio of length to thickness of coarse materials), and, to a lesser degree, the juxtapositional preference among the hydrostratigraphic facies. In transport normal to the sedimentary bedding plane, traveltime is not lognormally distributed as is often assumed. Also, macrodispersive behavior (variance of the traveltime) is found not to be a unique function of the conductivity variance. For the parameter range

  18. Quantum random walks and their convergence to Evans–Hudson ...

    Indian Academy of Sciences (India)

    Quantum dynamical semigroup; Evans–Hudson flow; quantum random walk. 1. Introduction. The aim of this article is to investigate convergence of random walks on von Neumann algebra to Evans–Hudson flows. Here the random walks and Evans–Hudson flows are gene- ralizations of classical Markov chains and Markov ...

  19. Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

    Directory of Open Access Journals (Sweden)

    Hea-Jung Kim

    2017-06-01

    Full Text Available This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT models with stochastic (or uncertain constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT models (such as log-normal, log-Cauchy, and log-logistic FT models as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

  20. Bayesian Optimization in High Dimensions via Random Embeddings

    NARCIS (Netherlands)

    Wang, Z.; Zoghi, M.; Hutter, F.; Matheson, D.; de Freitas, N.; Rossi, F.

    2013-01-01

    Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several

  1. The Fracture Mechanical Markov Chain Fatigue Model Compared with Empirical Data

    DEFF Research Database (Denmark)

    Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard

    The applicability of the FMF-model (Fracture Mechanical Markov Chain Fatigue Model) introduced in Gansted, L., R. Brincker and L. Pilegaard Hansen (1991) is tested by simulations and compared with empirical data. Two sets of data have been used, the Virkler data (aluminium alloy) and data...... established at the Laboratory of Structural Engineering at Aalborg University, the AUC-data, (mild steel). The model, which is based on the assumption, that the crack propagation process can be described by a discrete Space Markov theory, is applicable to constant as well as random loading. It is shown...

  2. A Bayesian inference approach to unveil supply curves in electricity markets

    DEFF Research Database (Denmark)

    Mitridati, Lesia Marie-Jeanne Mariane; Pinson, Pierre

    2017-01-01

    in the literature on modeling this uncertainty. In this study we introduce a Bayesian inference approach to reveal the aggregate supply curve in a day-ahead electricity market. The proposed algorithm relies on Markov Chain Monte Carlo and Sequential Monte Carlo methods. The major appeal of this approach......With increased competition in wholesale electricity markets, the need for new decision-making tools for strategic producers has arisen. Optimal bidding strategies have traditionally been modeled as stochastic profit maximization problems. However, for producers with non-negligible market power...

  3. Bayesian inference for multivariate point processes observed at sparsely distributed times

    DEFF Research Database (Denmark)

    Rasmussen, Jakob Gulddahl; Møller, Jesper; Aukema, B.H.

    We consider statistical and computational aspects of simulation-based Bayesian inference for a multivariate point process which is only observed at sparsely distributed times. For specicity we consider a particular data set which has earlier been analyzed by a discrete time model involving unknown...... normalizing constants. We discuss the advantages and disadvantages of using continuous time processes compared to discrete time processes in the setting of the present paper as well as other spatial-temporal situations. Keywords: Bark beetle, conditional intensity, forest entomology, Markov chain Monte Carlo...

  4. Hidden Markov Model of atomic quantum jump dynamics in an optically probed cavity

    DEFF Research Database (Denmark)

    Gammelmark, S.; Molmer, K.; Alt, W.

    2014-01-01

    We analyze the quantum jumps of an atom interacting with a cavity field. The strong atom- field interaction makes the cavity transmission depend on the time dependent atomic state, and we present a Hidden Markov Model description of the atomic state dynamics which is conditioned in a Bayesian...... manner on the detected signal. We suggest that small variations in the observed signal may be due to spatial motion of the atom within the cavity, and we represent the atomic system by a number of hidden states to account for both the small variations and the internal state jump dynamics. In our theory...

  5. Air kerma rate estimation by means of in-situ gamma spectrometry: A Bayesian approach

    International Nuclear Information System (INIS)

    Cabal, Gonzalo; Kluson, Jaroslav

    2008-01-01

    Full text: Bayesian inference is used to determine the Air Kerma Rate based on a set of in situ environmental gamma spectra measurements performed with a NaI(Tl) scintillation detector. A natural advantage of such approach is the possibility to quantify uncertainty not only in the Air Kerma Rate estimation but also for the gamma spectra which is unfolded within the procedure. The measurements were performed using a 3'' x 3'' NaI(Tl) scintillation detector. The response matrices of such detection system were calculated using a Monte Carlo code. For the calculations of the spectra as well as the Air Kerma Rate the WinBugs program was used. WinBugs is a dedicated software for Bayesian inference using Monte Carlo Markov chain methods (MCMC). The results of such calculations are shown and compared with other non-Bayesian approachs such as the Scofield-Gold iterative method and the Maximum Entropy Method

  6. Bayesian approach to analyzing holograms of colloidal particles.

    Science.gov (United States)

    Dimiduk, Thomas G; Manoharan, Vinothan N

    2016-10-17

    We demonstrate a Bayesian approach to tracking and characterizing colloidal particles from in-line digital holograms. We model the formation of the hologram using Lorenz-Mie theory. We then use a tempered Markov-chain Monte Carlo method to sample the posterior probability distributions of the model parameters: particle position, size, and refractive index. Compared to least-squares fitting, our approach allows us to more easily incorporate prior information about the parameters and to obtain more accurate uncertainties, which are critical for both particle tracking and characterization experiments. Our approach also eliminates the need to supply accurate initial guesses for the parameters, so it requires little tuning.

  7. Bayes Academy - An Educational Game for Learning Bayesian Networks

    OpenAIRE

    Sotala, Kaj

    2015-01-01

    This thesis describes the development of 'Bayes Academy', an educational game which aims to teach an understanding of Bayesian networks. A Bayesian network is a directed acyclic graph describing a joint probability distribution function over n random variables, where each node in the graph represents a random variable. To find a way to turn this subject into an interesting game, this work draws on the theoretical background of meaningful play. Among other requirements, actions in the game...

  8. A GM (1, 1 Markov Chain-Based Aeroengine Performance Degradation Forecast Approach Using Exhaust Gas Temperature

    Directory of Open Access Journals (Sweden)

    Ning-bo Zhao

    2014-01-01

    Full Text Available Performance degradation forecast technology for quantitatively assessing degradation states of aeroengine using exhaust gas temperature is an important technology in the aeroengine health management. In this paper, a GM (1, 1 Markov chain-based approach is introduced to forecast exhaust gas temperature by taking the advantages of GM (1, 1 model in time series and the advantages of Markov chain model in dealing with highly nonlinear and stochastic data caused by uncertain factors. In this approach, firstly, the GM (1, 1 model is used to forecast the trend by using limited data samples. Then, Markov chain model is integrated into GM (1, 1 model in order to enhance the forecast performance, which can solve the influence of random fluctuation data on forecasting accuracy and achieving an accurate estimate of the nonlinear forecast. As an example, the historical monitoring data of exhaust gas temperature from CFM56 aeroengine of China Southern is used to verify the forecast performance of the GM (1, 1 Markov chain model. The results show that the GM (1, 1 Markov chain model is able to forecast exhaust gas temperature accurately, which can effectively reflect the random fluctuation characteristics of exhaust gas temperature changes over time.

  9. BAYESIAN INFERENCE OF CMB GRAVITATIONAL LENSING

    Energy Technology Data Exchange (ETDEWEB)

    Anderes, Ethan [Department of Statistics, University of California, Davis, CA 95616 (United States); Wandelt, Benjamin D.; Lavaux, Guilhem [Sorbonne Universités, UPMC Univ Paris 06 and CNRS, UMR7095, Institut d’Astrophysique de Paris, F-75014, Paris (France)

    2015-08-01

    The Planck satellite, along with several ground-based telescopes, has mapped the cosmic microwave background (CMB) at sufficient resolution and signal-to-noise so as to allow a detection of the subtle distortions due to the gravitational influence of the intervening matter distribution. A natural modeling approach is to write a Bayesian hierarchical model for the lensed CMB in terms of the unlensed CMB and the lensing potential. So far there has been no feasible algorithm for inferring the posterior distribution of the lensing potential from the lensed CMB map. We propose a solution that allows efficient Markov Chain Monte Carlo sampling from the joint posterior of the lensing potential and the unlensed CMB map using the Hamiltonian Monte Carlo technique. The main conceptual step in the solution is a re-parameterization of CMB lensing in terms of the lensed CMB and the “inverse lensing” potential. We demonstrate a fast implementation on simulated data, including noise and a sky cut, that uses a further acceleration based on a very mild approximation of the inverse lensing potential. We find that the resulting Markov Chain has short correlation lengths and excellent convergence properties, making it promising for applications to high-resolution CMB data sets in the future.

  10. A Bayesian approach to modeling and predicting pitting flaws in steam generator tubes

    International Nuclear Information System (INIS)

    Yuan, X.-X.; Mao, D.; Pandey, M.D.

    2009-01-01

    Steam generators in nuclear power plants have experienced varying degrees of under-deposit pitting corrosion. A probabilistic model to accurately predict pitting damage is necessary for effective life-cycle management of steam generators. This paper presents an advanced probabilistic model of pitting corrosion characterizing the inherent randomness of the pitting process and measurement uncertainties of the in-service inspection (ISI) data obtained from eddy current (EC) inspections. A Markov chain Monte Carlo simulation-based Bayesian method, enhanced by a data augmentation technique, is developed for estimating the model parameters. The proposed model is able to predict the actual pit number, the actual pit depth as well as the maximum pit depth, which is the main interest of the pitting corrosion model. The study also reveals the significance of inspection uncertainties in the modeling of pitting flaws using the ISI data: Without considering the probability-of-detection issues and measurement errors, the leakage risk resulted from the pitting corrosion would be under-estimated, despite the fact that the actual pit depth would usually be over-estimated.

  11. Bayesian nonparametric dictionary learning for compressed sensing MRI.

    Science.gov (United States)

    Huang, Yue; Paisley, John; Lin, Qin; Ding, Xinghao; Fu, Xueyang; Zhang, Xiao-Ping

    2014-12-01

    We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRIs) from highly undersampled k -space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov chain Monte Carlo for the Bayesian model, and use the alternating direction method of multipliers for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.

  12. Development of uncertainty-based work injury model using Bayesian structural equation modelling.

    Science.gov (United States)

    Chatterjee, Snehamoy

    2014-01-01

    This paper proposed a Bayesian method-based structural equation model (SEM) of miners' work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts' opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts' opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

  13. Counting of oligomers in sequences generated by markov chains for DNA motif discovery.

    Science.gov (United States)

    Shan, Gao; Zheng, Wei-Mou

    2009-02-01

    By means of the technique of the imbedded Markov chain, an efficient algorithm is proposed to exactly calculate first, second moments of word counts and the probability for a word to occur at least once in random texts generated by a Markov chain. A generating function is introduced directly from the imbedded Markov chain to derive asymptotic approximations for the problem. Two Z-scores, one based on the number of sequences with hits and the other on the total number of word hits in a set of sequences, are examined for discovery of motifs on a set of promoter sequences extracted from A. thaliana genome. Source code is available at http://www.itp.ac.cn/zheng/oligo.c.

  14. A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information

    International Nuclear Information System (INIS)

    Wang, Lizhi; Pan, Rong; Li, Xiaoyang; Jiang, Tongmin

    2013-01-01

    Accelerated degradation testing (ADT) is a common approach in reliability prediction, especially for products with high reliability. However, oftentimes the laboratory condition of ADT is different from the field condition; thus, to predict field failure, one need to calibrate the prediction made by using ADT data. In this paper a Bayesian evaluation method is proposed to integrate the ADT data from laboratory with the failure data from field. Calibration factors are introduced to calibrate the difference between the lab and the field conditions so as to predict a product's actual field reliability more accurately. The information fusion and statistical inference procedure are carried out through a Bayesian approach and Markov chain Monte Carlo methods. The proposed method is demonstrated by two examples and the sensitivity analysis to prior distribution assumption

  15. spMC: an R-package for 3D lithological reconstructions based on spatial Markov chains

    Science.gov (United States)

    Sartore, Luca; Fabbri, Paolo; Gaetan, Carlo

    2016-09-01

    The paper presents the spatial Markov Chains (spMC) R-package and a case study of subsoil simulation/prediction located in a plain site of Northeastern Italy. spMC is a quite complete collection of advanced methods for data inspection, besides spMC implements Markov Chain models to estimate experimental transition probabilities of categorical lithological data. Furthermore, simulation methods based on most known prediction methods (as indicator Kriging and CoKriging) were implemented in spMC package. Moreover, other more advanced methods are available for simulations, e.g. path methods and Bayesian procedures, that exploit the maximum entropy. Since the spMC package was developed for intensive geostatistical computations, part of the code is implemented for parallel computations via the OpenMP constructs. A final analysis of this computational efficiency compares the simulation/prediction algorithms by using different numbers of CPU cores, and considering the example data set of the case study included in the package.

  16. Bayesian inference for hybrid discrete-continuous stochastic kinetic models

    International Nuclear Information System (INIS)

    Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S

    2014-01-01

    We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)

  17. Inference algorithms and learning theory for Bayesian sparse factor analysis

    International Nuclear Information System (INIS)

    Rattray, Magnus; Sharp, Kevin; Stegle, Oliver; Winn, John

    2009-01-01

    Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.

  18. Inference algorithms and learning theory for Bayesian sparse factor analysis

    Energy Technology Data Exchange (ETDEWEB)

    Rattray, Magnus; Sharp, Kevin [School of Computer Science, University of Manchester, Manchester M13 9PL (United Kingdom); Stegle, Oliver [Max-Planck-Institute for Biological Cybernetics, Tuebingen (Germany); Winn, John, E-mail: magnus.rattray@manchester.ac.u [Microsoft Research Cambridge, Roger Needham Building, Cambridge, CB3 0FB (United Kingdom)

    2009-12-01

    Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.

  19. Bayesian Hierarchical Random Effects Models in Forensic Science

    Directory of Open Access Journals (Sweden)

    Colin G. G. Aitken

    2018-04-01

    Full Text Available Statistical modeling of the evaluation of evidence with the use of the likelihood ratio has a long history. It dates from the Dreyfus case at the end of the nineteenth century through the work at Bletchley Park in the Second World War to the present day. The development received a significant boost in 1977 with a seminal work by Dennis Lindley which introduced a Bayesian hierarchical random effects model for the evaluation of evidence with an example of refractive index measurements on fragments of glass. Many models have been developed since then. The methods have now been sufficiently well-developed and have become so widespread that it is timely to try and provide a software package to assist in their implementation. With that in mind, a project (SAILR: Software for the Analysis and Implementation of Likelihood Ratios was funded by the European Network of Forensic Science Institutes through their Monopoly programme to develop a software package for use by forensic scientists world-wide that would assist in the statistical analysis and implementation of the approach based on likelihood ratios. It is the purpose of this document to provide a short review of a small part of this history. The review also provides a background, or landscape, for the development of some of the models within the SAILR package and references to SAILR as made as appropriate.

  20. Bayesian Hierarchical Random Effects Models in Forensic Science.

    Science.gov (United States)

    Aitken, Colin G G

    2018-01-01

    Statistical modeling of the evaluation of evidence with the use of the likelihood ratio has a long history. It dates from the Dreyfus case at the end of the nineteenth century through the work at Bletchley Park in the Second World War to the present day. The development received a significant boost in 1977 with a seminal work by Dennis Lindley which introduced a Bayesian hierarchical random effects model for the evaluation of evidence with an example of refractive index measurements on fragments of glass. Many models have been developed since then. The methods have now been sufficiently well-developed and have become so widespread that it is timely to try and provide a software package to assist in their implementation. With that in mind, a project (SAILR: Software for the Analysis and Implementation of Likelihood Ratios) was funded by the European Network of Forensic Science Institutes through their Monopoly programme to develop a software package for use by forensic scientists world-wide that would assist in the statistical analysis and implementation of the approach based on likelihood ratios. It is the purpose of this document to provide a short review of a small part of this history. The review also provides a background, or landscape, for the development of some of the models within the SAILR package and references to SAILR as made as appropriate.

  1. Semi-Markov Chains and Hidden Semi-Markov Models toward Applications Their Use in Reliability and DNA Analysis

    CERN Document Server

    Barbu, Vlad

    2008-01-01

    Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. This book concerns with the estimation of discrete-time semi-Markov and hidden semi-Markov processes

  2. A Bayesian Method for Weighted Sampling

    OpenAIRE

    Lo, Albert Y.

    1993-01-01

    Bayesian statistical inference for sampling from weighted distribution models is studied. Small-sample Bayesian bootstrap clone (BBC) approximations to the posterior distribution are discussed. A second-order property for the BBC in unweighted i.i.d. sampling is given. A consequence is that BBC approximations to a posterior distribution of the mean and to the sampling distribution of the sample average, can be made asymptotically accurate by a proper choice of the random variables that genera...

  3. Robust Dynamics and Control of a Partially Observed Markov Chain

    International Nuclear Information System (INIS)

    Elliott, R. J.; Malcolm, W. P.; Moore, J. P.

    2007-01-01

    In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721-734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear).Clark's method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established

  4. Doing bayesian data analysis a tutorial with R and BUGS

    CERN Document Server

    Kruschke, John K

    2011-01-01

    There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis obtainable to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS provides an accessible approach to Bayesian data analysis, as material is explained clearly with concrete examples. The book begins with the basics, including essential concepts of probability and random sampling, and gradually progresses to advanced hierarchical modeling methods for realistic data. The text delivers comprehensive coverage of all

  5. Markov transitions and the propagation of chaos

    International Nuclear Information System (INIS)

    Gottlieb, A.

    1998-01-01

    The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also show that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution

  6. Estimation and uncertainty of reversible Markov models.

    Science.gov (United States)

    Trendelkamp-Schroer, Benjamin; Wu, Hao; Paul, Fabian; Noé, Frank

    2015-11-07

    Reversibility is a key concept in Markov models and master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model rely heavily on the reversibility property. The estimation of a reversible transition matrix from simulation data is, therefore, crucial to the successful application of the previously developed theory. In this work, we discuss methods for the maximum likelihood estimation of transition matrices from finite simulation data and present a new algorithm for the estimation if reversibility with respect to a given stationary vector is desired. We also develop new methods for the Bayesian posterior inference of reversible transition matrices with and without given stationary vector taking into account the need for a suitable prior distribution preserving the meta-stable features of the observed process during posterior inference. All algorithms here are implemented in the PyEMMA software--http://pyemma.org--as of version 2.0.

  7. Metropolis-Hastings Algorithms in Function Space for Bayesian Inverse Problems

    KAUST Repository

    Ernst, Oliver

    2015-01-07

    We consider Markov Chain Monte Carlo methods adapted to a Hilbert space setting. Such algorithms occur in Bayesian inverse problems where the solution is a probability measure on a function space according to which one would like to integrate or sample. We focus on Metropolis-Hastings algorithms and, in particular, we introduce and analyze a generalization of the existing pCN-proposal. This new proposal allows to exploit the geometry or anisotropy of the target measure which in turn might improve the statistical efficiency of the corresponding MCMC method. Numerical experiments for a real-world problem confirm the improvement.

  8. Bayesian analysis of log Gaussian Cox processes for disease mapping

    DEFF Research Database (Denmark)

    Benes, Viktor; Bodlák, Karel; Møller, Jesper

    We consider a data set of locations where people in Central Bohemia have been infected by tick-borne encephalitis, and where population census data and covariates concerning vegetation and altitude are available. The aims are to estimate the risk map of the disease and to study the dependence...... of the risk on the covariates. Instead of using the common area level approaches we consider a Bayesian analysis for a log Gaussian Cox point process with covariates. Posterior characteristics for a discretized version of the log Gaussian Cox process are computed using markov chain Monte Carlo methods...

  9. Metropolis-Hastings Algorithms in Function Space for Bayesian Inverse Problems

    KAUST Repository

    Ernst, Oliver

    2015-01-01

    We consider Markov Chain Monte Carlo methods adapted to a Hilbert space setting. Such algorithms occur in Bayesian inverse problems where the solution is a probability measure on a function space according to which one would like to integrate or sample. We focus on Metropolis-Hastings algorithms and, in particular, we introduce and analyze a generalization of the existing pCN-proposal. This new proposal allows to exploit the geometry or anisotropy of the target measure which in turn might improve the statistical efficiency of the corresponding MCMC method. Numerical experiments for a real-world problem confirm the improvement.

  10. Stochastic Dynamics through Hierarchically Embedded Markov Chains.

    Science.gov (United States)

    Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M

    2017-02-03

    Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.

  11. Exact solution of the hidden Markov processes

    Science.gov (United States)

    Saakian, David B.

    2017-11-01

    We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .

  12. BAYESIAN MAGNETOHYDRODYNAMIC SEISMOLOGY OF CORONAL LOOPS

    International Nuclear Information System (INIS)

    Arregui, I.; Asensio Ramos, A.

    2011-01-01

    We perform a Bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube and thin boundary approximations. For the inverse problem, we adopt a Bayesian approach to infer the most probable values of the relevant parameters, for given observed periods and damping times, and to extract their confidence levels. The posterior probability distribution functions are obtained by means of Markov Chain Monte Carlo simulations, incorporating observed uncertainties in a consistent manner. We find well-localized solutions in the posterior probability distribution functions for two of the three parameters of interest, namely the Alfven travel time and the transverse inhomogeneity length scale. The obtained estimates for the Alfven travel time are consistent with previous inversion results, but the method enables us to additionally constrain the transverse inhomogeneity length scale and to estimate real error bars for each parameter. When observational estimates for the density contrast are used, the method enables us to fully constrain the three parameters of interest. These results can serve to improve our current estimates of unknown physical parameters in coronal loops and to test the assumed theoretical model.

  13. Mean-Variance Optimization in Markov Decision Processes

    OpenAIRE

    Mannor, Shie; Tsitsiklis, John N.

    2011-01-01

    We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for others. We finally offer pseudo-polynomial exact and approximation algorithms.

  14. Capturing changes in flood risk with Bayesian approaches for flood damage assessment

    Science.gov (United States)

    Vogel, Kristin; Schröter, Kai; Kreibich, Heidi; Thieken, Annegret; Müller, Meike; Sieg, Tobias; Laudan, Jonas; Kienzler, Sarah; Weise, Laura; Merz, Bruno; Scherbaum, Frank

    2016-04-01

    Flood risk is a function of hazard as well as of exposure and vulnerability. All three components are under change over space and time and have to be considered for reliable damage estimations and risk analyses, since this is the basis for an efficient, adaptable risk management. Hitherto, models for estimating flood damage are comparatively simple and cannot sufficiently account for changing conditions. The Bayesian network approach allows for a multivariate modeling of complex systems without relying on expert knowledge about physical constraints. In a Bayesian network each model component is considered to be a random variable. The way of interactions between those variables can be learned from observations or be defined by expert knowledge. Even a combination of both is possible. Moreover, the probabilistic framework captures uncertainties related to the prediction and provides a probability distribution for the damage instead of a point estimate. The graphical representation of Bayesian networks helps to study the change of probabilities for changing circumstances and may thus simplify the communication between scientists and public authorities. In the framework of the DFG-Research Training Group "NatRiskChange" we aim to develop Bayesian networks for flood damage and vulnerability assessments of residential buildings and companies under changing conditions. A Bayesian network learned from data, collected over the last 15 years in flooded regions in the Elbe and Danube catchments (Germany), reveals the impact of many variables like building characteristics, precaution and warning situation on flood damage to residential buildings. While the handling of incomplete and hybrid (discrete mixed with continuous) data are the most challenging issues in the study on residential buildings, a similar study, that focuses on the vulnerability of small to medium sized companies, bears new challenges. Relying on a much smaller data set for the determination of the model

  15. Polynomial Chaos Acceleration for the Bayesian Inference of Random Fields with Gaussian Priors and Uncertain Covariance Hyper-Parameters

    KAUST Repository

    Le Maitre, Olivier

    2015-01-07

    We address model dimensionality reduction in the Bayesian inference of Gaussian fields, considering prior covariance function with unknown hyper-parameters. The Karhunen-Loeve (KL) expansion of a prior Gaussian process is traditionally derived assuming fixed covariance function with pre-assigned hyperparameter values. Thus, the modes strengths of the Karhunen-Loeve expansion inferred using available observations, as well as the resulting inferred process, dependent on the pre-assigned values for the covariance hyper-parameters. Here, we seek to infer the process and its the covariance hyper-parameters in a single Bayesian inference. To this end, the uncertainty in the hyper-parameters is treated by means of a coordinate transformation, leading to a KL-type expansion on a fixed reference basis of spatial modes, but with random coordinates conditioned on the hyper-parameters. A Polynomial Chaos (PC) expansion of the model prediction is also introduced to accelerate the Bayesian inference and the sampling of the posterior distribution with MCMC method. The PC expansion of the model prediction also rely on a coordinates transformation, enabling us to avoid expanding the dependence of the prediction with respect to the covariance hyper-parameters. We demonstrate the efficiency of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data.

  16. ANALYSIS AND VALIDATION OF GRID DEM GENERATION BASED ON GAUSSIAN MARKOV RANDOM FIELD

    Directory of Open Access Journals (Sweden)

    F. J. Aguilar

    2016-06-01

    Full Text Available Digital Elevation Models (DEMs are considered as one of the most relevant geospatial data to carry out land-cover and land-use classification. This work deals with the application of a mathematical framework based on a Gaussian Markov Random Field (GMRF to interpolate grid DEMs from scattered elevation data. The performance of the GMRF interpolation model was tested on a set of LiDAR data (0.87 points/m2 provided by the Spanish Government (PNOA Programme over a complex working area mainly covered by greenhouses in Almería, Spain. The original LiDAR data was decimated by randomly removing different fractions of the original points (from 10% to up to 99% of points removed. In every case, the remaining points (scattered observed points were used to obtain a 1 m grid spacing GMRF-interpolated Digital Surface Model (DSM whose accuracy was assessed by means of the set of previously extracted checkpoints. The GMRF accuracy results were compared with those provided by the widely known Triangulation with Linear Interpolation (TLI. Finally, the GMRF method was applied to a real-world case consisting of filling the LiDAR-derived DSM gaps after manually filtering out non-ground points to obtain a Digital Terrain Model (DTM. Regarding accuracy, both GMRF and TLI produced visually pleasing and similar results in terms of vertical accuracy. As an added bonus, the GMRF mathematical framework makes possible to both retrieve the estimated uncertainty for every interpolated elevation point (the DEM uncertainty and include break lines or terrain discontinuities between adjacent cells to produce higher quality DTMs.

  17. Non-linear Bayesian update of PCE coefficients

    KAUST Repository

    Litvinenko, Alexander

    2014-01-06

    Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).

  18. Non-linear Bayesian update of PCE coefficients

    KAUST Repository

    Litvinenko, Alexander; Matthies, Hermann G.; Pojonk, Oliver; Rosic, Bojana V.; Zander, Elmar

    2014-01-01

    Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).

  19. Bayesian spatio-temporal modeling of particulate matter concentrations in Peninsular Malaysia

    Science.gov (United States)

    Manga, Edna; Awang, Norhashidah

    2016-06-01

    This article presents an application of a Bayesian spatio-temporal Gaussian process (GP) model on particulate matter concentrations from Peninsular Malaysia. We analyze daily PM10 concentration levels from 35 monitoring sites in June and July 2011. The spatiotemporal model set in a Bayesian hierarchical framework allows for inclusion of informative covariates, meteorological variables and spatiotemporal interactions. Posterior density estimates of the model parameters are obtained by Markov chain Monte Carlo methods. Preliminary data analysis indicate information on PM10 levels at sites classified as industrial locations could explain part of the space time variations. We include the site-type indicator in our modeling efforts. Results of the parameter estimates for the fitted GP model show significant spatio-temporal structure and positive effect of the location-type explanatory variable. We also compute some validation criteria for the out of sample sites that show the adequacy of the model for predicting PM10 at unmonitored sites.

  20. Non-stationary Markov chains

    OpenAIRE

    Mallak, Saed

    1996-01-01

    Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent University, 1996. Thesis (Master's) -- Bilkent University, 1996. Includes bibliographical references leaves leaf 29 In thi.s work, we studierl the Ergodicilv of Non-Stationary .Markov chains. We gave several e.xainples with different cases. We proved that given a sec[uence of Markov chains such that the limit of this sec|uence is an Ergodic Markov chain, then the limit of the combination ...

  1. Cost efficiency of Japanese steam power generation companies: A Bayesian comparison of random and fixed frontier models

    Energy Technology Data Exchange (ETDEWEB)

    Assaf, A. George [Isenberg School of Management, University of Massachusetts-Amherst, 90 Campus Center Way, Amherst 01002 (United States); Barros, Carlos Pestana [Instituto Superior de Economia e Gestao, Technical University of Lisbon, Rua Miguel Lupi, 20, 1249-078 Lisbon (Portugal); Managi, Shunsuke [Graduate School of Environmental Studies, Tohoku University, 6-6-20 Aramaki-Aza Aoba, Aoba-Ku, Sendai 980-8579 (Japan)

    2011-04-15

    This study analyses and compares the cost efficiency of Japanese steam power generation companies using the fixed and random Bayesian frontier models. We show that it is essential to account for heterogeneity in modelling the performance of energy companies. Results from the model estimation also indicate that restricting CO{sub 2} emissions can lead to a decrease in total cost. The study finally discusses the efficiency variations between the energy companies under analysis, and elaborates on the managerial and policy implications of the results. (author)

  2. Process Algebra and Markov Chains

    NARCIS (Netherlands)

    Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.

    This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

  3. Process algebra and Markov chains

    NARCIS (Netherlands)

    Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.

    2001-01-01

    This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

  4. Stochastic demand patterns for Markov service facilities with neutral and active periods

    International Nuclear Information System (INIS)

    Csenki, Attila

    2009-01-01

    In an earlier paper, a closed form expression was obtained for the joint interval reliability of a Markov system with a partitioned state space S=U union D, i.e. for the probability that the system will reside in the set of up states U throughout the union of some specific disjoint time intervals I l =[θ l ,θ l +ζ l ],l=1,...,k. The deterministic time intervals I l formed a demand pattern specifying the desired active periods. In the present paper, we admit stochastic demand patterns by assuming that the lengths of the active periods, ζ l , as well as the lengths of the neutral periods, θ l -(θ l-1 +ζ l-1 ), are random. We explore two mechanisms for modelling random demand: (1) by alternating renewal processes; (2) by sojourn times of some continuous time Markov chain with a partitioned state space. The first construction results in an expression in terms of a revised version of the moment generating functions of the sojourns of the alternating renewal process. The second construction involves the probability that a Markov chain follows certain patterns of visits to some groups of states and yields an expression using Kronecker matrix operations. The model of a small computer system is analysed to exemplify the ideas

  5. Random Finite Set Based Bayesian Filtering with OpenCL in a Heterogeneous Platform

    Directory of Open Access Journals (Sweden)

    Biao Hu

    2017-04-01

    Full Text Available While most filtering approaches based on random finite sets have focused on improving performance, in this paper, we argue that computation times are very important in order to enable real-time applications such as pedestrian detection. Towards this goal, this paper investigates the use of OpenCL to accelerate the computation of random finite set-based Bayesian filtering in a heterogeneous system. In detail, we developed an efficient and fully-functional pedestrian-tracking system implementation, which can run under real-time constraints, meanwhile offering decent tracking accuracy. An extensive evaluation analysis was carried out to ensure the fulfillment of sufficient accuracy requirements. This was followed by extensive profiling analysis to spot the potential bottlenecks in terms of execution performance, which were then targeted to come up with an OpenCL accelerated application. Video-throughput improvements from roughly 15 fps to 100 fps (6× were observed on average while processing typical MOT benchmark videos. Moreover, the worst-case frame processing yielded an 18× advantage from nearly 2 fps to 36 fps, thereby comfortably meeting the real-time constraints. Our implementation is released as open-source code.

  6. Bayesian networks in educational assessment

    CERN Document Server

    Almond, Russell G; Steinberg, Linda S; Yan, Duanli; Williamson, David M

    2015-01-01

    Bayesian inference networks, a synthesis of statistics and expert systems, have advanced reasoning under uncertainty in medicine, business, and social sciences. This innovative volume is the first comprehensive treatment exploring how they can be applied to design and analyze innovative educational assessments. Part I develops Bayes nets’ foundations in assessment, statistics, and graph theory, and works through the real-time updating algorithm. Part II addresses parametric forms for use with assessment, model-checking techniques, and estimation with the EM algorithm and Markov chain Monte Carlo (MCMC). A unique feature is the volume’s grounding in Evidence-Centered Design (ECD) framework for assessment design. This “design forward” approach enables designers to take full advantage of Bayes nets’ modularity and ability to model complex evidentiary relationships that arise from performance in interactive, technology-rich assessments such as simulations. Part III describes ECD, situates Bayes nets as ...

  7. Bayesian dynamic modeling of time series of dengue disease case counts.

    Science.gov (United States)

    Martínez-Bello, Daniel Adyro; López-Quílez, Antonio; Torres-Prieto, Alexander

    2017-07-01

    The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model's short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful

  8. Efficient Bayesian experimental design for contaminant source identification

    Science.gov (United States)

    Zhang, Jiangjiang; Zeng, Lingzao; Chen, Cheng; Chen, Dingjiang; Wu, Laosheng

    2015-01-01

    In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameters identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from concentration measurements in identifying unknown parameters. In this approach, the sampling locations that give the maximum expected relative entropy are selected as the optimal design. After the sampling locations are determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport equation. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. It is shown that the methods can be used to assist in both single sampling location and monitoring network design for contaminant source identifications in groundwater.

  9. Toward combining thematic information with hierarchical multiscale segmentations using tree Markov random field model

    Science.gov (United States)

    Zhang, Xueliang; Xiao, Pengfeng; Feng, Xuezhi

    2017-09-01

    It has been a common idea to produce multiscale segmentations to represent the various geographic objects in high-spatial resolution remote sensing (HR) images. However, it remains a great challenge to automatically select the proper segmentation scale(s) just according to the image information. In this study, we propose a novel way of information fusion at object level by combining hierarchical multiscale segmentations with existed thematic information produced by classification or recognition. The tree Markov random field (T-MRF) model is designed for the multiscale combination framework, through which the object type is determined as close as the existed thematic information. At the same time, the object boundary is jointly determined by the thematic labels and the multiscale segments through the minimization of the energy function. The benefits of the proposed T-MRF combination model include: (1) reducing the dependence of segmentation scale selection when utilizing multiscale segmentations; (2) exploring the hierarchical context naturally imbedded in the multiscale segmentations. The HR images in both urban and rural areas are used in the experiments to show the effectiveness of the proposed combination framework on these two aspects.

  10. Analysis of transtheoretical model of health behavioral changes in a nutrition intervention study--a continuous time Markov chain model with Bayesian approach.

    Science.gov (United States)

    Ma, Junsheng; Chan, Wenyaw; Tsai, Chu-Lin; Xiong, Momiao; Tilley, Barbara C

    2015-11-30

    Continuous time Markov chain (CTMC) models are often used to study the progression of chronic diseases in medical research but rarely applied to studies of the process of behavioral change. In studies of interventions to modify behaviors, a widely used psychosocial model is based on the transtheoretical model that often has more than three states (representing stages of change) and conceptually permits all possible instantaneous transitions. Very little attention is given to the study of the relationships between a CTMC model and associated covariates under the framework of transtheoretical model. We developed a Bayesian approach to evaluate the covariate effects on a CTMC model through a log-linear regression link. A simulation study of this approach showed that model parameters were accurately and precisely estimated. We analyzed an existing data set on stages of change in dietary intake from the Next Step Trial using the proposed method and the generalized multinomial logit model. We found that the generalized multinomial logit model was not suitable for these data because it ignores the unbalanced data structure and temporal correlation between successive measurements. Our analysis not only confirms that the nutrition intervention was effective but also provides information on how the intervention affected the transitions among the stages of change. We found that, compared with the control group, subjects in the intervention group, on average, spent substantively less time in the precontemplation stage and were more/less likely to move from an unhealthy/healthy state to a healthy/unhealthy state. Copyright © 2015 John Wiley & Sons, Ltd.

  11. One size does not fit all: On how Markov model order dictates performance of genomic sequence analyses

    Science.gov (United States)

    Narlikar, Leelavati; Mehta, Nidhi; Galande, Sanjeev; Arjunwadkar, Mihir

    2013-01-01

    The structural simplicity and ability to capture serial correlations make Markov models a popular modeling choice in several genomic analyses, such as identification of motifs, genes and regulatory elements. A critical, yet relatively unexplored, issue is the determination of the order of the Markov model. Most biological applications use a predetermined order for all data sets indiscriminately. Here, we show the vast variation in the performance of such applications with the order. To identify the ‘optimal’ order, we investigated two model selection criteria: Akaike information criterion and Bayesian information criterion (BIC). The BIC optimal order delivers the best performance for mammalian phylogeny reconstruction and motif discovery. Importantly, this order is different from orders typically used by many tools, suggesting that a simple additional step determining this order can significantly improve results. Further, we describe a novel classification approach based on BIC optimal Markov models to predict functionality of tissue-specific promoters. Our classifier discriminates between promoters active across 12 different tissues with remarkable accuracy, yielding 3 times the precision expected by chance. Application to the metagenomics problem of identifying the taxum from a short DNA fragment yields accuracies at least as high as the more complex mainstream methodologies, while retaining conceptual and computational simplicity. PMID:23267010

  12. Criterion of Semi-Markov Dependent Risk Model

    Institute of Scientific and Technical Information of China (English)

    Xiao Yun MO; Xiang Qun YANG

    2014-01-01

    A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi-Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.

  13. Detection of multiple damages employing best achievable eigenvectors under Bayesian inference

    Science.gov (United States)

    Prajapat, Kanta; Ray-Chaudhuri, Samit

    2018-05-01

    A novel approach is presented in this work to localize simultaneously multiple damaged elements in a structure along with the estimation of damage severity for each of the damaged elements. For detection of damaged elements, a best achievable eigenvector based formulation has been derived. To deal with noisy data, Bayesian inference is employed in the formulation wherein the likelihood of the Bayesian algorithm is formed on the basis of errors between the best achievable eigenvectors and the measured modes. In this approach, the most probable damage locations are evaluated under Bayesian inference by generating combinations of various possible damaged elements. Once damage locations are identified, damage severities are estimated using a Bayesian inference Markov chain Monte Carlo simulation. The efficiency of the proposed approach has been demonstrated by carrying out a numerical study involving a 12-story shear building. It has been found from this study that damage scenarios involving as low as 10% loss of stiffness in multiple elements are accurately determined (localized and severities quantified) even when 2% noise contaminated modal data are utilized. Further, this study introduces a term parameter impact (evaluated based on sensitivity of modal parameters towards structural parameters) to decide the suitability of selecting a particular mode, if some idea about the damaged elements are available. It has been demonstrated here that the accuracy and efficiency of the Bayesian quantification algorithm increases if damage localization is carried out a-priori. An experimental study involving a laboratory scale shear building and different stiffness modification scenarios shows that the proposed approach is efficient enough to localize the stories with stiffness modification.

  14. Analysis of aerial survey data on Florida manatee using Markov chain Monte Carlo.

    Science.gov (United States)

    Craig, B A; Newton, M A; Garrott, R A; Reynolds, J E; Wilcox, J R

    1997-06-01

    We assess population trends of the Atlantic coast population of Florida manatee, Trichechus manatus latirostris, by reanalyzing aerial survey data collected between 1982 and 1992. To do so, we develop an explicit biological model that accounts for the method by which the manatees are counted, the mammals' movement between surveys, and the behavior of the population total over time. Bayesian inference, enabled by Markov chain Monte Carlo, is used to combine the survey data with the biological model. We compute marginal posterior distributions for all model parameters and predictive distributions for future counts. Several conclusions, such as a decreasing population growth rate and low sighting probabilities, are consistent across different prior specifications.

  15. Hierarchical Bayesian Modeling of Fluid-Induced Seismicity

    Science.gov (United States)

    Broccardo, M.; Mignan, A.; Wiemer, S.; Stojadinovic, B.; Giardini, D.

    2017-11-01

    In this study, we present a Bayesian hierarchical framework to model fluid-induced seismicity. The framework is based on a nonhomogeneous Poisson process with a fluid-induced seismicity rate proportional to the rate of injected fluid. The fluid-induced seismicity rate model depends upon a set of physically meaningful parameters and has been validated for six fluid-induced case studies. In line with the vision of hierarchical Bayesian modeling, the rate parameters are considered as random variables. We develop both the Bayesian inference and updating rules, which are used to develop a probabilistic forecasting model. We tested the Basel 2006 fluid-induced seismic case study to prove that the hierarchical Bayesian model offers a suitable framework to coherently encode both epistemic uncertainty and aleatory variability. Moreover, it provides a robust and consistent short-term seismic forecasting model suitable for online risk quantification and mitigation.

  16. Markov process of muscle motors

    International Nuclear Information System (INIS)

    Kondratiev, Yu; Pechersky, E; Pirogov, S

    2008-01-01

    We study a Markov random process describing muscle molecular motor behaviour. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spends an exponential time depending on the state. The thin filament moves at a velocity proportional to the average of all displacements of all motors. We assume that the time which a motor stays in the bound state does not depend on its displacement. Then one can find an exact solution of a nonlinear equation appearing in the limit of an infinite number of motors

  17. Markov switching of the electricity supply curve and power prices dynamics

    Science.gov (United States)

    Mari, Carlo; Cananà, Lucianna

    2012-02-01

    Regime-switching models seem to well capture the main features of power prices behavior in deregulated markets. In a recent paper, we have proposed an equilibrium methodology to derive electricity prices dynamics from the interplay between supply and demand in a stochastic environment. In particular, assuming that the supply function is described by a power law where the exponent is a two-state strictly positive Markov process, we derived a regime switching dynamics of power prices in which regime switches are induced by transitions between Markov states. In this paper, we provide a dynamical model to describe the random behavior of power prices where the only non-Brownian component of the motion is endogenously introduced by Markov transitions in the exponent of the electricity supply curve. In this context, the stochastic process driving the switching mechanism becomes observable, and we will show that the non-Brownian component of the dynamics induced by transitions from Markov states is responsible for jumps and spikes of very high magnitude. The empirical analysis performed on three Australian markets confirms that the proposed approach seems quite flexible and capable of incorporating the main features of power prices time-series, thus reproducing the first four moments of log-returns empirical distributions in a satisfactory way.

  18. A comparison between Markovian models and Bayesian networks for treating some dependent events in reliability evaluations

    International Nuclear Information System (INIS)

    Duarte, Juliana P.; Leite, Victor C.; Melo, P.F. Frutuoso e

    2013-01-01

    Bayesian networks have become a very handy tool for solving problems in various application areas. This paper discusses the use of Bayesian networks to treat dependent events in reliability engineering typically modeled by Markovian models. Dependent events play an important role as, for example, when treating load-sharing systems, bridge systems, common-cause failures, and switching systems (those for which a standby component is activated after the main one fails by means of a switching mechanism). Repair plays an important role in all these cases (as, for example, the number of repairmen). All Bayesian network calculations are performed by means of the Netica™ software, of Norsys Software Corporation, and Fortran 90 to evaluate them over time. The discussion considers the development of time-dependent reliability figures of merit, which are easily obtained, through Markovian models, but not through Bayesian networks, because these latter need probability figures as input and not failure and repair rates. Bayesian networks produced results in very good agreement with those of Markov models and pivotal decomposition. Static and discrete time (DTBN) Bayesian networks were used in order to check their capabilities of modeling specific situations, like switching failures in cold-standby systems. The DTBN was more flexible to modeling systems where the time of occurrence of an event is important, for example, standby failure and repair. However, the static network model showed as good results as DTBN by a much more simplified approach. (author)

  19. A comparison between Markovian models and Bayesian networks for treating some dependent events in reliability evaluations

    Energy Technology Data Exchange (ETDEWEB)

    Duarte, Juliana P.; Leite, Victor C.; Melo, P.F. Frutuoso e, E-mail: julianapduarte@poli.ufrj.br, E-mail: victor.coppo.leite@poli.ufrj.br, E-mail: frutuoso@nuclear.ufrj.br [Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, RJ (Brazil)

    2013-07-01

    Bayesian networks have become a very handy tool for solving problems in various application areas. This paper discusses the use of Bayesian networks to treat dependent events in reliability engineering typically modeled by Markovian models. Dependent events play an important role as, for example, when treating load-sharing systems, bridge systems, common-cause failures, and switching systems (those for which a standby component is activated after the main one fails by means of a switching mechanism). Repair plays an important role in all these cases (as, for example, the number of repairmen). All Bayesian network calculations are performed by means of the Netica™ software, of Norsys Software Corporation, and Fortran 90 to evaluate them over time. The discussion considers the development of time-dependent reliability figures of merit, which are easily obtained, through Markovian models, but not through Bayesian networks, because these latter need probability figures as input and not failure and repair rates. Bayesian networks produced results in very good agreement with those of Markov models and pivotal decomposition. Static and discrete time (DTBN) Bayesian networks were used in order to check their capabilities of modeling specific situations, like switching failures in cold-standby systems. The DTBN was more flexible to modeling systems where the time of occurrence of an event is important, for example, standby failure and repair. However, the static network model showed as good results as DTBN by a much more simplified approach. (author)

  20. Bayesian image restoration, using configurations

    DEFF Research Database (Denmark)

    Thorarinsdottir, Thordis

    configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed...

  1. Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice

    KAUST Repository

    Park, Jincheol; Liang, Faming

    2012-01-01

    of observations is large. In this article, we propose an auxiliary lattice-based approach for tackling this difficulty. By introducing an auxiliary lattice to the space of observations and defining a Gaussian Markov random field on the auxiliary lattice, our model

  2. Encoding dependence in Bayesian causal networks

    Science.gov (United States)

    Bayesian networks (BNs) represent complex, uncertain spatio-temporal dynamics by propagation of conditional probabilities between identifiable states with a testable causal interaction model. Typically, they assume random variables are discrete in time and space with a static network structure that ...

  3. Bayesian inferences of generation and growth of corrosion defects on energy pipelines based on imperfect inspection data

    International Nuclear Information System (INIS)

    Qin, H.; Zhou, W.; Zhang, S.

    2015-01-01

    Stochastic process-based models are developed to characterize the generation and growth of metal-loss corrosion defects on oil and gas steel pipelines. The generation of corrosion defects over time is characterized by the non-homogenous Poisson process, and the growth of depths of individual defects is modeled by the non-homogenous gamma process (NHGP). The defect generation and growth models are formulated in a hierarchical Bayesian framework, whereby the parameters of the models are evaluated from the in-line inspection (ILI) data through the Bayesian updating by accounting for the probability of detection (POD) and measurement errors associated with the ILI data. The Markov Chain Monte Carlo (MCMC) simulation in conjunction with the data augmentation (DA) technique is employed to carry out the Bayesian updating. Numerical examples that involve simulated ILI data are used to illustrate and validate the proposed methodology. - Highlights: • Bayesian updating of growth and generation models of defects on energy pipelines. • Non-homogeneous Poisson process for defect generation. • Non-homogeneous gamma process for defect growth. • Updating based on inspection data with detecting and sizing uncertainties. • MCMC in conjunction with data augmentation technique employed for the updating.

  4. Activity recognition using semi-Markov models on real world smart home datasets

    NARCIS (Netherlands)

    van Kasteren, T.L.M.; Englebienne, G.; Kröse, B.J.A.

    2010-01-01

    Accurately recognizing human activities from sensor data recorded in a smart home setting is a challenging task. Typically, probabilistic models such as the hidden Markov model (HMM) or conditional random fields (CRF) are used to map the observed sensor data onto the hidden activity states. A

  5. A Bayesian random effects discrete-choice model for resource selection: Population-level selection inference

    Science.gov (United States)

    Thomas, D.L.; Johnson, D.; Griffith, B.

    2006-01-01

    Modeling the probability of use of land units characterized by discrete and continuous measures, we present a Bayesian random-effects model to assess resource selection. This model provides simultaneous estimation of both individual- and population-level selection. Deviance information criterion (DIC), a Bayesian alternative to AIC that is sample-size specific, is used for model selection. Aerial radiolocation data from 76 adult female caribou (Rangifer tarandus) and calf pairs during 1 year on an Arctic coastal plain calving ground were used to illustrate models and assess population-level selection of landscape attributes, as well as individual heterogeneity of selection. Landscape attributes included elevation, NDVI (a measure of forage greenness), and land cover-type classification. Results from the first of a 2-stage model-selection procedure indicated that there is substantial heterogeneity among cow-calf pairs with respect to selection of the landscape attributes. In the second stage, selection of models with heterogeneity included indicated that at the population-level, NDVI and land cover class were significant attributes for selection of different landscapes by pairs on the calving ground. Population-level selection coefficients indicate that the pairs generally select landscapes with higher levels of NDVI, but the relationship is quadratic. The highest rate of selection occurs at values of NDVI less than the maximum observed. Results for land cover-class selections coefficients indicate that wet sedge, moist sedge, herbaceous tussock tundra, and shrub tussock tundra are selected at approximately the same rate, while alpine and sparsely vegetated landscapes are selected at a lower rate. Furthermore, the variability in selection by individual caribou for moist sedge and sparsely vegetated landscapes is large relative to the variability in selection of other land cover types. The example analysis illustrates that, while sometimes computationally intense, a

  6. Stochastic-shielding approximation of Markov chains and its application to efficiently simulate random ion-channel gating.

    Science.gov (United States)

    Schmandt, Nicolaus T; Galán, Roberto F

    2012-09-14

    Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be replaced with their mean if state B is not directly connected to A, which shortens computing time considerably. We show the accuracy and efficacy of our approximation theoretically and in simulations of stochastic ion-channel gating in neurons.

  7. 2D Bayesian automated tilted-ring fitting of disc galaxies in large H I galaxy surveys: 2DBAT

    Science.gov (United States)

    Oh, Se-Heon; Staveley-Smith, Lister; Spekkens, Kristine; Kamphuis, Peter; Koribalski, Bärbel S.

    2018-01-01

    We present a novel algorithm based on a Bayesian method for 2D tilted-ring analysis of disc galaxy velocity fields. Compared to the conventional algorithms based on a chi-squared minimization procedure, this new Bayesian-based algorithm suffers less from local minima of the model parameters even with highly multimodal posterior distributions. Moreover, the Bayesian analysis, implemented via Markov Chain Monte Carlo sampling, only requires broad ranges of posterior distributions of the parameters, which makes the fitting procedure fully automated. This feature will be essential when performing kinematic analysis on the large number of resolved galaxies expected to be detected in neutral hydrogen (H I) surveys with the Square Kilometre Array and its pathfinders. The so-called 2D Bayesian Automated Tilted-ring fitter (2DBAT) implements Bayesian fits of 2D tilted-ring models in order to derive rotation curves of galaxies. We explore 2DBAT performance on (a) artificial H I data cubes built based on representative rotation curves of intermediate-mass and massive spiral galaxies, and (b) Australia Telescope Compact Array H I data from the Local Volume H I Survey. We find that 2DBAT works best for well-resolved galaxies with intermediate inclinations (20° < i < 70°), complementing 3D techniques better suited to modelling inclined galaxies.

  8. Markov chains of nonlinear Markov processes and an application to a winner-takes-all model for social conformity

    Energy Technology Data Exchange (ETDEWEB)

    Frank, T D [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)

    2008-07-18

    We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)

  9. Markov chains of nonlinear Markov processes and an application to a winner-takes-all model for social conformity

    International Nuclear Information System (INIS)

    Frank, T D

    2008-01-01

    We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)

  10. A New Mathematical Framework for Design Under Uncertainty

    Science.gov (United States)

    2016-05-05

    Kriging and Gaussian-Markov Random Fields, and 2. Bayesian optimization of the most crucial component of the H2-SWATH, namely, the supercavitating ...Brizzolara S. (-). Physics based Design by Opti- mization of Unconventional Supercavitating Hydrofoils. Under review for the Journal of Ship Research. 9

  11. Bayesian image restoration, using configurations

    DEFF Research Database (Denmark)

    Thorarinsdottir, Thordis Linda

    2006-01-01

    configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for the salt and pepper noise. The inference in the model is discussed...

  12. A Bayesian network model for predicting aquatic toxicity mode of action using two dimensional theoretical molecular descriptors

    Energy Technology Data Exchange (ETDEWEB)

    Carriger, John F. [U.S. Environmental Protection Agency, Office of Research and Development, Gulf Ecology Division, Gulf Breeze, FL, 32561 (United States); Martin, Todd M. [U.S. Environmental Protection Agency, Office of Research and Development, Sustainable Technology Division, Cincinnati, OH, 45220 (United States); Barron, Mace G., E-mail: barron.mace@epa.gov [U.S. Environmental Protection Agency, Office of Research and Development, Gulf Ecology Division, Gulf Breeze, FL, 32561 (United States)

    2016-11-15

    Highlights: • A Bayesian network was developed to classify chemical mode of action (MoA). • The network was based on the aquatic toxicity MoA for over 1000 chemicals. • A Markov blanket algorithm selected a subset of theoretical molecular descriptors. • Sensitivity analyses found influential descriptors for classifying the MoAs. • Overall precision of the Bayesian MoA classification model was 80%. - Abstract: The mode of toxic action (MoA) has been recognized as a key determinant of chemical toxicity, but development of predictive MoA classification models in aquatic toxicology has been limited. We developed a Bayesian network model to classify aquatic toxicity MoA using a recently published dataset containing over one thousand chemicals with MoA assignments for aquatic animal toxicity. Two dimensional theoretical chemical descriptors were generated for each chemical using the Toxicity Estimation Software Tool. The model was developed through augmented Markov blanket discovery from the dataset of 1098 chemicals with the MoA broad classifications as a target node. From cross validation, the overall precision for the model was 80.2%. The best precision was for the AChEI MoA (93.5%) where 257 chemicals out of 275 were correctly classified. Model precision was poorest for the reactivity MoA (48.5%) where 48 out of 99 reactive chemicals were correctly classified. Narcosis represented the largest class within the MoA dataset and had a precision and reliability of 80.0%, reflecting the global precision across all of the MoAs. False negatives for narcosis most often fell into electron transport inhibition, neurotoxicity or reactivity MoAs. False negatives for all other MoAs were most often narcosis. A probabilistic sensitivity analysis was undertaken for each MoA to examine the sensitivity to individual and multiple descriptor findings. The results show that the Markov blanket of a structurally complex dataset can simplify analysis and interpretation by

  13. Asymptotic evolution of quantum Markov chains

    Energy Technology Data Exchange (ETDEWEB)

    Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)

    2012-07-01

    The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.

  14. Structure-based Markov random field model for representing evolutionary constraints on functional sites.

    Science.gov (United States)

    Jeong, Chan-Seok; Kim, Dongsup

    2016-02-24

    Elucidating the cooperative mechanism of interconnected residues is an important component toward understanding the biological function of a protein. Coevolution analysis has been developed to model the coevolutionary information reflecting structural and functional constraints. Recently, several methods have been developed based on a probabilistic graphical model called the Markov random field (MRF), which have led to significant improvements for coevolution analysis; however, thus far, the performance of these models has mainly been assessed by focusing on the aspect of protein structure. In this study, we built an MRF model whose graphical topology is determined by the residue proximity in the protein structure, and derived a novel positional coevolution estimate utilizing the node weight of the MRF model. This structure-based MRF method was evaluated for three data sets, each of which annotates catalytic site, allosteric site, and comprehensively determined functional site information. We demonstrate that the structure-based MRF architecture can encode the evolutionary information associated with biological function. Furthermore, we show that the node weight can more accurately represent positional coevolution information compared to the edge weight. Lastly, we demonstrate that the structure-based MRF model can be reliably built with only a few aligned sequences in linear time. The results show that adoption of a structure-based architecture could be an acceptable approximation for coevolution modeling with efficient computation complexity.

  15. Theoretical evaluation of the detectability of random lesions in bayesian emission reconstruction

    International Nuclear Information System (INIS)

    Qi, Jinyi

    2003-01-01

    Detecting cancerous lesion is an important task in positron emission tomography (PET). Bayesian methods based on the maximum a posteriori principle (also called penalized maximum likelihood methods) have been developed to deal with the low signal to noise ratio in the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the prior parameters in Bayesian reconstruction control the resolution and noise trade-off and hence affect detectability of lesions in reconstructed images. Bayesian reconstructions are difficult to analyze because the resolution and noise properties are nonlinear and object-dependent. Most research has been based on Monte Carlo simulations, which are very time consuming. Building on the recent progress on the theoretical analysis of image properties of statistical reconstructions and the development of numerical observers, here we develop a theoretical approach for fast computation of lesion detectability in Bayesian reconstruction. The results can be used to choose the optimum hyperparameter for the maximum lesion detectability. New in this work is the use of theoretical expressions that explicitly model the statistical variation of the lesion and background without assuming that the object variation is (locally) stationary. The theoretical results are validated using Monte Carlo simulations. The comparisons show good agreement between the theoretical predications and the Monte Carlo results

  16. Semi-Markov Arnason-Schwarz models.

    Science.gov (United States)

    King, Ruth; Langrock, Roland

    2016-06-01

    We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis. © 2015, The International Biometric Society.

  17. Bayesian optimization for computationally extensive probability distributions.

    Science.gov (United States)

    Tamura, Ryo; Hukushima, Koji

    2018-01-01

    An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribution. Our Bayesian optimization technique is applied to the posterior distribution in the effective physical model estimation, which is a computationally extensive probability distribution. Even when the number of sampling points on the posterior distributions is fixed to be small, the Bayesian optimization provides a better maximizer of the posterior distributions in comparison to those by the random search method, the steepest descent method, or the Monte Carlo method. Furthermore, the Bayesian optimization improves the results efficiently by combining the steepest descent method and thus it is a powerful tool to search for a better maximizer of computationally extensive probability distributions.

  18. A population-based Bayesian approach to the minimal model of glucose and insulin homeostasis

    DEFF Research Database (Denmark)

    Andersen, Kim Emil; Højbjerre, Malene

    2005-01-01

    -posed estimation problem, where the reconstruction most often has been done by non-linear least squares techniques separately for each entity. The minmal model was originally specified for a single individual and does not combine several individuals with the advantage of estimating the metabolic portrait...... to a population-based model. The estimation of the parameters are efficiently implemented in a Bayesian approach where posterior inference is made through the use of Markov chain Monte Carlo techniques. Hereby we obtain a powerful and flexible modelling framework for regularizing the ill-posed estimation problem...

  19. Adaptive Markov Chain Monte Carlo

    KAUST Repository

    Jadoon, Khan

    2016-08-08

    A substantial interpretation of electromagnetic induction (EMI) measurements requires quantifying optimal model parameters and uncertainty of a nonlinear inverse problem. For this purpose, an adaptive Bayesian Markov chain Monte Carlo (MCMC) algorithm is used to assess multi-orientation and multi-offset EMI measurements in an agriculture field with non-saline and saline soil. In the MCMC simulations, posterior distribution was computed using Bayes rule. The electromagnetic forward model based on the full solution of Maxwell\\'s equations was used to simulate the apparent electrical conductivity measured with the configurations of EMI instrument, the CMD mini-Explorer. The model parameters and uncertainty for the three-layered earth model are investigated by using synthetic data. Our results show that in the scenario of non-saline soil, the parameters of layer thickness are not well estimated as compared to layers electrical conductivity because layer thicknesses in the model exhibits a low sensitivity to the EMI measurements, and is hence difficult to resolve. Application of the proposed MCMC based inversion to the field measurements in a drip irrigation system demonstrate that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil, and provide useful insight about parameter uncertainty for the assessment of the model outputs.

  20. Bayesian state space models for dynamic genetic network construction across multiple tissues.

    Science.gov (United States)

    Liang, Yulan; Kelemen, Arpad

    2016-08-01

    Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.

  1. Hyperspectral Image Classification With Markov Random Fields and a Convolutional Neural Network

    Science.gov (United States)

    Cao, Xiangyong; Zhou, Feng; Xu, Lin; Meng, Deyu; Xu, Zongben; Paisley, John

    2018-05-01

    This paper presents a new supervised classification algorithm for remotely sensed hyperspectral image (HSI) which integrates spectral and spatial information in a unified Bayesian framework. First, we formulate the HSI classification problem from a Bayesian perspective. Then, we adopt a convolutional neural network (CNN) to learn the posterior class distributions using a patch-wise training strategy to better use the spatial information. Next, spatial information is further considered by placing a spatial smoothness prior on the labels. Finally, we iteratively update the CNN parameters using stochastic gradient decent (SGD) and update the class labels of all pixel vectors using an alpha-expansion min-cut-based algorithm. Compared with other state-of-the-art methods, the proposed classification method achieves better performance on one synthetic dataset and two benchmark HSI datasets in a number of experimental settings.

  2. A surrogate-based sensitivity quantification and Bayesian inversion of a regional groundwater flow model

    Science.gov (United States)

    Chen, Mingjie; Izady, Azizallah; Abdalla, Osman A.; Amerjeed, Mansoor

    2018-02-01

    Bayesian inference using Markov Chain Monte Carlo (MCMC) provides an explicit framework for stochastic calibration of hydrogeologic models accounting for uncertainties; however, the MCMC sampling entails a large number of model calls, and could easily become computationally unwieldy if the high-fidelity hydrogeologic model simulation is time consuming. This study proposes a surrogate-based Bayesian framework to address this notorious issue, and illustrates the methodology by inverse modeling a regional MODFLOW model. The high-fidelity groundwater model is approximated by a fast statistical model using Bagging Multivariate Adaptive Regression Spline (BMARS) algorithm, and hence the MCMC sampling can be efficiently performed. In this study, the MODFLOW model is developed to simulate the groundwater flow in an arid region of Oman consisting of mountain-coast aquifers, and used to run representative simulations to generate training dataset for BMARS model construction. A BMARS-based Sobol' method is also employed to efficiently calculate input parameter sensitivities, which are used to evaluate and rank their importance for the groundwater flow model system. According to sensitivity analysis, insensitive parameters are screened out of Bayesian inversion of the MODFLOW model, further saving computing efforts. The posterior probability distribution of input parameters is efficiently inferred from the prescribed prior distribution using observed head data, demonstrating that the presented BMARS-based Bayesian framework is an efficient tool to reduce parameter uncertainties of a groundwater system.

  3. Automatic lung tumor segmentation on PET/CT images using fuzzy Markov random field model.

    Science.gov (United States)

    Guo, Yu; Feng, Yuanming; Sun, Jian; Zhang, Ning; Lin, Wang; Sa, Yu; Wang, Ping

    2014-01-01

    The combination of positron emission tomography (PET) and CT images provides complementary functional and anatomical information of human tissues and it has been used for better tumor volume definition of lung cancer. This paper proposed a robust method for automatic lung tumor segmentation on PET/CT images. The new method is based on fuzzy Markov random field (MRF) model. The combination of PET and CT image information is achieved by using a proper joint posterior probability distribution of observed features in the fuzzy MRF model which performs better than the commonly used Gaussian joint distribution. In this study, the PET and CT simulation images of 7 non-small cell lung cancer (NSCLC) patients were used to evaluate the proposed method. Tumor segmentations with the proposed method and manual method by an experienced radiation oncologist on the fused images were performed, respectively. Segmentation results obtained with the two methods were similar and Dice's similarity coefficient (DSC) was 0.85 ± 0.013. It has been shown that effective and automatic segmentations can be achieved with this method for lung tumors which locate near other organs with similar intensities in PET and CT images, such as when the tumors extend into chest wall or mediastinum.

  4. Automatic Lung Tumor Segmentation on PET/CT Images Using Fuzzy Markov Random Field Model

    Directory of Open Access Journals (Sweden)

    Yu Guo

    2014-01-01

    Full Text Available The combination of positron emission tomography (PET and CT images provides complementary functional and anatomical information of human tissues and it has been used for better tumor volume definition of lung cancer. This paper proposed a robust method for automatic lung tumor segmentation on PET/CT images. The new method is based on fuzzy Markov random field (MRF model. The combination of PET and CT image information is achieved by using a proper joint posterior probability distribution of observed features in the fuzzy MRF model which performs better than the commonly used Gaussian joint distribution. In this study, the PET and CT simulation images of 7 non-small cell lung cancer (NSCLC patients were used to evaluate the proposed method. Tumor segmentations with the proposed method and manual method by an experienced radiation oncologist on the fused images were performed, respectively. Segmentation results obtained with the two methods were similar and Dice’s similarity coefficient (DSC was 0.85 ± 0.013. It has been shown that effective and automatic segmentations can be achieved with this method for lung tumors which locate near other organs with similar intensities in PET and CT images, such as when the tumors extend into chest wall or mediastinum.

  5. Sharp Boundary Inversion of 2D Magnetotelluric Data using Bayesian Method.

    Science.gov (United States)

    Zhou, S.; Huang, Q.

    2017-12-01

    Normally magnetotelluric(MT) inversion method cannot show the distribution of underground resistivity with clear boundary, even if there are obviously different blocks. Aiming to solve this problem, we develop a Bayesian structure to inverse 2D MT sharp boundary data, using boundary location and inside resistivity as the random variables. Firstly, we use other MT inversion results, like ModEM, to analyze the resistivity distribution roughly. Then, we select the suitable random variables and change its data format to traditional staggered grid parameters, which can be used to do finite difference forward part. Finally, we can shape the posterior probability density(PPD), which contains all the prior information and model-data correlation, by Markov Chain Monte Carlo(MCMC) sampling from prior distribution. The depth, resistivity and their uncertainty can be valued. It also works for sensibility estimation. We applied the method to a synthetic case, which composes two large abnormal blocks in a trivial background. We consider the boundary smooth and the near true model weight constrains that mimic joint inversion or constrained inversion, then we find that the model results a more precise and focused depth distribution. And we also test the inversion without constrains and find that the boundary could also be figured, though not as well. Both inversions have a good valuation of resistivity. The constrained result has a lower root mean square than ModEM inversion result. The data sensibility obtained via PPD shows that the resistivity is the most sensible, center depth comes second and both sides are the worst.

  6. Optimization of Markov chains for a SUSY fitter: Fittino

    Energy Technology Data Exchange (ETDEWEB)

    Prudent, Xavier [IKTP, Technische Universitaet, Dresden (Germany); Bechtle, Philip [DESY, Hamburg (Germany); Desch, Klaus; Wienemann, Peter [Universitaet Bonn (Germany)

    2010-07-01

    A Markov chains is a ''random walk'' algorithm which allows an efficient scan of a given profile and the search of the absolute minimum, even when this profil suffers from the presence of many secondary minima. This property makes them particularly suited to the study of Supersymmetry (SUSY) models, where minima have to be found in up-to 18-dimensional space for the general MSSM. Hence the SUSY fitter ''Fittino'' uses a Metropolis*Hastings Markov chain in a frequentist interpretation to study the impact of current low -energy measurements, as well as expected measurements from LHC and ILC, on the SUSY parameter space. The expected properties of an optimal Markov chain should be the independence of final results with respect to the starting point and a fast convergence. These two points can be achieved by optimizing the width of the proposal distribution, that is the ''average step length'' between two links in the chain. We developped an algorithm for the optimization of the proposal width, by modifying iteratively the width so that the rejection rate be around fifty percent. This optimization leads to a starting point independent chain as well as a faster convergence.

  7. Bayesian networks and boundedly rational expectations

    OpenAIRE

    Ran Spiegler

    2014-01-01

    I present a framework for analyzing decision makers with an imperfect understanding of their environment's correlation structure. The framework borrows the tool of "Bayesian networks", which is ubiquitous in statistics and artificial intelligence. In the model, a decision maker faces an objective multivariate probability distribution (his own action is one of the random variables). He is characterized by a directed acyclic graph over the set of random variables. His subjective belief filters ...

  8. Quantifying Uncertainty in Near Surface Electromagnetic Imaging Using Bayesian Methods

    Science.gov (United States)

    Blatter, D. B.; Ray, A.; Key, K.

    2017-12-01

    Geoscientists commonly use electromagnetic methods to image the Earth's near surface. Field measurements of EM fields are made (often with the aid an artificial EM source) and then used to infer near surface electrical conductivity via a process known as inversion. In geophysics, the standard inversion tool kit is robust and can provide an estimate of the Earth's near surface conductivity that is both geologically reasonable and compatible with the measured field data. However, standard inverse methods struggle to provide a sense of the uncertainty in the estimate they provide. This is because the task of finding an Earth model that explains the data to within measurement error is non-unique - that is, there are many, many such models; but the standard methods provide only one "answer." An alternative method, known as Bayesian inversion, seeks to explore the full range of Earth model parameters that can adequately explain the measured data, rather than attempting to find a single, "ideal" model. Bayesian inverse methods can therefore provide a quantitative assessment of the uncertainty inherent in trying to infer near surface conductivity from noisy, measured field data. This study applies a Bayesian inverse method (called trans-dimensional Markov chain Monte Carlo) to transient airborne EM data previously collected over Taylor Valley - one of the McMurdo Dry Valleys in Antarctica. Our results confirm the reasonableness of previous estimates (made using standard methods) of near surface conductivity beneath Taylor Valley. In addition, we demonstrate quantitatively the uncertainty associated with those estimates. We demonstrate that Bayesian inverse methods can provide quantitative uncertainty to estimates of near surface conductivity.

  9. Bayesian Estimation of Small Effects in Exercise and Sports Science.

    Directory of Open Access Journals (Sweden)

    Kerrie L Mengersen

    Full Text Available The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL, and intermittent hypoxic exposure (IHE on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a 'magnitude-based inference' approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements.

  10. Bayesian Estimation of Small Effects in Exercise and Sports Science.

    Science.gov (United States)

    Mengersen, Kerrie L; Drovandi, Christopher C; Robert, Christian P; Pyne, David B; Gore, Christopher J

    2016-01-01

    The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a 'magnitude-based inference' approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements.

  11. Reviving Markov processes and applications

    International Nuclear Information System (INIS)

    Cai, H.

    1988-01-01

    In this dissertation we study a procedure which restarts a Markov process when the process is killed by some arbitrary multiplicative functional. The regenerative nature of this revival procedure is characterized through a Markov renewal equation. An interesting duality between the revival procedure and the classical killing operation is found. Under the condition that the multiplicative functional possesses an intensity, the generators of the revival process can be written down explicitly. An intimate connection is also found between the perturbation of the sample path of a Markov process and the perturbation of a generator (in Kato's sense). The applications of the theory include the study of the processes like piecewise-deterministic Markov process, virtual waiting time process and the first entrance decomposition (taboo probability)

  12. A Dynamic Bayesian Network Model for the Production and Inventory Control

    Science.gov (United States)

    Shin, Ji-Sun; Takazaki, Noriyuki; Lee, Tae-Hong; Kim, Jin-Il; Lee, Hee-Hyol

    In general, the production quantities and delivered goods are changed randomly and then the total stock is also changed randomly. This paper deals with the production and inventory control using the Dynamic Bayesian Network. Bayesian Network is a probabilistic model which represents the qualitative dependence between two or more random variables by the graph structure, and indicates the quantitative relations between individual variables by the conditional probability. The probabilistic distribution of the total stock is calculated through the propagation of the probability on the network. Moreover, an adjusting rule of the production quantities to maintain the probability of a lower limit and a ceiling of the total stock to certain values is shown.

  13. Bayesian approach to errors-in-variables in regression models

    Science.gov (United States)

    Rozliman, Nur Aainaa; Ibrahim, Adriana Irawati Nur; Yunus, Rossita Mohammad

    2017-05-01

    In many applications and experiments, data sets are often contaminated with error or mismeasured covariates. When at least one of the covariates in a model is measured with error, Errors-in-Variables (EIV) model can be used. Measurement error, when not corrected, would cause misleading statistical inferences and analysis. Therefore, our goal is to examine the relationship of the outcome variable and the unobserved exposure variable given the observed mismeasured surrogate by applying the Bayesian formulation to the EIV model. We shall extend the flexible parametric method proposed by Hossain and Gustafson (2009) to another nonlinear regression model which is the Poisson regression model. We shall then illustrate the application of this approach via a simulation study using Markov chain Monte Carlo sampling methods.

  14. Oriented Markov random field based dendritic spine segmentation for fluorescence microscopy images.

    Science.gov (United States)

    Cheng, Jie; Zhou, Xiaobo; Miller, Eric L; Alvarez, Veronica A; Sabatini, Bernardo L; Wong, Stephen T C

    2010-10-01

    Dendritic spines have been shown to be closely related to various functional properties of the neuron. Usually dendritic spines are manually labeled to analyze their morphological changes, which is very time-consuming and susceptible to operator bias, even with the assistance of computers. To deal with these issues, several methods have been recently proposed to automatically detect and measure the dendritic spines with little human interaction. However, problems such as degraded detection performance for images with larger pixel size (e.g. 0.125 μm/pixel instead of 0.08 μm/pixel) still exist in these methods. Moreover, the shapes of detected spines are also distorted. For example, the "necks" of some spines are missed. Here we present an oriented Markov random field (OMRF) based algorithm which improves spine detection as well as their geometric characterization. We begin with the identification of a region of interest (ROI) containing all the dendrites and spines to be analyzed. For this purpose, we introduce an adaptive procedure for identifying the image background. Next, the OMRF model is discussed within a statistical framework and the segmentation is solved as a maximum a posteriori estimation (MAP) problem, whose optimal solution is found by a knowledge-guided iterative conditional mode (KICM) algorithm. Compared with the existing algorithms, the proposed algorithm not only provides a more accurate representation of the spine shape, but also improves the detection performance by more than 50% with regard to reducing both the misses and false detection.

  15. MCMCpack: Markov Chain Monte Carlo in R

    Directory of Open Access Journals (Sweden)

    Andrew D. Martin

    2011-08-01

    Full Text Available We introduce MCMCpack, an R package that contains functions to perform Bayesian inference using posterior simulation for a number of statistical models. In addition to code that can be used to fit commonly used models, MCMCpack also contains some useful utility functions, including some additional density functions and pseudo-random number generators for statistical distributions, a general purpose Metropolis sampling algorithm, and tools for visualization.

  16. Performance Modeling of Communication Networks with Markov Chains

    CERN Document Server

    Mo, Jeonghoon

    2010-01-01

    This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMe and continuous time Markov chain (CTMe. We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probab

  17. Fields From Markov Chains

    DEFF Research Database (Denmark)

    Justesen, Jørn

    2005-01-01

    A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly.......A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly....

  18. Genome-wide prediction of discrete traits using bayesian regressions and machine learning

    Directory of Open Access Journals (Sweden)

    Forni Selma

    2011-02-01

    Full Text Available Abstract Background Genomic selection has gained much attention and the main goal is to increase the predictive accuracy and the genetic gain in livestock using dense marker information. Most methods dealing with the large p (number of covariates small n (number of observations problem have dealt only with continuous traits, but there are many important traits in livestock that are recorded in a discrete fashion (e.g. pregnancy outcome, disease resistance. It is necessary to evaluate alternatives to analyze discrete traits in a genome-wide prediction context. Methods This study shows two threshold versions of Bayesian regressions (Bayes A and Bayesian LASSO and two machine learning algorithms (boosting and random forest to analyze discrete traits in a genome-wide prediction context. These methods were evaluated using simulated and field data to predict yet-to-be observed records. Performances were compared based on the models' predictive ability. Results The simulation showed that machine learning had some advantages over Bayesian regressions when a small number of QTL regulated the trait under pure additivity. However, differences were small and disappeared with a large number of QTL. Bayesian threshold LASSO and boosting achieved the highest accuracies, whereas Random Forest presented the highest classification performance. Random Forest was the most consistent method in detecting resistant and susceptible animals, phi correlation was up to 81% greater than Bayesian regressions. Random Forest outperformed other methods in correctly classifying resistant and susceptible animals in the two pure swine lines evaluated. Boosting and Bayes A were more accurate with crossbred data. Conclusions The results of this study suggest that the best method for genome-wide prediction may depend on the genetic basis of the population analyzed. All methods were less accurate at correctly classifying intermediate animals than extreme animals. Among the different

  19. First-passage percolation on the random graph

    NARCIS (Netherlands)

    Hofstad, van der R.W.; Hooghiemstra, G.; Van Mieghem, P.

    2001-01-01

    We study first-passage percolation on the random graph Gp(N) with exponentially distributed weights on the links. For the special case of the complete graph, this problem can be described in terms of a continuous-time Markov chain and recursive trees. The Markov chain X(t) describes the number of

  20. Regeneration and general Markov chains

    Directory of Open Access Journals (Sweden)

    Vladimir V. Kalashnikov

    1994-01-01

    Full Text Available Ergodicity, continuity, finite approximations and rare visits of general Markov chains are investigated. The obtained results permit further quantitative analysis of characteristics, such as, rates of convergence, continuity (measured as a distance between perturbed and non-perturbed characteristics, deviations between Markov chains, accuracy of approximations and bounds on the distribution function of the first visit time to a chosen subset, etc. The underlying techniques use the embedding of the general Markov chain into a wide sense regenerative process with the help of splitting construction.

  1. Observer-Based Controller Design for a Class of Nonlinear Networked Control Systems with Random Time-Delays Modeled by Markov Chains

    Directory of Open Access Journals (Sweden)

    Yanfeng Wang

    2017-01-01

    Full Text Available This paper investigates the observer-based controller design problem for a class of nonlinear networked control systems with random time-delays. The nonlinearity is assumed to satisfy a global Lipschitz condition and two dependent Markov chains are employed to describe the time-delay from sensor to controller (S-C delay and the time-delay from controller to actuator (C-A delay, respectively. The transition probabilities of S-C delay and C-A delay are both assumed to be partly inaccessible. Sufficient conditions on the stochastic stability for the closed-loop systems are obtained by constructing proper Lyapunov functional. The methods of calculating the controller and the observer gain matrix are also given. Two numerical examples are used to illustrate the effectiveness of the proposed method.

  2. Markov set-chains

    CERN Document Server

    Hartfiel, Darald J

    1998-01-01

    In this study extending classical Markov chain theory to handle fluctuating transition matrices, the author develops a theory of Markov set-chains and provides numerous examples showing how that theory can be applied. Chapters are concluded with a discussion of related research. Readers who can benefit from this monograph are those interested in, or involved with, systems whose data is imprecise or that fluctuate with time. A background equivalent to a course in linear algebra and one in probability theory should be sufficient.

  3. Hidden Markov models: the best models for forager movements?

    Science.gov (United States)

    Joo, Rocio; Bertrand, Sophie; Tam, Jorge; Fablet, Ronan

    2013-01-01

    One major challenge in the emerging field of movement ecology is the inference of behavioural modes from movement patterns. This has been mainly addressed through Hidden Markov models (HMMs). We propose here to evaluate two sets of alternative and state-of-the-art modelling approaches. First, we consider hidden semi-Markov models (HSMMs). They may better represent the behavioural dynamics of foragers since they explicitly model the duration of the behavioural modes. Second, we consider discriminative models which state the inference of behavioural modes as a classification issue, and may take better advantage of multivariate and non linear combinations of movement pattern descriptors. For this work, we use a dataset of >200 trips from human foragers, Peruvian fishermen targeting anchovy. Their movements were recorded through a Vessel Monitoring System (∼1 record per hour), while their behavioural modes (fishing, searching and cruising) were reported by on-board observers. We compare the efficiency of hidden Markov, hidden semi-Markov, and three discriminative models (random forests, artificial neural networks and support vector machines) for inferring the fishermen behavioural modes, using a cross-validation procedure. HSMMs show the highest accuracy (80%), significantly outperforming HMMs and discriminative models. Simulations show that data with higher temporal resolution, HSMMs reach nearly 100% of accuracy. Our results demonstrate to what extent the sequential nature of movement is critical for accurately inferring behavioural modes from a trajectory and we strongly recommend the use of HSMMs for such purpose. In addition, this work opens perspectives on the use of hybrid HSMM-discriminative models, where a discriminative setting for the observation process of HSMMs could greatly improve inference performance.

  4. Hidden Markov models: the best models for forager movements?

    Directory of Open Access Journals (Sweden)

    Rocio Joo

    Full Text Available One major challenge in the emerging field of movement ecology is the inference of behavioural modes from movement patterns. This has been mainly addressed through Hidden Markov models (HMMs. We propose here to evaluate two sets of alternative and state-of-the-art modelling approaches. First, we consider hidden semi-Markov models (HSMMs. They may better represent the behavioural dynamics of foragers since they explicitly model the duration of the behavioural modes. Second, we consider discriminative models which state the inference of behavioural modes as a classification issue, and may take better advantage of multivariate and non linear combinations of movement pattern descriptors. For this work, we use a dataset of >200 trips from human foragers, Peruvian fishermen targeting anchovy. Their movements were recorded through a Vessel Monitoring System (∼1 record per hour, while their behavioural modes (fishing, searching and cruising were reported by on-board observers. We compare the efficiency of hidden Markov, hidden semi-Markov, and three discriminative models (random forests, artificial neural networks and support vector machines for inferring the fishermen behavioural modes, using a cross-validation procedure. HSMMs show the highest accuracy (80%, significantly outperforming HMMs and discriminative models. Simulations show that data with higher temporal resolution, HSMMs reach nearly 100% of accuracy. Our results demonstrate to what extent the sequential nature of movement is critical for accurately inferring behavioural modes from a trajectory and we strongly recommend the use of HSMMs for such purpose. In addition, this work opens perspectives on the use of hybrid HSMM-discriminative models, where a discriminative setting for the observation process of HSMMs could greatly improve inference performance.

  5. Entropy, Information Theory, Information Geometry and Bayesian Inference in Data, Signal and Image Processing and Inverse Problems

    Directory of Open Access Journals (Sweden)

    Ali Mohammad-Djafari

    2015-06-01

    Full Text Available The main content of this review article is first to review the main inference tools using Bayes rule, the maximum entropy principle (MEP, information theory, relative entropy and the Kullback–Leibler (KL divergence, Fisher information and its corresponding geometries. For each of these tools, the precise context of their use is described. The second part of the paper is focused on the ways these tools have been used in data, signal and image processing and in the inverse problems, which arise in different physical sciences and engineering applications. A few examples of the applications are described: entropy in independent components analysis (ICA and in blind source separation, Fisher information in data model selection, different maximum entropy-based methods in time series spectral estimation and in linear inverse problems and, finally, the Bayesian inference for general inverse problems. Some original materials concerning the approximate Bayesian computation (ABC and, in particular, the variational Bayesian approximation (VBA methods are also presented. VBA is used for proposing an alternative Bayesian computational tool to the classical Markov chain Monte Carlo (MCMC methods. We will also see that VBA englobes joint maximum a posteriori (MAP, as well as the different expectation-maximization (EM algorithms as particular cases.

  6. A Bayesian Hierarchical Model for Relating Multiple SNPs within Multiple Genes to Disease Risk

    Directory of Open Access Journals (Sweden)

    Lewei Duan

    2013-01-01

    Full Text Available A variety of methods have been proposed for studying the association of multiple genes thought to be involved in a common pathway for a particular disease. Here, we present an extension of a Bayesian hierarchical modeling strategy that allows for multiple SNPs within each gene, with external prior information at either the SNP or gene level. The model involves variable selection at the SNP level through latent indicator variables and Bayesian shrinkage at the gene level towards a prior mean vector and covariance matrix that depend on external information. The entire model is fitted using Markov chain Monte Carlo methods. Simulation studies show that the approach is capable of recovering many of the truly causal SNPs and genes, depending upon their frequency and size of their effects. The method is applied to data on 504 SNPs in 38 candidate genes involved in DNA damage response in the WECARE study of second breast cancers in relation to radiotherapy exposure.

  7. Introduction to Bayesian statistics

    CERN Document Server

    Koch, Karl-Rudolf

    2007-01-01

    This book presents Bayes' theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters. It does so in a simple manner that is easy to comprehend. The book compares traditional and Bayesian methods with the rules of probability presented in a logical way allowing an intuitive understanding of random variables and their probability distributions to be formed.

  8. Bayesian estimation of the discrete coefficient of determination.

    Science.gov (United States)

    Chen, Ting; Braga-Neto, Ulisses M

    2016-12-01

    The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.

  9. Markov chains theory and applications

    CERN Document Server

    Sericola, Bruno

    2013-01-01

    Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the

  10. Quadratic Variation by Markov Chains

    DEFF Research Database (Denmark)

    Hansen, Peter Reinhard; Horel, Guillaume

    We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...

  11. IMAGE ENHANCEMENT AND SPECKLE REDUCTION OF FULL POLARIMETRIC SAR DATA BY GAUSSIAN MARKOV RANDOM FIELD

    Directory of Open Access Journals (Sweden)

    M. Mahdian

    2013-09-01

    Full Text Available In recent years, the use of Polarimetric Synthetic Aperture Radar (PolSAR data in different applications dramatically has been increased. In SAR imagery an interference phenomenon with random behavior exists which is called speckle noise. The interpretation of data encounters some troubles due to the presence of speckle which can be considered as a multiplicative noise affecting all coherent imaging systems. Indeed, speckle degrade radiometric resolution of PolSAR images, therefore it is needful to perform speckle filtering on the SAR data type. Markov Random Field (MRF has proven to be a powerful method for drawing out eliciting contextual information from remotely sensed images. In the present paper, a probability density function (PDF, which is fitted well with the PolSAR data based on the goodness-of-fit test, is first obtained for the pixel-wise analysis. Then the contextual smoothing is achieved with the MRF method. This novel speckle reduction method combines an advanced statistical distribution with spatial contextual information for PolSAR data. These two parts of information are combined based on weighted summation of pixel-wise and contextual models. This approach not only preserves edge information in the images, but also improves signal-to-noise ratio of the results. The method maintains the mean value of original signal in the homogenous areas and preserves the edges of features in the heterogeneous regions. Experiments on real medium resolution ALOS data from Tehran, and also high resolution full polarimetric SAR data over the Oberpfaffenhofen test-site in Germany, demonstrate the effectiveness of the algorithm compared with well-known despeckling methods.

  12. Confluence reduction for Markov automata

    NARCIS (Netherlands)

    Timmer, Mark; Katoen, Joost P.; van de Pol, Jaco; Stoelinga, Mariëlle Ida Antoinette

    2016-01-01

    Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. As expected, the state space explosion threatens the analysability of these models. We therefore introduce confluence reduction for Markov automata, a powerful reduction

  13. MARKOV CHAIN MODELING OF PERFORMANCE DEGRADATION OF PHOTOVOLTAIC SYSTEM

    OpenAIRE

    E. Suresh Kumar; Asis Sarkar; Dhiren kumar Behera

    2012-01-01

    Modern probability theory studies chance processes for which theknowledge of previous outcomes influence predictions for future experiments. In principle, when a sequence of chance experiments, all of the past outcomes could influence the predictions for the next experiment. In Markov chain type of chance, the outcome of a given experiment can affect the outcome of the next experiment. The system state changes with time and the state X and time t are two random variables. Each of these variab...

  14. Machine health prognostics using the Bayesian-inference-based probabilistic indication and high-order particle filtering framework

    Science.gov (United States)

    Yu, Jianbo

    2015-12-01

    Prognostics is much efficient to achieve zero-downtime performance, maximum productivity and proactive maintenance of machines. Prognostics intends to assess and predict the time evolution of machine health degradation so that machine failures can be predicted and prevented. A novel prognostics system is developed based on the data-model-fusion scheme using the Bayesian inference-based self-organizing map (SOM) and an integration of logistic regression (LR) and high-order particle filtering (HOPF). In this prognostics system, a baseline SOM is constructed to model the data distribution space of healthy machine under an assumption that predictable fault patterns are not available. Bayesian inference-based probability (BIP) derived from the baseline SOM is developed as a quantification indication of machine health degradation. BIP is capable of offering failure probability for the monitored machine, which has intuitionist explanation related to health degradation state. Based on those historic BIPs, the constructed LR and its modeling noise constitute a high-order Markov process (HOMP) to describe machine health propagation. HOPF is used to solve the HOMP estimation to predict the evolution of the machine health in the form of a probability density function (PDF). An on-line model update scheme is developed to adapt the Markov process changes to machine health dynamics quickly. The experimental results on a bearing test-bed illustrate the potential applications of the proposed system as an effective and simple tool for machine health prognostics.

  15. Verification of Open Interactive Markov Chains

    OpenAIRE

    Brazdil, Tomas; Hermanns, Holger; Krcal, Jan; Kretinsky, Jan; Rehak, Vojtech

    2012-01-01

    Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation....

  16. Bayesian models for comparative analysis integrating phylogenetic uncertainty

    Directory of Open Access Journals (Sweden)

    Villemereuil Pierre de

    2012-06-01

    Full Text Available Abstract Background Uncertainty in comparative analyses can come from at least two sources: a phylogenetic uncertainty in the tree topology or branch lengths, and b uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow and inflated significance in hypothesis testing (e.g. p-values will be too small. Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible

  17. Bayesian models for comparative analysis integrating phylogenetic uncertainty

    Science.gov (United States)

    2012-01-01

    Background Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for

  18. Modelling the Errors of EIA’s Oil Prices and Production Forecasts by the Grey Markov Model

    Directory of Open Access Journals (Sweden)

    Gholam Hossein Hasantash

    2012-01-01

    Full Text Available Grey theory is about systematic analysis of limited information. The Grey-Markov model can improve the accuracy of forecast range in the random fluctuating data sequence. In this paper, we employed this model in energy system. The average errors of Energy Information Administrations predictions for world oil price and domestic crude oil production from 1982 to 2007 and from 1985 to 2008 respectively were used as two forecasted examples. We showed that the proposed Grey-Markov model can improve the forecast accuracy of original Grey forecast model.

  19. Bayesian model comparison using Gauss approximation on multicomponent mass spectra from CH4 plasma

    International Nuclear Information System (INIS)

    Kang, H.D.; Dose, V.

    2004-01-01

    We performed Bayesian model comparison on mass spectra from CH4 rf process plasmas to detect radicals produced in the plasma. The key ingredient for its implementation is the high-dimensional evidence integral. We apply Gauss approximation to evaluate the evidence. The results were compared with those calculated by the thermodynamic integration method using Markov Chain Monte Carlo technique. In spite of very large difference in the computation time between two methods a very good agreement was obtained. Alternatively, a Monte Carlo integration method based on the approximated Gaussian posterior density is presented. Its applicability to the problem of mass spectrometry is discussed

  20. Using hidden Markov models to align multiple sequences.

    Science.gov (United States)

    Mount, David W

    2009-07-01

    A hidden Markov model (HMM) is a probabilistic model of a multiple sequence alignment (msa) of proteins. In the model, each column of symbols in the alignment is represented by a frequency distribution of the symbols (called a "state"), and insertions and deletions are represented by other states. One moves through the model along a particular path from state to state in a Markov chain (i.e., random choice of next move), trying to match a given sequence. The next matching symbol is chosen from each state, recording its probability (frequency) and also the probability of going to that state from a previous one (the transition probability). State and transition probabilities are multiplied to obtain a probability of the given sequence. The hidden nature of the HMM is due to the lack of information about the value of a specific state, which is instead represented by a probability distribution over all possible values. This article discusses the advantages and disadvantages of HMMs in msa and presents algorithms for calculating an HMM and the conditions for producing the best HMM.

  1. Extreme event statistics in a drifting Markov chain

    Science.gov (United States)

    Kindermann, Farina; Hohmann, Michael; Lausch, Tobias; Mayer, Daniel; Schmidt, Felix; Widera, Artur

    2017-07-01

    We analyze extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one-dimensional periodic potential. Based on more than 500 individual atomic traces we verify the applicability of the Sparre Andersen theorem to our system despite the presence of a drift. We present detailed analysis of four different rare-event statistics for our system: the distributions of extreme values, of record values, of extreme value occurrence in the chain, and of the number of records in the chain. We observe that, for our data, the shape of the extreme event distributions is dominated by the underlying exponential distance distribution extracted from the atomic traces. Furthermore, we find that even small drifts influence the statistics of extreme events and record values, which is supported by numerical simulations, and we identify cases in which the drift can be determined without information about the underlying random variable distributions. Our results facilitate the use of extreme event statistics as a signal for small drifts in correlated trajectories.

  2. Influence of partially known parameter on flaw characterization in Eddy Current Testing by using a random walk MCMC method based on metamodeling

    International Nuclear Information System (INIS)

    Cai, Caifang; Lambert, Marc; Rodet, Thomas

    2014-01-01

    First, we present the implementation of a random walk Metropolis-within-Gibbs (MWG) sampling method in flaw characterization based on a metamodeling method. The role of metamodeling is to reduce the computational time cost in Eddy Current Testing (ECT) forward model calculation. In such a way, the use of Markov Chain Monte Carlo (MCMC) methods becomes possible. Secondly, we analyze the influence of partially known parameters in Bayesian estimation. The objective is to evaluate the importance of providing more specific prior information. Simulation results show that even partially known information has great interest in providing more accurate flaw parameter estimations. The improvement ratio depends on the parameter dependence and the interest shows only when the provided information is specific enough

  3. Markov Chain Analysis of Musical Dice Games

    Science.gov (United States)

    Volchenkov, D.; Dawin, J. R.

    2012-07-01

    A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.

  4. Classification Using Markov Blanket for Feature Selection

    DEFF Research Database (Denmark)

    Zeng, Yifeng; Luo, Jian

    2009-01-01

    Selecting relevant features is in demand when a large data set is of interest in a classification task. It produces a tractable number of features that are sufficient and possibly improve the classification performance. This paper studies a statistical method of Markov blanket induction algorithm...... for filtering features and then applies a classifier using the Markov blanket predictors. The Markov blanket contains a minimal subset of relevant features that yields optimal classification performance. We experimentally demonstrate the improved performance of several classifiers using a Markov blanket...... induction as a feature selection method. In addition, we point out an important assumption behind the Markov blanket induction algorithm and show its effect on the classification performance....

  5. Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.

    Science.gov (United States)

    Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J

    2010-12-01

    Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies

  6. Consistency and refinement for Interval Markov Chains

    DEFF Research Database (Denmark)

    Delahaye, Benoit; Larsen, Kim Guldstrand; Legay, Axel

    2012-01-01

    Interval Markov Chains (IMC), or Markov Chains with probability intervals in the transition matrix, are the base of a classic specification theory for probabilistic systems [18]. The standard semantics of IMCs assigns to a specification the set of all Markov Chains that satisfy its interval...

  7. Marginal Bayesian nonparametric model for time to disease arrival of threatened amphibian populations.

    Science.gov (United States)

    Zhou, Haiming; Hanson, Timothy; Knapp, Roland

    2015-12-01

    The global emergence of Batrachochytrium dendrobatidis (Bd) has caused the extinction of hundreds of amphibian species worldwide. It has become increasingly important to be able to precisely predict time to Bd arrival in a population. The data analyzed herein present a unique challenge in terms of modeling because there is a strong spatial component to Bd arrival time and the traditional proportional hazards assumption is grossly violated. To address these concerns, we develop a novel marginal Bayesian nonparametric survival model for spatially correlated right-censored data. This class of models assumes that the logarithm of survival times marginally follow a mixture of normal densities with a linear-dependent Dirichlet process prior as the random mixing measure, and their joint distribution is induced by a Gaussian copula model with a spatial correlation structure. To invert high-dimensional spatial correlation matrices, we adopt a full-scale approximation that can capture both large- and small-scale spatial dependence. An efficient Markov chain Monte Carlo algorithm with delayed rejection is proposed for posterior computation, and an R package spBayesSurv is provided to fit the model. This approach is first evaluated through simulations, then applied to threatened frog populations in Sequoia-Kings Canyon National Park. © 2015, The International Biometric Society.

  8. The neighborhood MCMC sampler for learning Bayesian networks

    Science.gov (United States)

    Alyami, Salem A.; Azad, A. K. M.; Keith, Jonathan M.

    2016-07-01

    Getting stuck in local maxima is a problem that arises while learning Bayesian networks (BNs) structures. In this paper, we studied a recently proposed Markov chain Monte Carlo (MCMC) sampler, called the Neighbourhood sampler (NS), and examined how efficiently it can sample BNs when local maxima are present. We assume that a posterior distribution f(N,E|D) has been defined, where D represents data relevant to the inference, N and E are the sets of nodes and directed edges, respectively. We illustrate the new approach by sampling from such a distribution, and inferring BNs. The simulations conducted in this paper show that the new learning approach substantially avoids getting stuck in local modes of the distribution, and achieves a more rapid rate of convergence, compared to other common algorithms e.g. the MCMC Metropolis-Hastings sampler.

  9. Use of a Bayesian hierarchical model to study the allometric scaling of the fetoplacental weight ratio

    Directory of Open Access Journals (Sweden)

    Fidel Ernesto Castro Morales

    2016-03-01

    Full Text Available Abstract Objectives: to propose the use of a Bayesian hierarchical model to study the allometric scaling of the fetoplacental weight ratio, including possible confounders. Methods: data from 26 singleton pregnancies with gestational age at birth between 37 and 42 weeks were analyzed. The placentas were collected immediately after delivery and stored under refrigeration until the time of analysis, which occurred within up to 12 hours. Maternal data were collected from medical records. A Bayesian hierarchical model was proposed and Markov chain Monte Carlo simulation methods were used to obtain samples from distribution a posteriori. Results: the model developed showed a reasonable fit, even allowing for the incorporation of variables and a priori information on the parameters used. Conclusions: new variables can be added to the modelfrom the available code, allowing many possibilities for data analysis and indicating the potential for use in research on the subject.

  10. Comprehensive maternal characteristics associated with birth weight: Bayesian modeling in a prospective cohort study from Iran

    Directory of Open Access Journals (Sweden)

    Marjan Mansourian

    2017-01-01

    Full Text Available Background: In this study, we aimed to determine comprehensive maternal characteristics associated with birth weight using Bayesian modeling. Materials and Methods: A total of 526 participants were included in this prospective study. Nutritional status, supplement consumption during the pregnancy, demographic and socioeconomic characteristics, anthropometric measures, physical activity, and pregnancy outcomes were considered as effective variables on the birth weight. Bayesian approach of complex statistical models using Markov chain Monte Carlo approach was used for modeling the data considering the real distribution of the response variable. Results: There was strong positive correlation between infant birth weight and the maternal intake of Vitamin C, folic acid, Vitamin B3, Vitamin A, selenium, calcium, iron, phosphorus, potassium, magnesium as micronutrients, and fiber and protein as macronutrients based on the 95% high posterior density regions for parameters in the Bayesian model. None of the maternal characteristics had statistical association with birth weight. Conclusion: Higher maternal macro- and micro-nutrient intake during pregnancy was associated with a lower risk of delivering low birth weight infants. These findings support recommendations to expand intake of nutrients during pregnancy to high level.

  11. cudaBayesreg: Parallel Implementation of a Bayesian Multilevel Model for fMRI Data Analysis

    Directory of Open Access Journals (Sweden)

    Adelino R. Ferreira da Silva

    2011-10-01

    Full Text Available Graphic processing units (GPUs are rapidly gaining maturity as powerful general parallel computing devices. A key feature in the development of modern GPUs has been the advancement of the programming model and programming tools. Compute Unified Device Architecture (CUDA is a software platform for massively parallel high-performance computing on Nvidia many-core GPUs. In functional magnetic resonance imaging (fMRI, the volume of the data to be processed, and the type of statistical analysis to perform call for high-performance computing strategies. In this work, we present the main features of the R-CUDA package cudaBayesreg which implements in CUDA the core of a Bayesian multilevel model for the analysis of brain fMRI data. The statistical model implements a Gibbs sampler for multilevel/hierarchical linear models with a normal prior. The main contribution for the increased performance comes from the use of separate threads for fitting the linear regression model at each voxel in parallel. The R-CUDA implementation of the Bayesian model proposed here has been able to reduce significantly the run-time processing of Markov chain Monte Carlo (MCMC simulations used in Bayesian fMRI data analyses. Presently, cudaBayesreg is only configured for Linux systems with Nvidia CUDA support.

  12. A Bayesian joint probability modeling approach for seasonal forecasting of streamflows at multiple sites

    Science.gov (United States)

    Wang, Q. J.; Robertson, D. E.; Chiew, F. H. S.

    2009-05-01

    Seasonal forecasting of streamflows can be highly valuable for water resources management. In this paper, a Bayesian joint probability (BJP) modeling approach for seasonal forecasting of streamflows at multiple sites is presented. A Box-Cox transformed multivariate normal distribution is proposed to model the joint distribution of future streamflows and their predictors such as antecedent streamflows and El Niño-Southern Oscillation indices and other climate indicators. Bayesian inference of model parameters and uncertainties is implemented using Markov chain Monte Carlo sampling, leading to joint probabilistic forecasts of streamflows at multiple sites. The model provides a parametric structure for quantifying relationships between variables, including intersite correlations. The Box-Cox transformed multivariate normal distribution has considerable flexibility for modeling a wide range of predictors and predictands. The Bayesian inference formulated allows the use of data that contain nonconcurrent and missing records. The model flexibility and data-handling ability means that the BJP modeling approach is potentially of wide practical application. The paper also presents a number of statistical measures and graphical methods for verification of probabilistic forecasts of continuous variables. Results for streamflows at three river gauges in the Murrumbidgee River catchment in southeast Australia show that the BJP modeling approach has good forecast quality and that the fitted model is consistent with observed data.

  13. Ant Colony Clustering Algorithm and Improved Markov Random Fusion Algorithm in Image Segmentation of Brain Images

    Directory of Open Access Journals (Sweden)

    Guohua Zou

    2016-12-01

    Full Text Available New medical imaging technology, such as Computed Tomography and Magnetic Resonance Imaging (MRI, has been widely used in all aspects of medical diagnosis. The purpose of these imaging techniques is to obtain various qualitative and quantitative data of the patient comprehensively and accurately, and provide correct digital information for diagnosis, treatment planning and evaluation after surgery. MR has a good imaging diagnostic advantage for brain diseases. However, as the requirements of the brain image definition and quantitative analysis are always increasing, it is necessary to have better segmentation of MR brain images. The FCM (Fuzzy C-means algorithm is widely applied in image segmentation, but it has some shortcomings, such as long computation time and poor anti-noise capability. In this paper, firstly, the Ant Colony algorithm is used to determine the cluster centers and the number of FCM algorithm so as to improve its running speed. Then an improved Markov random field model is used to improve the algorithm, so that its antinoise ability can be improved. Experimental results show that the algorithm put forward in this paper has obvious advantages in image segmentation speed and segmentation effect.

  14. Histogram equalization with Bayesian estimation for noise robust speech recognition.

    Science.gov (United States)

    Suh, Youngjoo; Kim, Hoirin

    2018-02-01

    The histogram equalization approach is an efficient feature normalization technique for noise robust automatic speech recognition. However, it suffers from performance degradation when some fundamental conditions are not satisfied in the test environment. To remedy these limitations of the original histogram equalization methods, class-based histogram equalization approach has been proposed. Although this approach showed substantial performance improvement under noise environments, it still suffers from performance degradation due to the overfitting problem when test data are insufficient. To address this issue, the proposed histogram equalization technique employs the Bayesian estimation method in the test cumulative distribution function estimation. It was reported in a previous study conducted on the Aurora-4 task that the proposed approach provided substantial performance gains in speech recognition systems based on the acoustic modeling of the Gaussian mixture model-hidden Markov model. In this work, the proposed approach was examined in speech recognition systems with deep neural network-hidden Markov model (DNN-HMM), the current mainstream speech recognition approach where it also showed meaningful performance improvement over the conventional maximum likelihood estimation-based method. The fusion of the proposed features with the mel-frequency cepstral coefficients provided additional performance gains in DNN-HMM systems, which otherwise suffer from performance degradation in the clean test condition.

  15. Quantum Graphical Models and Belief Propagation

    International Nuclear Information System (INIS)

    Leifer, M.S.; Poulin, D.

    2008-01-01

    Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described

  16. Uncovering and testing the fuzzy clusters based on lumped Markov chain in complex network.

    Science.gov (United States)

    Jing, Fan; Jianbin, Xie; Jinlong, Wang; Jinshuai, Qu

    2013-01-01

    Identifying clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. By means of a lumped Markov chain model of a random walker, we propose two novel ways of inferring the lumped markov transition matrix. Furthermore, some useful results are proposed based on the analysis of the properties of the lumped Markov process. To find the best partition of complex networks, a novel framework including two algorithms for network partition based on the optimal lumped Markovian dynamics is derived to solve this problem. The algorithms are constructed to minimize the objective function under this framework. It is demonstrated by the simulation experiments that our algorithms can efficiently determine the probabilities with which a node belongs to different clusters during the learning process and naturally supports the fuzzy partition. Moreover, they are successfully applied to real-world network, including the social interactions between members of a karate club.

  17. Exact distribution of a pattern in a set of random sequences generated by a Markov source: applications to biological data.

    Science.gov (United States)

    Nuel, Gregory; Regad, Leslie; Martin, Juliette; Camproux, Anne-Claude

    2010-01-26

    In bioinformatics it is common to search for a pattern of interest in a potentially large set of rather short sequences (upstream gene regions, proteins, exons, etc.). Although many methodological approaches allow practitioners to compute the distribution of a pattern count in a random sequence generated by a Markov source, no specific developments have taken into account the counting of occurrences in a set of independent sequences. We aim to address this problem by deriving efficient approaches and algorithms to perform these computations both for low and high complexity patterns in the framework of homogeneous or heterogeneous Markov models. The latest advances in the field allowed us to use a technique of optimal Markov chain embedding based on deterministic finite automata to introduce three innovative algorithms. Algorithm 1 is the only one able to deal with heterogeneous models. It also permits to avoid any product of convolution of the pattern distribution in individual sequences. When working with homogeneous models, Algorithm 2 yields a dramatic reduction in the complexity by taking advantage of previous computations to obtain moment generating functions efficiently. In the particular case of low or moderate complexity patterns, Algorithm 3 exploits power computation and binary decomposition to further reduce the time complexity to a logarithmic scale. All these algorithms and their relative interest in comparison with existing ones were then tested and discussed on a toy-example and three biological data sets: structural patterns in protein loop structures, PROSITE signatures in a bacterial proteome, and transcription factors in upstream gene regions. On these data sets, we also compared our exact approaches to the tempting approximation that consists in concatenating the sequences in the data set into a single sequence. Our algorithms prove to be effective and able to handle real data sets with multiple sequences, as well as biological patterns of

  18. Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

    Science.gov (United States)

    Hadjidoukas, P. E.; Angelikopoulos, P.; Papadimitriou, C.; Koumoutsakos, P.

    2015-03-01

    We present Π4U, an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.

  19. Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

    International Nuclear Information System (INIS)

    Hadjidoukas, P.E.; Angelikopoulos, P.; Papadimitriou, C.; Koumoutsakos, P.

    2015-01-01

    We present Π4U, 1 an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow

  20. Nonlinearly perturbed semi-Markov processes

    CERN Document Server

    Silvestrov, Dmitrii

    2017-01-01

    The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will cont...

  1. Variational data assimilation using targetted random walks

    KAUST Repository

    Cotter, S. L.

    2011-02-15

    The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis. In either of these scenarios, it can be important to assess uncertainties in the assimilated state. Ideally, it is desirable to have complete information concerning the Bayesian posterior distribution for unknown state given data. We show that complete computational probing of this posterior distribution is now within the reach in the offline situation. We introduce a Markov chain-Monte Carlo (MCMC) method which enables us to directly sample from the Bayesian posterior distribution on the unknown functions of interest given observations. Since we are aware that these methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however, more sophisticated MCMC methods are available which exploit derivative information. For simplicity of exposition, we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number flow in a two-dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces. © 2011 John Wiley & Sons, Ltd.

  2. Random walk of the baryon number

    International Nuclear Information System (INIS)

    Kazaryan, A.M.; Khlebnikov, S.Y.; Shaposhnikov, M.E.

    1989-01-01

    A new approach is suggested for the anomalous nonconservation of baryon number in the electroweak theory at high temperatures. Arguments are presented in support of the idea that the baryon-number changing reactions may be viewed as random Markov processes. Making use of the general theory of Markov processes, the Fokker--Planck equation for the baryon-number distribution density is obtained and kinetic coefficients are calculated

  3. Nonlinear Markov processes: Deterministic case

    International Nuclear Information System (INIS)

    Frank, T.D.

    2008-01-01

    Deterministic Markov processes that exhibit nonlinear transition mechanisms for probability densities are studied. In this context, the following issues are addressed: Markov property, conditional probability densities, propagation of probability densities, multistability in terms of multiple stationary distributions, stability analysis of stationary distributions, and basin of attraction of stationary distribution

  4. Ensemble Bayesian forecasting system Part I: Theory and algorithms

    Science.gov (United States)

    Herr, Henry D.; Krzysztofowicz, Roman

    2015-05-01

    The ensemble Bayesian forecasting system (EBFS), whose theory was published in 2001, is developed for the purpose of quantifying the total uncertainty about a discrete-time, continuous-state, non-stationary stochastic process such as a time series of stages, discharges, or volumes at a river gauge. The EBFS is built of three components: an input ensemble forecaster (IEF), which simulates the uncertainty associated with random inputs; a deterministic hydrologic model (of any complexity), which simulates physical processes within a river basin; and a hydrologic uncertainty processor (HUP), which simulates the hydrologic uncertainty (an aggregate of all uncertainties except input). It works as a Monte Carlo simulator: an ensemble of time series of inputs (e.g., precipitation amounts) generated by the IEF is transformed deterministically through a hydrologic model into an ensemble of time series of outputs, which is next transformed stochastically by the HUP into an ensemble of time series of predictands (e.g., river stages). Previous research indicated that in order to attain an acceptable sampling error, the ensemble size must be on the order of hundreds (for probabilistic river stage forecasts and probabilistic flood forecasts) or even thousands (for probabilistic stage transition forecasts). The computing time needed to run the hydrologic model this many times renders the straightforward simulations operationally infeasible. This motivates the development of the ensemble Bayesian forecasting system with randomization (EBFSR), which takes full advantage of the analytic meta-Gaussian HUP and generates multiple ensemble members after each run of the hydrologic model; this auxiliary randomization reduces the required size of the meteorological input ensemble and makes it operationally feasible to generate a Bayesian ensemble forecast of large size. Such a forecast quantifies the total uncertainty, is well calibrated against the prior (climatic) distribution of

  5. Gaussian process-based Bayesian nonparametric inference of population size trajectories from gene genealogies.

    Science.gov (United States)

    Palacios, Julia A; Minin, Vladimir N

    2013-03-01

    Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method. Copyright © 2013, The International Biometric Society.

  6. Spectral methods for quantum Markov chains

    Energy Technology Data Exchange (ETDEWEB)

    Szehr, Oleg

    2014-05-08

    The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.

  7. Spectral methods for quantum Markov chains

    International Nuclear Information System (INIS)

    Szehr, Oleg

    2014-01-01

    The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.

  8. Comparing energy sources for surgical ablation of atrial fibrillation: a Bayesian network meta-analysis of randomized, controlled trials.

    Science.gov (United States)

    Phan, Kevin; Xie, Ashleigh; Kumar, Narendra; Wong, Sophia; Medi, Caroline; La Meir, Mark; Yan, Tristan D

    2015-08-01

    Simplified maze procedures involving radiofrequency, cryoenergy and microwave energy sources have been increasingly utilized for surgical treatment of atrial fibrillation as an alternative to the traditional cut-and-sew approach. In the absence of direct comparisons, a Bayesian network meta-analysis is another alternative to assess the relative effect of different treatments, using indirect evidence. A Bayesian meta-analysis of indirect evidence was performed using 16 published randomized trials identified from 6 databases. Rank probability analysis was used to rank each intervention in terms of their probability of having the best outcome. Sinus rhythm prevalence beyond the 12-month follow-up was similar between the cut-and-sew, microwave and radiofrequency approaches, which were all ranked better than cryoablation (respectively, 39, 36, and 25 vs 1%). The cut-and-sew maze was ranked worst in terms of mortality outcomes compared with microwave, radiofrequency and cryoenergy (2 vs 19, 34, and 24%, respectively). The cut-and-sew maze procedure was associated with significantly lower stroke rates compared with microwave ablation [odds ratio <0.01; 95% confidence interval 0.00, 0.82], and ranked the best in terms of pacemaker requirements compared with microwave, radiofrequency and cryoenergy (81 vs 14, and 1, <0.01% respectively). Bayesian rank probability analysis shows that the cut-and-sew approach is associated with the best outcomes in terms of sinus rhythm prevalence and stroke outcomes, and remains the gold standard approach for AF treatment. Given the limitations of indirect comparison analysis, these results should be viewed with caution and not over-interpreted. © The Author 2014. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery. All rights reserved.

  9. Bayesian methods for hackers probabilistic programming and Bayesian inference

    CERN Document Server

    Davidson-Pilon, Cameron

    2016-01-01

    Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples a...

  10. Multi-level Bayesian analyses for single- and multi-vehicle freeway crashes.

    Science.gov (United States)

    Yu, Rongjie; Abdel-Aty, Mohamed

    2013-09-01

    This study presents multi-level analyses for single- and multi-vehicle crashes on a mountainous freeway. Data from a 15-mile mountainous freeway section on I-70 were investigated. Both aggregate and disaggregate models for the two crash conditions were developed. Five years of crash data were used in the aggregate investigation, while the disaggregate models utilized one year of crash data along with real-time traffic and weather data. For the aggregate analyses, safety performance functions were developed for the purpose of revealing the contributing factors for each crash type. Two methodologies, a Bayesian bivariate Poisson-lognormal model and a Bayesian hierarchical Poisson model with correlated random effects, were estimated to simultaneously analyze the two crash conditions with consideration of possible correlations. Except for the factors related to geometric characteristics, two exposure parameters (annual average daily traffic and segment length) were included. Two different sets of significant explanatory and exposure variables were identified for the single-vehicle (SV) and multi-vehicle (MV) crashes. It was found that the Bayesian bivariate Poisson-lognormal model is superior to the Bayesian hierarchical Poisson model, the former with a substantially lower DIC and more significant variables. In addition to the aggregate analyses, microscopic real-time crash risk evaluation models were developed for the two crash conditions. Multi-level Bayesian logistic regression models were estimated with the random parameters accounting for seasonal variations, crash-unit-level diversity and segment-level random effects capturing unobserved heterogeneity caused by the geometric characteristics. The model results indicate that the effects of the selected variables on crash occurrence vary across seasons and crash units; and that geometric characteristic variables contribute to the segment variations: the more unobserved heterogeneity have been accounted, the better

  11. Monte Carlo simulation of Markov unreliability models

    International Nuclear Information System (INIS)

    Lewis, E.E.; Boehm, F.

    1984-01-01

    A Monte Carlo method is formulated for the evaluation of the unrealibility of complex systems with known component failure and repair rates. The formulation is in terms of a Markov process allowing dependences between components to be modeled and computational efficiencies to be achieved in the Monte Carlo simulation. Two variance reduction techniques, forced transition and failure biasing, are employed to increase computational efficiency of the random walk procedure. For an example problem these result in improved computational efficiency by more than three orders of magnitudes over analog Monte Carlo. The method is generalized to treat problems with distributed failure and repair rate data, and a batching technique is introduced and shown to result in substantial increases in computational efficiency for an example problem. A method for separating the variance due to the data uncertainty from that due to the finite number of random walks is presented. (orig.)

  12. Markov Chains for Investigating and Predicting Migration: A Case from Southwestern China

    Science.gov (United States)

    Qin, Bo; Wang, Yiyu; Xu, Haoming

    2018-03-01

    In order to accurately predict the population’s happiness, this paper conducted two demographic surveys on a new district of a city in western China, and carried out a dynamic analysis using related mathematical methods. This paper argues that the migration of migrants in the city will change the pattern of spatial distribution of human resources in the city and thus affect the social and economic development in all districts. The migration status of the population will change randomly with the passage of time, so it can be predicted and analyzed through the Markov process. The Markov process provides the local government and decision-making bureau a valid basis for the dynamic analysis of the mobility of migrants in the city as well as the ways for promoting happiness of local people’s lives.

  13. Polynomial Chaos Surrogates for Bayesian Inference

    KAUST Repository

    Le Maitre, Olivier

    2016-01-06

    The Bayesian inference is a popular probabilistic method to solve inverse problems, such as the identification of field parameter in a PDE model. The inference rely on the Bayes rule to update the prior density of the sought field, from observations, and derive its posterior distribution. In most cases the posterior distribution has no explicit form and has to be sampled, for instance using a Markov-Chain Monte Carlo method. In practice the prior field parameter is decomposed and truncated (e.g. by means of Karhunen- Lo´eve decomposition) to recast the inference problem into the inference of a finite number of coordinates. Although proved effective in many situations, the Bayesian inference as sketched above faces several difficulties requiring improvements. First, sampling the posterior can be a extremely costly task as it requires multiple resolutions of the PDE model for different values of the field parameter. Second, when the observations are not very much informative, the inferred parameter field can highly depends on its prior which can be somehow arbitrary. These issues have motivated the introduction of reduced modeling or surrogates for the (approximate) determination of the parametrized PDE solution and hyperparameters in the description of the prior field. Our contribution focuses on recent developments in these two directions: the acceleration of the posterior sampling by means of Polynomial Chaos expansions and the efficient treatment of parametrized covariance functions for the prior field. We also discuss the possibility of making such approach adaptive to further improve its efficiency.

  14. Bayesian neural network modeling of tree-ring temperature variability record from the Western Himalayas

    Directory of Open Access Journals (Sweden)

    R. K. Tiwari

    2011-08-01

    Full Text Available A novel technique based on the Bayesian neural network (BNN theory is developed and employed to model the temperature variation record from the Western Himalayas. In order to estimate an a posteriori probability function, the BNN is trained with the Hybrid Monte Carlo (HMC/Markov Chain Monte Carlo (MCMC simulations algorithm. The efficacy of the new algorithm is tested on the well known chaotic, first order autoregressive (AR and random models and then applied to model the temperature variation record decoded from the tree-ring widths of the Western Himalayas for the period spanning over 1226–2000 AD. For modeling the actual tree-ring temperature data, optimum network parameters are chosen appropriately and then cross-validation test is performed to ensure the generalization skill of the network on the new data set. Finally, prediction result based on the BNN model is compared with the conventional artificial neural network (ANN and the AR linear models results. The comparative results show that the BNN based analysis makes better prediction than the ANN and the AR models. The new BNN modeling approach provides a viable tool for climate studies and could also be exploited for modeling other kinds of environmental data.

  15. Decision Making under Uncertainty: A Neural Model based on Partially Observable Markov Decision Processes

    Directory of Open Access Journals (Sweden)

    Rajesh P N Rao

    2010-11-01

    Full Text Available A fundamental problem faced by animals is learning to select actions based on noisy sensory information and incomplete knowledge of the world. It has been suggested that the brain engages in Bayesian inference during perception but how such probabilistic representations are used to select actions has remained unclear. Here we propose a neural model of action selection and decision making based on the theory of partially observable Markov decision processes (POMDPs. Actions are selected based not on a single optimal estimate of state but on the posterior distribution over states (the belief state. We show how such a model provides a unified framework for explaining experimental results in decision making that involve both information gathering and overt actions. The model utilizes temporal difference (TD learning for maximizing expected reward. The resulting neural architecture posits an active role for the neocortex in belief computation while ascribing a role to the basal ganglia in belief representation, value computation, and action selection. When applied to the random dots motion discrimination task, model neurons representing belief exhibit responses similar to those of LIP neurons in primate neocortex. The appropriate threshold for switching from information gathering to overt actions emerges naturally during reward maximization. Additionally, the time course of reward prediction error in the model shares similarities with dopaminergic responses in the basal ganglia during the random dots task. For tasks with a deadline, the model learns a decision making strategy that changes with elapsed time, predicting a collapsing decision threshold consistent with some experimental studies. The model provides a new framework for understanding neural decision making and suggests an important role for interactions between the neocortex and the basal ganglia in learning the mapping between probabilistic sensory representations and actions that maximize

  16. Bayesian Modeling of ChIP-chip Data Through a High-Order Ising Model

    KAUST Repository

    Mo, Qianxing

    2010-01-29

    ChIP-chip experiments are procedures that combine chromatin immunoprecipitation (ChIP) and DNA microarray (chip) technology to study a variety of biological problems, including protein-DNA interaction, histone modification, and DNA methylation. The most important feature of ChIP-chip data is that the intensity measurements of probes are spatially correlated because the DNA fragments are hybridized to neighboring probes in the experiments. We propose a simple, but powerful Bayesian hierarchical approach to ChIP-chip data through an Ising model with high-order interactions. The proposed method naturally takes into account the intrinsic spatial structure of the data and can be used to analyze data from multiple platforms with different genomic resolutions. The model parameters are estimated using the Gibbs sampler. The proposed method is illustrated using two publicly available data sets from Affymetrix and Agilent platforms, and compared with three alternative Bayesian methods, namely, Bayesian hierarchical model, hierarchical gamma mixture model, and Tilemap hidden Markov model. The numerical results indicate that the proposed method performs as well as the other three methods for the data from Affymetrix tiling arrays, but significantly outperforms the other three methods for the data from Agilent promoter arrays. In addition, we find that the proposed method has better operating characteristics in terms of sensitivities and false discovery rates under various scenarios. © 2010, The International Biometric Society.

  17. Spectral analysis of the IntCal98 calibration curve: a Bayesian view

    International Nuclear Information System (INIS)

    Palonen, V.; Tikkanen, P.

    2004-01-01

    Preliminary results from a Bayesian approach to find periodicities in the IntCal98 calibration curve are given. It has been shown in the literature that the discrete Fourier transform (Schuster periodogram) corresponds to the use of an approximate Bayesian model of one harmonic frequency and Gaussian noise. Advantages of the Bayesian approach include the possibility to use models for variable, attenuated and multiple frequencies, the capability to analyze unevenly spaced data and the possibility to assess the significance and uncertainties of spectral estimates. In this work, a new Bayesian model using random walk noise to take care of the trend in the data is developed. Both Bayesian models are described and the first results of the new model are reported and compared with results from straightforward discrete-Fourier-transform and maximum-entropy-method spectral analyses

  18. A Bayesian method for assessing multiscalespecies-habitat relationships

    Science.gov (United States)

    Stuber, Erica F.; Gruber, Lutz F.; Fontaine, Joseph J.

    2017-01-01

    ContextScientists face several theoretical and methodological challenges in appropriately describing fundamental wildlife-habitat relationships in models. The spatial scales of habitat relationships are often unknown, and are expected to follow a multi-scale hierarchy. Typical frequentist or information theoretic approaches often suffer under collinearity in multi-scale studies, fail to converge when models are complex or represent an intractable computational burden when candidate model sets are large.ObjectivesOur objective was to implement an automated, Bayesian method for inference on the spatial scales of habitat variables that best predict animal abundance.MethodsWe introduce Bayesian latent indicator scale selection (BLISS), a Bayesian method to select spatial scales of predictors using latent scale indicator variables that are estimated with reversible-jump Markov chain Monte Carlo sampling. BLISS does not suffer from collinearity, and substantially reduces computation time of studies. We present a simulation study to validate our method and apply our method to a case-study of land cover predictors for ring-necked pheasant (Phasianus colchicus) abundance in Nebraska, USA.ResultsOur method returns accurate descriptions of the explanatory power of multiple spatial scales, and unbiased and precise parameter estimates under commonly encountered data limitations including spatial scale autocorrelation, effect size, and sample size. BLISS outperforms commonly used model selection methods including stepwise and AIC, and reduces runtime by 90%.ConclusionsGiven the pervasiveness of scale-dependency in ecology, and the implications of mismatches between the scales of analyses and ecological processes, identifying the spatial scales over which species are integrating habitat information is an important step in understanding species-habitat relationships. BLISS is a widely applicable method for identifying important spatial scales, propagating scale uncertainty, and

  19. Vulnerability of networks of interacting Markov chains.

    Science.gov (United States)

    Kocarev, L; Zlatanov, N; Trajanov, D

    2010-05-13

    The concept of vulnerability is introduced for a model of random, dynamical interactions on networks. In this model, known as the influence model, the nodes are arranged in an arbitrary network, while the evolution of the status at a node is according to an internal Markov chain, but with transition probabilities that depend not only on the current status of that node but also on the statuses of the neighbouring nodes. Vulnerability is treated analytically and numerically for several networks with different topological structures, as well as for two real networks--the network of infrastructures and the EU power grid--identifying the most vulnerable nodes of these networks.

  20. Mixed Vehicle Flow At Signalized Intersection: Markov Chain Analysis

    Directory of Open Access Journals (Sweden)

    Gertsbakh Ilya B.

    2015-09-01

    Full Text Available We assume that a Poisson flow of vehicles arrives at isolated signalized intersection, and each vehicle, independently of others, represents a random number X of passenger car units (PCU’s. We analyze numerically the stationary distribution of the queue process {Zn}, where Zn is the number of PCU’s in a queue at the beginning of the n-th red phase, n → ∞. We approximate the number Yn of PCU’s arriving during one red-green cycle by a two-parameter Negative Binomial Distribution (NBD. The well-known fact is that {Zn} follow an infinite-state Markov chain. We approximate its stationary distribution using a finite-state Markov chain. We show numerically that there is a strong dependence of the mean queue length E[Zn] in equilibrium on the input distribution of Yn and, in particular, on the ”over dispersion” parameter γ= Var[Yn]/E[Yn]. For Poisson input, γ = 1. γ > 1 indicates presence of heavy-tailed input. In reality it means that a relatively large ”portion” of PCU’s, considerably exceeding the average, may arrive with high probability during one red-green cycle. Empirical formulas are presented for an accurate estimation of mean queue length as a function of load and g of the input flow. Using the Markov chain technique, we analyze the mean ”virtual” delay time for a car which always arrives at the beginning of the red phase.

  1. An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations

    Science.gov (United States)

    Farr, W. M.; Mandel, I.; Stevens, D.

    2015-01-01

    Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient ‘global’ proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580

  2. Bayesian non parametric modelling of Higgs pair production

    Directory of Open Access Journals (Sweden)

    Scarpa Bruno

    2017-01-01

    Full Text Available Statistical classification models are commonly used to separate a signal from a background. In this talk we face the problem of isolating the signal of Higgs pair production using the decay channel in which each boson decays into a pair of b-quarks. Typically in this context non parametric methods are used, such as Random Forests or different types of boosting tools. We remain in the same non-parametric framework, but we propose to face the problem following a Bayesian approach. A Dirichlet process is used as prior for the random effects in a logit model which is fitted by leveraging the Polya-Gamma data augmentation. Refinements of the model include the insertion in the simple model of P-splines to relate explanatory variables with the response and the use of Bayesian trees (BART to describe the atoms in the Dirichlet process.

  3. SAR-based change detection using hypothesis testing and Markov random field modelling

    Science.gov (United States)

    Cao, W.; Martinis, S.

    2015-04-01

    The objective of this study is to automatically detect changed areas caused by natural disasters from bi-temporal co-registered and calibrated TerraSAR-X data. The technique in this paper consists of two steps: Firstly, an automatic coarse detection step is applied based on a statistical hypothesis test for initializing the classification. The original analytical formula as proposed in the constant false alarm rate (CFAR) edge detector is reviewed and rewritten in a compact form of the incomplete beta function, which is a builtin routine in commercial scientific software such as MATLAB and IDL. Secondly, a post-classification step is introduced to optimize the noisy classification result in the previous step. Generally, an optimization problem can be formulated as a Markov random field (MRF) on which the quality of a classification is measured by an energy function. The optimal classification based on the MRF is related to the lowest energy value. Previous studies provide methods for the optimization problem using MRFs, such as the iterated conditional modes (ICM) algorithm. Recently, a novel algorithm was presented based on graph-cut theory. This method transforms a MRF to an equivalent graph and solves the optimization problem by a max-flow/min-cut algorithm on the graph. In this study this graph-cut algorithm is applied iteratively to improve the coarse classification. At each iteration the parameters of the energy function for the current classification are set by the logarithmic probability density function (PDF). The relevant parameters are estimated by the method of logarithmic cumulants (MoLC). Experiments are performed using two flood events in Germany and Australia in 2011 and a forest fire on La Palma in 2009 using pre- and post-event TerraSAR-X data. The results show convincing coarse classifications and considerable improvement by the graph-cut post-classification step.

  4. Bayesian methodology for reliability model acceptance

    International Nuclear Information System (INIS)

    Zhang Ruoxue; Mahadevan, Sankaran

    2003-01-01

    This paper develops a methodology to assess the reliability computation model validity using the concept of Bayesian hypothesis testing, by comparing the model prediction and experimental observation, when there is only one computational model available to evaluate system behavior. Time-independent and time-dependent problems are investigated, with consideration of both cases: with and without statistical uncertainty in the model. The case of time-independent failure probability prediction with no statistical uncertainty is a straightforward application of Bayesian hypothesis testing. However, for the life prediction (time-dependent reliability) problem, a new methodology is developed in this paper to make the same Bayesian hypothesis testing concept applicable. With the existence of statistical uncertainty in the model, in addition to the application of a predictor estimator of the Bayes factor, the uncertainty in the Bayes factor is explicitly quantified through treating it as a random variable and calculating the probability that it exceeds a specified value. The developed method provides a rational criterion to decision-makers for the acceptance or rejection of the computational model

  5. Tokunaga and Horton self-similarity for level set trees of Markov chains

    International Nuclear Information System (INIS)

    Zaliapin, Ilia; Kovchegov, Yevgeniy

    2012-01-01

    Highlights: ► Self-similar properties of the level set trees for Markov chains are studied. ► Tokunaga and Horton self-similarity are established for symmetric Markov chains and regular Brownian motion. ► Strong, distributional self-similarity is established for symmetric Markov chains with exponential jumps. ► It is conjectured that fractional Brownian motions are Tokunaga self-similar. - Abstract: The Horton and Tokunaga branching laws provide a convenient framework for studying self-similarity in random trees. The Horton self-similarity is a weaker property that addresses the principal branching in a tree; it is a counterpart of the power-law size distribution for elements of a branching system. The stronger Tokunaga self-similarity addresses so-called side branching. The Horton and Tokunaga self-similarity have been empirically established in numerous observed and modeled systems, and proven for two paradigmatic models: the critical Galton–Watson branching process with finite progeny and the finite-tree representation of a regular Brownian excursion. This study establishes the Tokunaga and Horton self-similarity for a tree representation of a finite symmetric homogeneous Markov chain. We also extend the concept of Horton and Tokunaga self-similarity to infinite trees and establish self-similarity for an infinite-tree representation of a regular Brownian motion. We conjecture that fractional Brownian motions are also Tokunaga and Horton self-similar, with self-similarity parameters depending on the Hurst exponent.

  6. Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling

    Directory of Open Access Journals (Sweden)

    Rathinasamy Sakthivel

    2018-01-01

    Full Text Available The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.

  7. Stochastic models with heteroskedasticity: a Bayesian approach for Ibovespa returns - doi: 10.4025/actascitechnol.v35i2.13547

    Directory of Open Access Journals (Sweden)

    Sandra Cristina de Oliveira

    2013-04-01

    Full Text Available Current research compares the Bayesian estimates obtained for the parameters of processes of ARCH family with normal and Student’s t distributions for the conditional distribution of the return series. A non-informative prior distribution was adopted and a reparameterization of models under analysis was taken into account to map parameters’ space into real space. The procedure adopts a normal prior distribution for the transformed parameters. The posterior summaries were obtained by Monte Carlo Markov Chain (MCMC simulation methods. The methodology was evaluated by a series of Bovespa Index returns and the predictive ordinate criterion was employed to select the best adjustment model to the data. Results show that, as a rule, the proposed Bayesian approach provides satisfactory estimates and that the GARCH process with Student’s t distribution adjusted better to the data.  

  8. A Novel Method for Decoding Any High-Order Hidden Markov Model

    Directory of Open Access Journals (Sweden)

    Fei Ye

    2014-01-01

    Full Text Available This paper proposes a novel method for decoding any high-order hidden Markov model. First, the high-order hidden Markov model is transformed into an equivalent first-order hidden Markov model by Hadar’s transformation. Next, the optimal state sequence of the equivalent first-order hidden Markov model is recognized by the existing Viterbi algorithm of the first-order hidden Markov model. Finally, the optimal state sequence of the high-order hidden Markov model is inferred from the optimal state sequence of the equivalent first-order hidden Markov model. This method provides a unified algorithm framework for decoding hidden Markov models including the first-order hidden Markov model and any high-order hidden Markov model.

  9. Bayesian energy landscape tilting: towards concordant models of molecular ensembles.

    Science.gov (United States)

    Beauchamp, Kyle A; Pande, Vijay S; Das, Rhiju

    2014-03-18

    Predicting biological structure has remained challenging for systems such as disordered proteins that take on myriad conformations. Hybrid simulation/experiment strategies have been undermined by difficulties in evaluating errors from computational model inaccuracies and data uncertainties. Building on recent proposals from maximum entropy theory and nonequilibrium thermodynamics, we address these issues through a Bayesian energy landscape tilting (BELT) scheme for computing Bayesian hyperensembles over conformational ensembles. BELT uses Markov chain Monte Carlo to directly sample maximum-entropy conformational ensembles consistent with a set of input experimental observables. To test this framework, we apply BELT to model trialanine, starting from disagreeing simulations with the force fields ff96, ff99, ff99sbnmr-ildn, CHARMM27, and OPLS-AA. BELT incorporation of limited chemical shift and (3)J measurements gives convergent values of the peptide's α, β, and PPII conformational populations in all cases. As a test of predictive power, all five BELT hyperensembles recover set-aside measurements not used in the fitting and report accurate errors, even when starting from highly inaccurate simulations. BELT's principled framework thus enables practical predictions for complex biomolecular systems from discordant simulations and sparse data. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  10. Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model

    KAUST Repository

    Mondal, Anirban

    2014-07-03

    We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. The Karhunen-Loeve expansion is used for dimension reduction of the random field. Furthermore, we use a hierarchical Bayes model to inject multiscale data in the modeling framework. In this Bayesian framework, we show that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of MCMC) and are compounded by high dimensionality of the posterior. We develop two-stage reversible jump MCMC that has the ability to screen the bad proposals in the first inexpensive stage. Numerical results are presented by analyzing simulated as well as real data from hydrocarbon reservoir. This article has supplementary material available online. © 2014 American Statistical Association and the American Society for Quality.

  11. Comparing nonparametric Bayesian tree priors for clonal reconstruction of tumors.

    Science.gov (United States)

    Deshwar, Amit G; Vembu, Shankar; Morris, Quaid

    2015-01-01

    Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the phylogeny and genotype of major subclonal lineages represented in the population of cancer cells. We also propose new split-merge updates tailored to the subclonal reconstruction problem that improve the mixing time of Markov chains. In comparisons with the tree-structured stick breaking prior used in PhyloSub, we demonstrate superior mixing and running time using the treeCRP with our new split-merge procedures. We also show that given the same number of samples, TSSB and treeCRP have similar ability to recover the subclonal structure of a tumor…

  12. Bayesian informative dropout model for longitudinal binary data with random effects using conditional and joint modeling approaches.

    Science.gov (United States)

    Chan, Jennifer S K

    2016-05-01

    Dropouts are common in longitudinal study. If the dropout probability depends on the missing observations at or after dropout, this type of dropout is called informative (or nonignorable) dropout (ID). Failure to accommodate such dropout mechanism into the model will bias the parameter estimates. We propose a conditional autoregressive model for longitudinal binary data with an ID model such that the probabilities of positive outcomes as well as the drop-out indicator in each occasion are logit linear in some covariates and outcomes. This model adopting a marginal model for outcomes and a conditional model for dropouts is called a selection model. To allow for the heterogeneity and clustering effects, the outcome model is extended to incorporate mixture and random effects. Lastly, the model is further extended to a novel model that models the outcome and dropout jointly such that their dependency is formulated through an odds ratio function. Parameters are estimated by a Bayesian approach implemented using the user-friendly Bayesian software WinBUGS. A methadone clinic dataset is analyzed to illustrate the proposed models. Result shows that the treatment time effect is still significant but weaker after allowing for an ID process in the data. Finally the effect of drop-out on parameter estimates is evaluated through simulation studies. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  13. A Bayesian Analysis of Unobserved Component Models Using Ox

    Directory of Open Access Journals (Sweden)

    Charles S. Bos

    2011-05-01

    Full Text Available This article details a Bayesian analysis of the Nile river flow data, using a similar state space model as other articles in this volume. For this data set, Metropolis-Hastings and Gibbs sampling algorithms are implemented in the programming language Ox. These Markov chain Monte Carlo methods only provide output conditioned upon the full data set. For filtered output, conditioning only on past observations, the particle filter is introduced. The sampling methods are flexible, and this advantage is used to extend the model to incorporate a stochastic volatility process. The volatility changes both in the Nile data and also in daily S&P 500 return data are investigated. The posterior density of parameters and states is found to provide information on which elements of the model are easily identifiable, and which elements are estimated with less precision.

  14. Bayesian Non-Parametric Mixtures of GARCH(1,1 Models

    Directory of Open Access Journals (Sweden)

    John W. Lau

    2012-01-01

    Full Text Available Traditional GARCH models describe volatility levels that evolve smoothly over time, generated by a single GARCH regime. However, nonstationary time series data may exhibit abrupt changes in volatility, suggesting changes in the underlying GARCH regimes. Further, the number and times of regime changes are not always obvious. This article outlines a nonparametric mixture of GARCH models that is able to estimate the number and time of volatility regime changes by mixing over the Poisson-Kingman process. The process is a generalisation of the Dirichlet process typically used in nonparametric models for time-dependent data provides a richer clustering structure, and its application to time series data is novel. Inference is Bayesian, and a Markov chain Monte Carlo algorithm to explore the posterior distribution is described. The methodology is illustrated on the Standard and Poor's 500 financial index.

  15. Finite Markov processes and their applications

    CERN Document Server

    Iosifescu, Marius

    2007-01-01

    A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch

  16. Markov chains models, algorithms and applications

    CERN Document Server

    Ching, Wai-Ki; Ng, Michael K; Siu, Tak-Kuen

    2013-01-01

    This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters.  Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods

  17. A scaling analysis of a cat and mouse Markov chain

    NARCIS (Netherlands)

    Litvak, Nelli; Robert, Philippe

    2012-01-01

    If ($C_n$) a Markov chain on a discrete state space $S$, a Markov chain ($C_n, M_n$) on the product space $S \\times S$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain behaves like the original Markov chain and the second component changes only when both

  18. A high-fidelity weather time series generator using the Markov Chain process on a piecewise level

    Science.gov (United States)

    Hersvik, K.; Endrerud, O.-E. V.

    2017-12-01

    A method is developed for generating a set of unique weather time-series based on an existing weather series. The method allows statistically valid weather variations to take place within repeated simulations of offshore operations. The numerous generated time series need to share the same statistical qualities as the original time series. Statistical qualities here refer mainly to the distribution of weather windows available for work, including durations and frequencies of such weather windows, and seasonal characteristics. The method is based on the Markov chain process. The core new development lies in how the Markov Process is used, specifically by joining small pieces of random length time series together rather than joining individual weather states, each from a single time step, which is a common solution found in the literature. This new Markov model shows favorable characteristics with respect to the requirements set forth and all aspects of the validation performed.

  19. An empirical Bayesian approach for model-based inference of cellular signaling networks

    Directory of Open Access Journals (Sweden)

    Klinke David J

    2009-11-01

    Full Text Available Abstract Background A common challenge in systems biology is to infer mechanistic descriptions of biological process given limited observations of a biological system. Mathematical models are frequently used to represent a belief about the causal relationships among proteins within a signaling network. Bayesian methods provide an attractive framework for inferring the validity of those beliefs in the context of the available data. However, efficient sampling of high-dimensional parameter space and appropriate convergence criteria provide barriers for implementing an empirical Bayesian approach. The objective of this study was to apply an Adaptive Markov chain Monte Carlo technique to a typical study of cellular signaling pathways. Results As an illustrative example, a kinetic model for the early signaling events associated with the epidermal growth factor (EGF signaling network was calibrated against dynamic measurements observed in primary rat hepatocytes. A convergence criterion, based upon the Gelman-Rubin potential scale reduction factor, was applied to the model predictions. The posterior distributions of the parameters exhibited complicated structure, including significant covariance between specific parameters and a broad range of variance among the parameters. The model predictions, in contrast, were narrowly distributed and were used to identify areas of agreement among a collection of experimental studies. Conclusion In summary, an empirical Bayesian approach was developed for inferring the confidence that one can place in a particular model that describes signal transduction mechanisms and for inferring inconsistencies in experimental measurements.

  20. An efficient Bayesian meta-analysis approach for studying cross-phenotype genetic associations.

    Directory of Open Access Journals (Sweden)

    Arunabha Majumdar

    2018-02-01

    Full Text Available Simultaneous analysis of genetic associations with multiple phenotypes may reveal shared genetic susceptibility across traits (pleiotropy. For a locus exhibiting overall pleiotropy, it is important to identify which specific traits underlie this association. We propose a Bayesian meta-analysis approach (termed CPBayes that uses summary-level data across multiple phenotypes to simultaneously measure the evidence of aggregate-level pleiotropic association and estimate an optimal subset of traits associated with the risk locus. This method uses a unified Bayesian statistical framework based on a spike and slab prior. CPBayes performs a fully Bayesian analysis by employing the Markov Chain Monte Carlo (MCMC technique Gibbs sampling. It takes into account heterogeneity in the size and direction of the genetic effects across traits. It can be applied to both cohort data and separate studies of multiple traits having overlapping or non-overlapping subjects. Simulations show that CPBayes can produce higher accuracy in the selection of associated traits underlying a pleiotropic signal than the subset-based meta-analysis ASSET. We used CPBayes to undertake a genome-wide pleiotropic association study of 22 traits in the large Kaiser GERA cohort and detected six independent pleiotropic loci associated with at least two phenotypes. This includes a locus at chromosomal region 1q24.2 which exhibits an association simultaneously with the risk of five different diseases: Dermatophytosis, Hemorrhoids, Iron Deficiency, Osteoporosis and Peripheral Vascular Disease. We provide an R-package 'CPBayes' implementing the proposed method.

  1. Perturbation theory for Markov chains via Wasserstein distance

    NARCIS (Netherlands)

    Rudolf, Daniel; Schweizer, Nikolaus

    2017-01-01

    Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the nth step distributions of two Markov chains

  2. Bayesian binary regression model: an application to in-hospital death after AMI prediction

    Directory of Open Access Journals (Sweden)

    Aparecida D. P. Souza

    2004-08-01

    Full Text Available A Bayesian binary regression model is developed to predict death of patients after acute myocardial infarction (AMI. Markov Chain Monte Carlo (MCMC methods are used to make inference and to evaluate Bayesian binary regression models. A model building strategy based on Bayes factor is proposed and aspects of model validation are extensively discussed in the paper, including the posterior distribution for the c-index and the analysis of residuals. Risk assessment, based on variables easily available within minutes of the patients' arrival at the hospital, is very important to decide the course of the treatment. The identified model reveals itself strongly reliable and accurate, with a rate of correct classification of 88% and a concordance index of 83%.Um modelo bayesiano de regressão binária é desenvolvido para predizer óbito hospitalar em pacientes acometidos por infarto agudo do miocárdio. Métodos de Monte Carlo via Cadeias de Markov (MCMC são usados para fazer inferência e validação. Uma estratégia para construção de modelos, baseada no uso do fator de Bayes, é proposta e aspectos de validação são extensivamente discutidos neste artigo, incluindo a distribuição a posteriori para o índice de concordância e análise de resíduos. A determinação de fatores de risco, baseados em variáveis disponíveis na chegada do paciente ao hospital, é muito importante para a tomada de decisão sobre o curso do tratamento. O modelo identificado se revela fortemente confiável e acurado, com uma taxa de classificação correta de 88% e um índice de concordância de 83%.

  3. Joint Bayesian Stochastic Inversion of Well Logs and Seismic Data for Volumetric Uncertainty Analysis

    Directory of Open Access Journals (Sweden)

    Moslem Moradi

    2015-06-01

    Full Text Available Here in, an application of a new seismic inversion algorithm in one of Iran’s oilfields is described. Stochastic (geostatistical seismic inversion, as a complementary method to deterministic inversion, is perceived as contribution combination of geostatistics and seismic inversion algorithm. This method integrates information from different data sources with different scales, as prior information in Bayesian statistics. Data integration leads to a probability density function (named as a posteriori probability that can yield a model of subsurface. The Markov Chain Monte Carlo (MCMC method is used to sample the posterior probability distribution, and the subsurface model characteristics can be extracted by analyzing a set of the samples. In this study, the theory of stochastic seismic inversion in a Bayesian framework was described and applied to infer P-impedance and porosity models. The comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more detailed information of subsurface character. Since multiple realizations are extracted by this method, an estimation of pore volume and uncertainty in the estimation were analyzed.

  4. Bayesian artificial intelligence

    CERN Document Server

    Korb, Kevin B

    2010-01-01

    Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second EditionNew chapter on Bayesian network classifiersNew section on object-oriente

  5. Neuroevolution Mechanism for Hidden Markov Model

    Directory of Open Access Journals (Sweden)

    Nabil M. Hewahi

    2011-12-01

    Full Text Available Hidden Markov Model (HMM is a statistical model based on probabilities. HMM is becoming one of the major models involved in many applications such as natural language
    processing, handwritten recognition, image processing, prediction systems and many more. In this research we are concerned with finding out the best HMM for a certain application domain. We propose a neuroevolution process that is based first on converting the HMM to a neural network, then generating many neural networks at random where each represents a HMM. We proceed by
    applying genetic operators to obtain new set of neural networks where each represents HMMs, and updating the population. Finally select the best neural network based on a fitness function.

  6. Approximate quantum Markov chains

    CERN Document Server

    Sutter, David

    2018-01-01

    This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...

  7. Derivation of Markov processes that violate detailed balance

    Science.gov (United States)

    Lee, Julian

    2018-03-01

    Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.

  8. Quantum Markov Chain Mixing and Dissipative Engineering

    DEFF Research Database (Denmark)

    Kastoryano, Michael James

    2012-01-01

    This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state...... of the system at the present point in time, but not on the history of events. Very many important processes in nature are of this type, therefore a good understanding of their behaviour has turned out to be very fruitful for science. Markov chains always have a non-empty set of limiting distributions...... (stationary states). The aim of Markov chain mixing is to obtain (upper and/or lower) bounds on the number of steps it takes for the Markov chain to reach a stationary state. The natural quantum extensions of these notions are density matrices and quantum channels. We set out to develop a general mathematical...

  9. Markov chains and semi-Markov models in time-to-event analysis.

    Science.gov (United States)

    Abner, Erin L; Charnigo, Richard J; Kryscio, Richard J

    2013-10-25

    A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields.

  10. Narrowband interference parameterization for sparse Bayesian recovery

    KAUST Repository

    Ali, Anum

    2015-09-11

    This paper addresses the problem of narrowband interference (NBI) in SC-FDMA systems by using tools from compressed sensing and stochastic geometry. The proposed NBI cancellation scheme exploits the frequency domain sparsity of the unknown signal and adopts a Bayesian sparse recovery procedure. This is done by keeping a few randomly chosen sub-carriers data free to sense the NBI signal at the receiver. As Bayesian recovery requires knowledge of some NBI parameters (i.e., mean, variance and sparsity rate), we use tools from stochastic geometry to obtain analytical expressions for the required parameters. Our simulation results validate the analysis and depict suitability of the proposed recovery method for NBI mitigation. © 2015 IEEE.

  11. Simulation-based algorithms for Markov decision processes

    CERN Document Server

    Chang, Hyeong Soo; Fu, Michael C; Marcus, Steven I

    2013-01-01

    Markov decision process (MDP) models are widely used for modeling sequential decision-making problems that arise in engineering, economics, computer science, and the social sciences.  Many real-world problems modeled by MDPs have huge state and/or action spaces, giving an opening to the curse of dimensionality and so making practical solution of the resulting models intractable.  In other cases, the system of interest is too complex to allow explicit specification of some of the MDP model parameters, but simulation samples are readily available (e.g., for random transitions and costs). For these settings, various sampling and population-based algorithms have been developed to overcome the difficulties of computing an optimal solution in terms of a policy and/or value function.  Specific approaches include adaptive sampling, evolutionary policy iteration, evolutionary random policy search, and model reference adaptive search. This substantially enlarged new edition reflects the latest developments in novel ...

  12. Bayesian Sensitivity Analysis of Statistical Models with Missing Data.

    Science.gov (United States)

    Zhu, Hongtu; Ibrahim, Joseph G; Tang, Niansheng

    2014-04-01

    Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures.

  13. Bayesian statistics applied to neutron activation data for reactor flux spectrum analysis

    International Nuclear Information System (INIS)

    Chiesa, Davide; Previtali, Ezio; Sisti, Monica

    2014-01-01

    Highlights: • Bayesian statistics to analyze the neutron flux spectrum from activation data. • Rigorous statistical approach for accurate evaluation of the neutron flux groups. • Cross section and activation data uncertainties included for the problem solution. • Flexible methodology applied to analyze different nuclear reactor flux spectra. • The results are in good agreement with the MCNP simulations of neutron fluxes. - Abstract: In this paper, we present a statistical method, based on Bayesian statistics, to analyze the neutron flux spectrum from the activation data of different isotopes. The experimental data were acquired during a neutron activation experiment performed at the TRIGA Mark II reactor of Pavia University (Italy) in four irradiation positions characterized by different neutron spectra. In order to evaluate the neutron flux spectrum, subdivided in energy groups, a system of linear equations, containing the group effective cross sections and the activation rate data, has to be solved. However, since the system’s coefficients are experimental data affected by uncertainties, a rigorous statistical approach is fundamental for an accurate evaluation of the neutron flux groups. For this purpose, we applied the Bayesian statistical analysis, that allows to include the uncertainties of the coefficients and the a priori information about the neutron flux. A program for the analysis of Bayesian hierarchical models, based on Markov Chain Monte Carlo (MCMC) simulations, was used to define the problem statistical model and solve it. The first analysis involved the determination of the thermal, resonance-intermediate and fast flux components and the dependence of the results on the Prior distribution choice was investigated to confirm the reliability of the Bayesian analysis. After that, the main resonances of the activation cross sections were analyzed to implement multi-group models with finer energy subdivisions that would allow to determine the

  14. Fitting Hidden Markov Models to Psychological Data

    Directory of Open Access Journals (Sweden)

    Ingmar Visser

    2002-01-01

    Full Text Available Markov models have been used extensively in psychology of learning. Applications of hidden Markov models are rare however. This is partially due to the fact that comprehensive statistics for model selection and model assessment are lacking in the psychological literature. We present model selection and model assessment statistics that are particularly useful in applying hidden Markov models in psychology. These statistics are presented and evaluated by simulation studies for a toy example. We compare AIC, BIC and related criteria and introduce a prediction error measure for assessing goodness-of-fit. In a simulation study, two methods of fitting equality constraints are compared. In two illustrative examples with experimental data we apply selection criteria, fit models with constraints and assess goodness-of-fit. First, data from a concept identification task is analyzed. Hidden Markov models provide a flexible approach to analyzing such data when compared to other modeling methods. Second, a novel application of hidden Markov models in implicit learning is presented. Hidden Markov models are used in this context to quantify knowledge that subjects express in an implicit learning task. This method of analyzing implicit learning data provides a comprehensive approach for addressing important theoretical issues in the field.

  15. Inverse Modeling Using Markov Chain Monte Carlo Aided by Adaptive Stochastic Collocation Method with Transformation

    Science.gov (United States)

    Zhang, D.; Liao, Q.

    2016-12-01

    The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of

  16. Zipf exponent of trajectory distribution in the hidden Markov model

    Science.gov (United States)

    Bochkarev, V. V.; Lerner, E. Yu

    2014-03-01

    This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.

  17. Zipf exponent of trajectory distribution in the hidden Markov model

    International Nuclear Information System (INIS)

    Bochkarev, V V; Lerner, E Yu

    2014-01-01

    This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different

  18. Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium

    Science.gov (United States)

    Kapfer, Sebastian C.; Krauth, Werner

    2017-12-01

    We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.

  19. Quantitative utilization of prior biological knowledge in the Bayesian network modeling of gene expression data

    Directory of Open Access Journals (Sweden)

    Gao Shouguo

    2011-08-01

    Full Text Available Abstract Background Bayesian Network (BN is a powerful approach to reconstructing genetic regulatory networks from gene expression data. However, expression data by itself suffers from high noise and lack of power. Incorporating prior biological knowledge can improve the performance. As each type of prior knowledge on its own may be incomplete or limited by quality issues, integrating multiple sources of prior knowledge to utilize their consensus is desirable. Results We introduce a new method to incorporate the quantitative information from multiple sources of prior knowledge. It first uses the Naïve Bayesian classifier to assess the likelihood of functional linkage between gene pairs based on prior knowledge. In this study we included cocitation in PubMed and schematic similarity in Gene Ontology annotation. A candidate network edge reservoir is then created in which the copy number of each edge is proportional to the estimated likelihood of linkage between the two corresponding genes. In network simulation the Markov Chain Monte Carlo sampling algorithm is adopted, and samples from this reservoir at each iteration to generate new candidate networks. We evaluated the new algorithm using both simulated and real gene expression data including that from a yeast cell cycle and a mouse pancreas development/growth study. Incorporating prior knowledge led to a ~2 fold increase in the number of known transcription regulations recovered, without significant change in false positive rate. In contrast, without the prior knowledge BN modeling is not always better than a random selection, demonstrating the necessity in network modeling to supplement the gene expression data with additional information. Conclusion our new development provides a statistical means to utilize the quantitative information in prior biological knowledge in the BN modeling of gene expression data, which significantly improves the performance.

  20. Exact distribution of a pattern in a set of random sequences generated by a Markov source: applications to biological data

    Directory of Open Access Journals (Sweden)

    Regad Leslie

    2010-01-01

    Full Text Available Abstract Background In bioinformatics it is common to search for a pattern of interest in a potentially large set of rather short sequences (upstream gene regions, proteins, exons, etc.. Although many methodological approaches allow practitioners to compute the distribution of a pattern count in a random sequence generated by a Markov source, no specific developments have taken into account the counting of occurrences in a set of independent sequences. We aim to address this problem by deriving efficient approaches and algorithms to perform these computations both for low and high complexity patterns in the framework of homogeneous or heterogeneous Markov models. Results The latest advances in the field allowed us to use a technique of optimal Markov chain embedding based on deterministic finite automata to introduce three innovative algorithms. Algorithm 1 is the only one able to deal with heterogeneous models. It also permits to avoid any product of convolution of the pattern distribution in individual sequences. When working with homogeneous models, Algorithm 2 yields a dramatic reduction in the complexity by taking advantage of previous computations to obtain moment generating functions efficiently. In the particular case of low or moderate complexity patterns, Algorithm 3 exploits power computation and binary decomposition to further reduce the time complexity to a logarithmic scale. All these algorithms and their relative interest in comparison with existing ones were then tested and discussed on a toy-example and three biological data sets: structural patterns in protein loop structures, PROSITE signatures in a bacterial proteome, and transcription factors in upstream gene regions. On these data sets, we also compared our exact approaches to the tempting approximation that consists in concatenating the sequences in the data set into a single sequence. Conclusions Our algorithms prove to be effective and able to handle real data sets with

  1. Bayesian Graphical Models

    DEFF Research Database (Denmark)

    Jensen, Finn Verner; Nielsen, Thomas Dyhre

    2016-01-01

    Mathematically, a Bayesian graphical model is a compact representation of the joint probability distribution for a set of variables. The most frequently used type of Bayesian graphical models are Bayesian networks. The structural part of a Bayesian graphical model is a graph consisting of nodes...

  2. Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models.

    Science.gov (United States)

    Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I

    2018-01-01

    Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

  3. Probabilistic Reachability for Parametric Markov Models

    DEFF Research Database (Denmark)

    Hahn, Ernst Moritz; Hermanns, Holger; Zhang, Lijun

    2011-01-01

    Given a parametric Markov model, we consider the problem of computing the rational function expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression...

  4. Dual Sticky Hierarchical Dirichlet Process Hidden Markov Model and Its Application to Natural Language Description of Motions.

    Science.gov (United States)

    Hu, Weiming; Tian, Guodong; Kang, Yongxin; Yuan, Chunfeng; Maybank, Stephen

    2017-09-25

    In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. On combining the learnt sources and sinks, semantic motion regions, and the learnt sequence of atomic activities, the action represented by the trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.

  5. Prediction of inspection intervals using the Markov analysis; Prediccion de intervalos de inspeccion utilizando analisis de Markov

    Energy Technology Data Exchange (ETDEWEB)

    Rea, R.; Arellano, J. [IIE, Calle Reforma 113, Col. Palmira, Cuernavaca, Morelos (Mexico)]. e-mail: rrea@iie.org.mx

    2005-07-01

    To solve the unmanageable number of states of Markov of systems that have a great number of components, it is intends a modification to the method of Markov, denominated Markov truncated analysis, in which is assumed that it is worthless the dependence among faults of components. With it the number of states is increased in a lineal way (not exponential) with the number of components of the system, simplifying the analysis vastly. As example, the proposed method was applied to the system HPCS of the CLV considering its 18 main components. It thinks about that each component can take three states: operational, with hidden fault and with revealed fault. Additionally, it takes into account the configuration of the system HPCS by means of a block diagram of dependability to estimate their unavailability at level system. The results of the model here proposed are compared with other methods and approaches used to simplify the Markov analysis. It also intends the modification of the intervals of inspection of three components of the system HPCS. This finishes with base in the developed Markov model and in the maximum time allowed by the code ASME (NUREG-1482) to inspect components of systems that are in reservation in nuclear power plants. (Author)

  6. Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification

    Science.gov (United States)

    Arnst, M.; Abello Álvarez, B.; Ponthot, J.-P.; Boman, R.

    2017-11-01

    This paper is concerned with the characterization and the propagation of errors associated with data limitations in polynomial-chaos-based stochastic methods for uncertainty quantification. Such an issue can arise in uncertainty quantification when only a limited amount of data is available. When the available information does not suffice to accurately determine the probability distributions that must be assigned to the uncertain variables, the Bayesian method for assigning these probability distributions becomes attractive because it allows the stochastic model to account explicitly for insufficiency of the available information. In previous work, such applications of the Bayesian method had already been implemented by using the Metropolis-Hastings and Gibbs Markov Chain Monte Carlo (MCMC) methods. In this paper, we present an alternative implementation, which uses an alternative MCMC method built around an Itô stochastic differential equation (SDE) that is ergodic for the Bayesian posterior. We draw together from the mathematics literature a number of formal properties of this Itô SDE that lend support to its use in the implementation of the Bayesian method, and we describe its discretization, including the choice of the free parameters, by using the implicit Euler method. We demonstrate the proposed methodology on a problem of uncertainty quantification in a complex nonlinear engineering application relevant to metal forming.

  7. Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

    Science.gov (United States)

    Antown, Fadi; Dragičević, Davor; Froyland, Gary

    2018-03-01

    The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

  8. Stencil method: a Markov model for transport in porous media

    Science.gov (United States)

    Delgoshaie, A. H.; Tchelepi, H.; Jenny, P.

    2016-12-01

    In porous media the transport of fluid is dominated by flow-field heterogeneity resulting from the underlying transmissibility field. Since the transmissibility is highly uncertain, many realizations of a geological model are used to describe the statistics of the transport phenomena in a Monte Carlo framework. One possible way to avoid the high computational cost of physics-based Monte Carlo simulations is to model the velocity field as a Markov process and use Markov Chain Monte Carlo. In previous works multiple Markov models for discrete velocity processes have been proposed. These models can be divided into two general classes of Markov models in time and Markov models in space. Both of these choices have been shown to be effective to some extent. However some studies have suggested that the Markov property cannot be confirmed for a temporal Markov process; Therefore there is not a consensus about the validity and value of Markov models in time. Moreover, previous spacial Markov models have only been used for modeling transport on structured networks and can not be readily applied to model transport in unstructured networks. In this work we propose a novel approach for constructing a Markov model in time (stencil method) for a discrete velocity process. The results form the stencil method are compared to previously proposed spacial Markov models for structured networks. The stencil method is also applied to unstructured networks and can successfully describe the dispersion of particles in this setting. Our conclusion is that both temporal Markov models and spacial Markov models for discrete velocity processes can be valid for a range of model parameters. Moreover, we show that the stencil model can be more efficient in many practical settings and is suited to model dispersion both on structured and unstructured networks.

  9. Bayesian artificial intelligence

    CERN Document Server

    Korb, Kevin B

    2003-01-01

    As the power of Bayesian techniques has become more fully realized, the field of artificial intelligence has embraced Bayesian methodology and integrated it to the point where an introduction to Bayesian techniques is now a core course in many computer science programs. Unlike other books on the subject, Bayesian Artificial Intelligence keeps mathematical detail to a minimum and covers a broad range of topics. The authors integrate all of Bayesian net technology and learning Bayesian net technology and apply them both to knowledge engineering. They emphasize understanding and intuition but also provide the algorithms and technical background needed for applications. Software, exercises, and solutions are available on the authors' website.

  10. Timed Comparisons of Semi-Markov Processes

    DEFF Research Database (Denmark)

    Pedersen, Mathias Ruggaard; Larsen, Kim Guldstrand; Bacci, Giorgio

    2018-01-01

    -Markov processes, and investigate the question of how to compare two semi-Markov processes with respect to their time-dependent behaviour. To this end, we introduce the relation of being “faster than” between processes and study its algorithmic complexity. Through a connection to probabilistic automata we obtain...

  11. ANALYSIS OF MARKOV NETWORK WITH INCOMES, POSITIVE AND NEGATIVE MESSAGES

    Directory of Open Access Journals (Sweden)

    V. V. Naumenko

    2014-01-01

    Full Text Available Markov queuing network with income in transient regime is considered. It has positive and negative messages, which can be used in forecasting income of information and telecommunication systems and networks affected by viruses. Investigations are carried out in the cases when incomes from transitions between network states are deterministic functions dependent on states, or they are random variables with given mean values. In the last case it is assumed that all network systems operate in a high load mode. An example is given.

  12. Efficient hierarchical trans-dimensional Bayesian inversion of magnetotelluric data

    Science.gov (United States)

    Xiang, Enming; Guo, Rongwen; Dosso, Stan E.; Liu, Jianxin; Dong, Hao; Ren, Zhengyong

    2018-06-01

    This paper develops an efficient hierarchical trans-dimensional (trans-D) Bayesian algorithm to invert magnetotelluric (MT) data for subsurface geoelectrical structure, with unknown geophysical model parameterization (the number of conductivity-layer interfaces) and data-error models parameterized by an auto-regressive (AR) process to account for potential error correlations. The reversible-jump Markov-chain Monte Carlo algorithm, which adds/removes interfaces and AR parameters in birth/death steps, is applied to sample the trans-D posterior probability density for model parameterization, model parameters, error variance and AR parameters, accounting for the uncertainties of model dimension and data-error statistics in the uncertainty estimates of the conductivity profile. To provide efficient sampling over the multiple subspaces of different dimensions, advanced proposal schemes are applied. Parameter perturbations are carried out in principal-component space, defined by eigen-decomposition of the unit-lag model covariance matrix, to minimize the effect of inter-parameter correlations and provide effective perturbation directions and length scales. Parameters of new layers in birth steps are proposed from the prior, instead of focused distributions centred at existing values, to improve birth acceptance rates. Parallel tempering, based on a series of parallel interacting Markov chains with successively relaxed likelihoods, is applied to improve chain mixing over model dimensions. The trans-D inversion is applied in a simulation study to examine the resolution of model structure according to the data information content. The inversion is also applied to a measured MT data set from south-central Australia.

  13. Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

    Energy Technology Data Exchange (ETDEWEB)

    Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)

    2016-07-01

    A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

  14. Fast Bayesian Inference in Dirichlet Process Mixture Models.

    Science.gov (United States)

    Wang, Lianming; Dunson, David B

    2011-01-01

    There has been increasing interest in applying Bayesian nonparametric methods in large samples and high dimensions. As Markov chain Monte Carlo (MCMC) algorithms are often infeasible, there is a pressing need for much faster algorithms. This article proposes a fast approach for inference in Dirichlet process mixture (DPM) models. Viewing the partitioning of subjects into clusters as a model selection problem, we propose a sequential greedy search algorithm for selecting the partition. Then, when conjugate priors are chosen, the resulting posterior conditionally on the selected partition is available in closed form. This approach allows testing of parametric models versus nonparametric alternatives based on Bayes factors. We evaluate the approach using simulation studies and compare it with four other fast nonparametric methods in the literature. We apply the proposed approach to three datasets including one from a large epidemiologic study. Matlab codes for the simulation and data analyses using the proposed approach are available online in the supplemental materials.

  15. Finding metastabilities in reversible Markov chains based on incomplete sampling

    Directory of Open Access Journals (Sweden)

    Fackeldey Konstantin

    2017-01-01

    Full Text Available In order to fully characterize the state-transition behaviour of finite Markov chains one needs to provide the corresponding transition matrix P. In many applications such as molecular simulation and drug design, the entries of the transition matrix P are estimated by generating realizations of the Markov chain and determining the one-step conditional probability Pij for a transition from one state i to state j. This sampling can be computational very demanding. Therefore, it is a good idea to reduce the sampling effort. The main purpose of this paper is to design a sampling strategy, which provides a partial sampling of only a subset of the rows of such a matrix P. Our proposed approach fits very well to stochastic processes stemming from simulation of molecular systems or random walks on graphs and it is different from the matrix completion approaches which try to approximate the transition matrix by using a low-rank-assumption. It will be shown how Markov chains can be analyzed on the basis of a partial sampling. More precisely. First, we will estimate the stationary distribution from a partially given matrix P. Second, we will estimate the infinitesimal generator Q of P on the basis of this stationary distribution. Third, from the generator we will compute the leading invariant subspace, which should be identical to the leading invariant subspace of P. Forth, we will apply Robust Perron Cluster Analysis (PCCA+ in order to identify metastabilities using this subspace.

  16. A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces

    NARCIS (Netherlands)

    Braak, ter C.J.F.

    2006-01-01

    Differential Evolution (DE) is a simple genetic algorithm for numerical optimization in real parameter spaces. In a statistical context one would not just want the optimum but also its uncertainty. The uncertainty distribution can be obtained by a Bayesian analysis (after specifying prior and

  17. The impulse cutoff an entropy functional measure on trajectories of Markov diffusion process integrating in information path functional

    OpenAIRE

    Lerner, Vladimir S.

    2012-01-01

    The impulses, cutting entropy functional (EF) measure on trajectories Markov diffusion process, integrate information path functional (IPF) composing discrete information Bits extracted from observing random process. Each cut brings memory of the cutting entropy, which provides both reduction of the process entropy and discrete unit of the cutting entropy a Bit. Consequently, information is memorized entropy cutting in random observations which process interactions. The origin of information ...

  18. A Bayesian approach for parameter estimation and prediction using a computationally intensive model

    International Nuclear Information System (INIS)

    Higdon, Dave; McDonnell, Jordan D; Schunck, Nicolas; Sarich, Jason; Wild, Stefan M

    2015-01-01

    Bayesian methods have been successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model η(θ), where θ denotes the uncertain, best input setting. Hence the statistical model is of the form y=η(θ)+ϵ, where ϵ accounts for measurement, and possibly other, error sources. When nonlinearity is present in η(⋅), the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model η(⋅). This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. We also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory. (paper)

  19. Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

    Energy Technology Data Exchange (ETDEWEB)

    Hadjidoukas, P.E.; Angelikopoulos, P. [Computational Science and Engineering Laboratory, ETH Zürich, CH-8092 (Switzerland); Papadimitriou, C. [Department of Mechanical Engineering, University of Thessaly, GR-38334 Volos (Greece); Koumoutsakos, P., E-mail: petros@ethz.ch [Computational Science and Engineering Laboratory, ETH Zürich, CH-8092 (Switzerland)

    2015-03-01

    We present Π4U,{sup 1} an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.

  20. Ensemble of Neural Network Conditional Random Fields for Self-Paced Brain Computer Interfaces

    Directory of Open Access Journals (Sweden)

    Hossein Bashashati

    2017-07-01

    Full Text Available Classification of EEG signals in self-paced Brain Computer Interfaces (BCI is an extremely challenging task. The main difficulty stems from the fact that start time of a control task is not defined. Therefore it is imperative to exploit the characteristics of the EEG data to the extent possible. In sensory motor self-paced BCIs, while performing the mental task, the user’s brain goes through several well-defined internal state changes. Applying appropriate classifiers that can capture these state changes and exploit the temporal correlation in EEG data can enhance the performance of the BCI. In this paper, we propose an ensemble learning approach for self-paced BCIs. We use Bayesian optimization to train several different classifiers on different parts of the BCI hyper- parameter space. We call each of these classifiers Neural Network Conditional Random Field (NNCRF. NNCRF is a combination of a neural network and conditional random field (CRF. As in the standard CRF, NNCRF is able to model the correlation between adjacent EEG samples. However, NNCRF can also model the nonlinear dependencies between the input and the output, which makes it more powerful than the standard CRF. We compare the performance of our algorithm to those of three popular sequence labeling algorithms (Hidden Markov Models, Hidden Markov Support Vector Machines and CRF, and to two classical classifiers (Logistic Regression and Support Vector Machines. The classifiers are compared for the two cases: when the ensemble learning approach is not used and when it is. The data used in our studies are those from the BCI competition IV and the SM2 dataset. We show that our algorithm is considerably superior to the other approaches in terms of the Area Under the Curve (AUC of the BCI system.