A Hierarchical Bayesian Model for Crowd Emotions
Urizar, Oscar J.; Baig, Mirza S.; Barakova, Emilia I.; Regazzoni, Carlo S.; Marcenaro, Lucio; Rauterberg, Matthias
2016-01-01
Estimation of emotions is an essential aspect in developing intelligent systems intended for crowded environments. However, emotion estimation in crowds remains a challenging problem due to the complexity in which human emotions are manifested and the capability of a system to perceive them in such conditions. This paper proposes a hierarchical Bayesian model to learn in unsupervised manner the behavior of individuals and of the crowd as a single entity, and explore the relation between behavior and emotions to infer emotional states. Information about the motion patterns of individuals are described using a self-organizing map, and a hierarchical Bayesian network builds probabilistic models to identify behaviors and infer the emotional state of individuals and the crowd. This model is trained and tested using data produced from simulated scenarios that resemble real-life environments. The conducted experiments tested the efficiency of our method to learn, detect and associate behaviors with emotional states yielding accuracy levels of 74% for individuals and 81% for the crowd, similar in performance with existing methods for pedestrian behavior detection but with novel concepts regarding the analysis of crowds. PMID:27458366
Applied Bayesian Hierarchical Methods
Congdon, Peter D
2010-01-01
Bayesian methods facilitate the analysis of complex models and data structures. Emphasizing data applications, alternative modeling specifications, and computer implementation, this book provides a practical overview of methods for Bayesian analysis of hierarchical models.
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2016-06-07
year. Our goal is to develop an ensemble ocean forecast methodology, using Bayesian Hierarchical Modelling (BHM) tools . The ocean ensemble forecast...from above); i.e. we assume Ut ~ Z Λt1/2. WORK COMPLETED The prototype MFS-Wind-BHM was designed and implemented based on stochastic...coding refinements we implemented on the prototype surface wind BHM. A DWF event in February 2005, in the Gulf of Lions, was identified for reforecast
Bayesian structural equation modeling method for hierarchical model validation
Energy Technology Data Exchange (ETDEWEB)
Jiang Xiaomo [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: xiaomo.jiang@vanderbilt.edu; Mahadevan, Sankaran [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: sankaran.mahadevan@vanderbilt.edu
2009-04-15
A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A Bayesian network with Markov chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.
Road network safety evaluation using Bayesian hierarchical joint model.
Wang, Jie; Huang, Helai
2016-05-01
Safety and efficiency are commonly regarded as two significant performance indicators of transportation systems. In practice, road network planning has focused on road capacity and transport efficiency whereas the safety level of a road network has received little attention in the planning stage. This study develops a Bayesian hierarchical joint model for road network safety evaluation to help planners take traffic safety into account when planning a road network. The proposed model establishes relationships between road network risk and micro-level variables related to road entities and traffic volume, as well as socioeconomic, trip generation and network density variables at macro level which are generally used for long term transportation plans. In addition, network spatial correlation between intersections and their connected road segments is also considered in the model. A road network is elaborately selected in order to compare the proposed hierarchical joint model with a previous joint model and a negative binomial model. According to the results of the model comparison, the hierarchical joint model outperforms the joint model and negative binomial model in terms of the goodness-of-fit and predictive performance, which indicates the reasonableness of considering the hierarchical data structure in crash prediction and analysis. Moreover, both random effects at the TAZ level and the spatial correlation between intersections and their adjacent segments are found to be significant, supporting the employment of the hierarchical joint model as an alternative in road-network-level safety modeling as well.
Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.
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
Introduction to Hierarchical Bayesian Modeling for Ecological Data
Parent, Eric
2012-01-01
Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models. The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts a
Spatial Bayesian hierarchical modelling of extreme sea states
Clancy, Colm; O'Sullivan, John; Sweeney, Conor; Dias, Frédéric; Parnell, Andrew C.
2016-11-01
A Bayesian hierarchical framework is used to model extreme sea states, incorporating a latent spatial process to more effectively capture the spatial variation of the extremes. The model is applied to a 34-year hindcast of significant wave height off the west coast of Ireland. The generalised Pareto distribution is fitted to declustered peaks over a threshold given by the 99.8th percentile of the data. Return levels of significant wave height are computed and compared against those from a model based on the commonly-used maximum likelihood inference method. The Bayesian spatial model produces smoother maps of return levels. Furthermore, this approach greatly reduces the uncertainty in the estimates, thus providing information on extremes which is more useful for practical applications.
[A medical image semantic modeling based on hierarchical Bayesian networks].
Lin, Chunyi; Ma, Lihong; Yin, Junxun; Chen, Jianyu
2009-04-01
A semantic modeling approach for medical image semantic retrieval based on hierarchical Bayesian networks was proposed, in allusion to characters of medical images. It used GMM (Gaussian mixture models) to map low-level image features into object semantics with probabilities, then it captured high-level semantics through fusing these object semantics using a Bayesian network, so that it built a multi-layer medical image semantic model, aiming to enable automatic image annotation and semantic retrieval by using various keywords at different semantic levels. As for the validity of this method, we have built a multi-level semantic model from a small set of astrocytoma MRI (magnetic resonance imaging) samples, in order to extract semantics of astrocytoma in malignant degree. Experiment results show that this is a superior approach.
Dissecting magnetar variability with Bayesian hierarchical models
Huppenkothen, D; Hogg, D W; Murray, I; Frean, M; Elenbaas, C; Watts, A L; Levin, Y; van der Horst, A J; Kouveliotou, C
2015-01-01
Neutron stars are a prime laboratory for testing physical processes under conditions of strong gravity, high density, and extreme magnetic fields. Among the zoo of neutron star phenomena, magnetars stand out for their bursting behaviour, ranging from extremely bright, rare giant flares to numerous, less energetic recurrent bursts. The exact trigger and emission mechanisms for these bursts are not known; favoured models involve either a crust fracture and subsequent energy release into the magnetosphere, or explosive reconnection of magnetic field lines. In the absence of a predictive model, understanding the physical processes responsible for magnetar burst variability is difficult. Here, we develop an empirical model that decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. The cascades of spikes that we model might be formed by avalanches of reconnection, or crust rupture afte...
Bayesian hierarchical modeling for detecting safety signals in clinical trials.
Xia, H Amy; Ma, Haijun; Carlin, Bradley P
2011-09-01
Detection of safety signals from clinical trial adverse event data is critical in drug development, but carries a challenging statistical multiplicity problem. Bayesian hierarchical mixture modeling is appealing for its ability to borrow strength across subgroups in the data, as well as moderate extreme findings most likely due merely to chance. We implement such a model for subject incidence (Berry and Berry, 2004 ) using a binomial likelihood, and extend it to subject-year adjusted incidence rate estimation under a Poisson likelihood. We use simulation to choose a signal detection threshold, and illustrate some effective graphics for displaying the flagged signals.
Bayesian hierarchical modelling of weak lensing - the golden goal
Heavens, Alan; Jaffe, Andrew; Hoffmann, Till; Kiessling, Alina; Wandelt, Benjamin
2016-01-01
To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into component steps. Starting with a catalogue of shear estimates in tomographic bins, we build a model that allows us to sample simultaneously from the the underlying tomographic shear fields and the relevant power spectra (E-mode, B-mode, and E-B, for auto- and cross-power spectra). The procedure deals easily with masked data and intrinsic alignments. Using Gibbs sampling and messenger fields, we show with simulated data that the large (over 67000-)dimensional parameter space can be efficiently sampled and the full joint posterior probability density function for the parameters can feasibly be obtained. The method correctly recovers the underlying shear fields and all of the power spectra, including at levels well below the shot noise.
Sparse Event Modeling with Hierarchical Bayesian Kernel Methods
2016-01-05
SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model, is able to model the rate of occurrence of... kernel methods made use of: (i) the Bayesian property of improving predictive accuracy as data are dynamically obtained, and (ii) the kernel function
A Bayesian hierarchical model for accident and injury surveillance.
MacNab, Ying C
2003-01-01
This article presents a recent study which applies Bayesian hierarchical methodology to model and analyse accident and injury surveillance data. A hierarchical Poisson random effects spatio-temporal model is introduced and an analysis of inter-regional variations and regional trends in hospitalisations due to motor vehicle accident injuries to boys aged 0-24 in the province of British Columbia, Canada, is presented. The objective of this article is to illustrate how the modelling technique can be implemented as part of an accident and injury surveillance and prevention system where transportation and/or health authorities may routinely examine accidents, injuries, and hospitalisations to target high-risk regions for prevention programs, to evaluate prevention strategies, and to assist in health planning and resource allocation. The innovation of the methodology is its ability to uncover and highlight important underlying structure of the data. Between 1987 and 1996, British Columbia hospital separation registry registered 10,599 motor vehicle traffic injury related hospitalisations among boys aged 0-24 who resided in British Columbia, of which majority (89%) of the injuries occurred to boys aged 15-24. The injuries were aggregated by three age groups (0-4, 5-14, and 15-24), 20 health regions (based of place-of-residence), and 10 calendar years (1987 to 1996) and the corresponding mid-year population estimates were used as 'at risk' population. An empirical Bayes inference technique using penalised quasi-likelihood estimation was implemented to model both rates and counts, with spline smoothing accommodating non-linear temporal effects. The results show that (a) crude rates and ratios at health region level are unstable, (b) the models with spline smoothing enable us to explore possible shapes of injury trends at both the provincial level and the regional level, and (c) the fitted models provide a wealth of information about the patterns (both over space and time
A Bayesian hierarchical diffusion model decomposition of performance in Approach-Avoidance Tasks.
Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan
2015-01-01
Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach-Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest.
Scheibehenne, Benjamin; Pachur, Thorsten
2015-04-01
To be useful, cognitive models with fitted parameters should show generalizability across time and allow accurate predictions of future observations. It has been proposed that hierarchical procedures yield better estimates of model parameters than do nonhierarchical, independent approaches, because the formers' estimates for individuals within a group can mutually inform each other. Here, we examine Bayesian hierarchical approaches to evaluating model generalizability in the context of two prominent models of risky choice-cumulative prospect theory (Tversky & Kahneman, 1992) and the transfer-of-attention-exchange model (Birnbaum & Chavez, 1997). Using empirical data of risky choices collected for each individual at two time points, we compared the use of hierarchical versus independent, nonhierarchical Bayesian estimation techniques to assess two aspects of model generalizability: parameter stability (across time) and predictive accuracy. The relative performance of hierarchical versus independent estimation varied across the different measures of generalizability. The hierarchical approach improved parameter stability (in terms of a lower absolute discrepancy of parameter values across time) and predictive accuracy (in terms of deviance; i.e., likelihood). With respect to test-retest correlations and posterior predictive accuracy, however, the hierarchical approach did not outperform the independent approach. Further analyses suggested that this was due to strong correlations between some parameters within both models. Such intercorrelations make it difficult to identify and interpret single parameters and can induce high degrees of shrinkage in hierarchical models. Similar findings may also occur in the context of other cognitive models of choice.
Osei, Frank B.; Duker, Alfred A.; Stein, Alfred
2011-01-01
This study analyses the joint effects of the two transmission routes of cholera on the space-time diffusion dynamics. Statistical models are developed and presented to investigate the transmission network routes of cholera diffusion. A hierarchical Bayesian modelling approach is employed for a joint
Application of Bayesian Hierarchical Prior Modeling to Sparse Channel Estimation
DEFF Research Database (Denmark)
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Shutin, Dmitriy
2012-01-01
. The estimators result as an application of the variational message-passing algorithm on the factor graph representing the signal model extended with the hierarchical prior models. Numerical results demonstrate the superior performance of our channel estimators as compared to traditional and state......Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the l1-norm of the parameter of interest. However, other penalization......-of-the-art sparse methods....
Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno
2016-01-01
Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China.
Directory of Open Access Journals (Sweden)
Xiongqing Zhang
Full Text Available Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (Cunninghamia lanceolata (Lamb.Hook. plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF. Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc. on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.
Directory of Open Access Journals (Sweden)
Moritz eBoos
2016-05-01
Full Text Available Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modelling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities by two (likelihoods design. Five computational models of cognitive processes were compared with the observed behaviour. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model’s success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modelling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modelling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
Directory of Open Access Journals (Sweden)
Brodjol Sutijo Supri Ulama
2012-01-01
Full Text Available Problem statement: Household expenditure analysis was highly demanding for government in order to formulate its policy. Since household data was viewed as hierarchical structure with household nested in its regional residence which varies inter region, the contextual welfare analysis was needed. This study proposed to develop a hierarchical model for estimating household expenditure in an attempt to measure the effect of regional diversity by taking into account district characteristics and household attributes using a Bayesian approach. Approach: Due to the variation of household expenditure data which was captured by the three parameters of Log-Normal (LN3 distribution, the model was developed based on LN3 distribution. Data used in this study was household expenditure data in Central Java, Indonesia. Since, data were unbalanced and hierarchical models using a classical approach work well for balanced data, thus the estimation process was done by using Bayesian method with MCMC and Gibbs sampling. Results: The hierarchical Bayesian model based on LN3 distribution could be implemented to explain the variation of household expenditure using district characteristics and household attributes. Conclusion: The model shows that districts characteristics which include demographic and economic conditions of districts and the availability of public facilities which are strongly associated with a dimension of human development index, i.e., economic, education and health, do affect to household expenditure through its household attributes."
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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.
Hierarchical Bayesian Model for Simultaneous EEG Source and Forward Model Reconstruction (SOFOMORE)
DEFF Research Database (Denmark)
Stahlhut, Carsten; Mørup, Morten; Winther, Ole;
2009-01-01
In this paper we propose an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model is motivated by the many uncertain contributions that form the forward propagation model including the tissue conductivity distribution, the cortical surface, and ele......In this paper we propose an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model is motivated by the many uncertain contributions that form the forward propagation model including the tissue conductivity distribution, the cortical surface......, and electrode positions. We first present a hierarchical Bayesian framework for EEG source localization that jointly performs source and forward model reconstruction (SOFOMORE). Secondly, we evaluate the SOFOMORE model by comparison with source reconstruction methods that use fixed forward models. Simulated...... and real EEG data demonstrate that invoking a stochastic forward model leads to improved source estimates....
Wu, Stephen; Angelikopoulos, Panagiotis; Tauriello, Gerardo; Papadimitriou, Costas; Koumoutsakos, Petros
2016-12-28
We propose a hierarchical Bayesian framework to systematically integrate heterogeneous data for the calibration of force fields in Molecular Dynamics (MD) simulations. Our approach enables the fusion of diverse experimental data sets of the physico-chemical properties of a system at different thermodynamic conditions. We demonstrate the value of this framework for the robust calibration of MD force-fields for water using experimental data of its diffusivity, radial distribution function, and density. In order to address the high computational cost associated with the hierarchical Bayesian models, we develop a novel surrogate model based on the empirical interpolation method. Further computational savings are achieved by implementing a highly parallel transitional Markov chain Monte Carlo technique. The present method bypasses possible subjective weightings of the experimental data in identifying MD force-field parameters.
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J. P. Werner
2015-03-01
Full Text Available Reconstructions of the late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurements of tree rings, ice cores, and varved lake sediments. Considerable advances could be achieved if time-uncertain proxies were able to be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches for accounting for time uncertainty are generally limited to repeating the reconstruction using each one of an ensemble of age models, thereby inflating the final estimated uncertainty – in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space–time covariance structure of the climate to re-weight the possible age models. Here, we demonstrate how Bayesian hierarchical climate reconstruction models can be augmented to account for time-uncertain proxies. Critically, although a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the resulting reconstructions, as compared with the current de facto standard of sampling over all age models, provided there is sufficient information from other data sources in the spatial region of the time-uncertain proxy. This approach can readily be generalized to non-layer-counted proxies, such as those derived from marine sediments.
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J. P. Werner
2014-12-01
Full Text Available Reconstructions of late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurement on tree rings, ice cores, and varved lake sediments. Considerable advances may be achievable if time uncertain proxies could be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches to accounting for time uncertainty are generally limited to repeating the reconstruction using each of an ensemble of age models, thereby inflating the final estimated uncertainty – in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space–time covariance structure of the climate to re-weight the possible age models. Here we demonstrate how Bayesian Hierarchical climate reconstruction models can be augmented to account for time uncertain proxies. Critically, while a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age-model probabilities decreases uncertainty in the climate reconstruction, as compared with the current de-facto standard of sampling over all age models, provided there is sufficient information from other data sources in the region of the time-uncertain proxy. This approach can readily be generalized to non-layer counted proxies, such as those derived from marine sediments.
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X. Chen
2013-09-01
Full Text Available A Hierarchal Bayesian model for forecasting regional summer rainfall and streamflow season-ahead using exogenous climate variables for East Central China is presented. The model provides estimates of the posterior forecasted probability distribution for 12 rainfall and 2 streamflow stations considering parameter uncertainty, and cross-site correlation. The model has a multilevel structure with regression coefficients modeled from a common multivariate normal distribution results in partial-pooling of information across multiple stations and better representation of parameter and posterior distribution uncertainty. Covariance structure of the residuals across stations is explicitly modeled. Model performance is tested under leave-10-out cross-validation. Frequentist and Bayesian performance metrics used include Receiver Operating Characteristic, Reduction of Error, Coefficient of Efficiency, Rank Probability Skill Scores, and coverage by posterior credible intervals. The ability of the model to reliably forecast regional summer rainfall and streamflow season-ahead offers potential for developing adaptive water risk management strategies.
A Bayesian Hierarchical Model for Relating Multiple SNPs within Multiple Genes to Disease Risk
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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.
Application of Bayesian hierarchical models for phase I/II clinical trials in oncology.
Yada, Shinjo; Hamada, Chikuma
2017-03-01
Treatment during cancer clinical trials sometimes involves the combination of multiple drugs. In addition, in recent years there has been a trend toward phase I/II trials in which a phase I and a phase II trial are combined into a single trial to accelerate drug development. Methods for the seamless combination of phases I and II parts are currently under investigation. In the phase II part, adaptive randomization on the basis of patient efficacy outcomes allocates more patients to the dose combinations considered to have higher efficacy. Patient toxicity outcomes are used for determining admissibility to each dose combination and are not used for selection of the dose combination itself. In cases where the objective is not to find the optimum dose combination solely for efficacy but regarding both toxicity and efficacy, the need exists to allocate patients to dose combinations with consideration of the balance of existing trade-offs between toxicity and efficacy. We propose a Bayesian hierarchical model and an adaptive randomization with consideration for the relationship with toxicity and efficacy. Using the toxicity and efficacy outcomes of patients, the Bayesian hierarchical model is used to estimate the toxicity probability and efficacy probability in each of the dose combinations. Here, we use Bayesian moving-reference adaptive randomization on the basis of desirability computed from the obtained estimator. Computer simulations suggest that the proposed method will likely recommend a higher percentage of target dose combinations than a previously proposed method.
Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model
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.
HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python
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Thomas V Wiecki
2013-08-01
Full Text Available The diffusion model is a commonly used tool to infer latent psychological processes underlying decision making, and to link them to neural mechanisms based on reaction times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of reaction time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model, which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject / condition than non-hierarchical method, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g. fMRI influence decision making parameters. This paper will first describe the theoretical background of drift-diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the chi-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs
Gas turbine engine prognostics using Bayesian hierarchical models: A variational approach
Zaidan, Martha A.; Mills, Andrew R.; Harrison, Robert F.; Fleming, Peter J.
2016-03-01
Prognostics is an emerging requirement of modern health monitoring that aims to increase the fidelity of failure-time predictions by the appropriate use of sensory and reliability information. In the aerospace industry it is a key technology to reduce life-cycle costs, improve reliability and asset availability for a diverse fleet of gas turbine engines. In this work, a Bayesian hierarchical model is selected to utilise fleet data from multiple assets to perform probabilistic estimation of remaining useful life (RUL) for civil aerospace gas turbine engines. The hierarchical formulation allows Bayesian updates of an individual predictive model to be made, based upon data received asynchronously from a fleet of assets with different in-service lives and for the entry of new assets into the fleet. In this paper, variational inference is applied to the hierarchical formulation to overcome the computational and convergence concerns that are raised by the numerical sampling techniques needed for inference in the original formulation. The algorithm is tested on synthetic data, where the quality of approximation is shown to be satisfactory with respect to prediction performance, computational speed, and ease of use. A case study of in-service gas turbine engine data demonstrates the value of integrating fleet data for accurately predicting degradation trajectories of assets.
A hierarchical bayesian model to quantify uncertainty of stream water temperature forecasts.
Directory of Open Access Journals (Sweden)
Guillaume Bal
Full Text Available Providing generic and cost effective modelling approaches to reconstruct and forecast freshwater temperature using predictors as air temperature and water discharge is a prerequisite to understanding ecological processes underlying the impact of water temperature and of global warming on continental aquatic ecosystems. Using air temperature as a simple linear predictor of water temperature can lead to significant bias in forecasts as it does not disentangle seasonality and long term trends in the signal. Here, we develop an alternative approach based on hierarchical Bayesian statistical time series modelling of water temperature, air temperature and water discharge using seasonal sinusoidal periodic signals and time varying means and amplitudes. Fitting and forecasting performances of this approach are compared with that of simple linear regression between water and air temperatures using i an emotive simulated example, ii application to three French coastal streams with contrasting bio-geographical conditions and sizes. The time series modelling approach better fit data and does not exhibit forecasting bias in long term trends contrary to the linear regression. This new model also allows for more accurate forecasts of water temperature than linear regression together with a fair assessment of the uncertainty around forecasting. Warming of water temperature forecast by our hierarchical Bayesian model was slower and more uncertain than that expected with the classical regression approach. These new forecasts are in a form that is readily usable in further ecological analyses and will allow weighting of outcomes from different scenarios to manage climate change impacts on freshwater wildlife.
Xu, Lizhen; Paterson, Andrew D; Xu, Wei
2017-04-01
Motivated by the multivariate nature of microbiome data with hierarchical taxonomic clusters, counts that are often skewed and zero inflated, and repeated measures, we propose a Bayesian latent variable methodology to jointly model multiple operational taxonomic units within a single taxonomic cluster. This novel method can incorporate both negative binomial and zero-inflated negative binomial responses, and can account for serial and familial correlations. We develop a Markov chain Monte Carlo algorithm that is built on a data augmentation scheme using Pólya-Gamma random variables. Hierarchical centering and parameter expansion techniques are also used to improve the convergence of the Markov chain. We evaluate the performance of our proposed method through extensive simulations. We also apply our method to a human microbiome study.
Directory of Open Access Journals (Sweden)
C Elizabeth McCarron
Full Text Available BACKGROUND: Bayesian hierarchical models have been proposed to combine evidence from different types of study designs. However, when combining evidence from randomised and non-randomised controlled studies, imbalances in patient characteristics between study arms may bias the results. The objective of this study was to assess the performance of a proposed Bayesian approach to adjust for imbalances in patient level covariates when combining evidence from both types of study designs. METHODOLOGY/PRINCIPAL FINDINGS: Simulation techniques, in which the truth is known, were used to generate sets of data for randomised and non-randomised studies. Covariate imbalances between study arms were introduced in the non-randomised studies. The performance of the Bayesian hierarchical model adjusted for imbalances was assessed in terms of bias. The data were also modelled using three other Bayesian approaches for synthesising evidence from randomised and non-randomised studies. The simulations considered six scenarios aimed at assessing the sensitivity of the results to changes in the impact of the imbalances and the relative number and size of studies of each type. For all six scenarios considered, the Bayesian hierarchical model adjusted for differences within studies gave results that were unbiased and closest to the true value compared to the other models. CONCLUSIONS/SIGNIFICANCE: Where informed health care decision making requires the synthesis of evidence from randomised and non-randomised study designs, the proposed hierarchical Bayesian method adjusted for differences in patient characteristics between study arms may facilitate the optimal use of all available evidence leading to unbiased results compared to unadjusted analyses.
Xu, Lei; Johnson, Timothy D.; Nichols, Thomas E.; Nee, Derek E.
2010-01-01
Summary The aim of this work is to develop a spatial model for multi-subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi-subject data, some work on spatial modeling of single-subject data, and some recent work on spatial modeling of multi-subject data. However, there has been no work on spatial models that explicitly account for inter-subject variability in activation locations. In this work, we use the idea of activation centers and model the inter-subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical frame work which allows us to draw inferences at all levels: the population level, the individual level and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question which is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov Chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass-univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data. PMID:19210732
Skataric, Maja; Bose, Sandip; Zeroug, Smaine; Tilke, Peter
2017-02-01
It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications. In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.
A Bayesian Hierarchical Model for Reconstructing Sea Levels: From Raw Data to Rates of Change
Cahill, Niamh; Horton, Benjamin P; Parnell, Andrew C
2015-01-01
We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical ({\\delta}13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) A Bayesian transfer function for the calibration of foraminifera into tidal elevation, which is flexible enough to formally accommodate additional proxies (in this case bulk-sediment {\\delta}13C values); (2) A chronology developed from an existing Bchron age-depth model, and (3) An existing errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. We illustrate our approach using a case study of Common Era sea-level variability from New Jersey, U.S.A. We develop a new Bayesian transfer function (B-TF), with and without the {\\delta}13C proxy and compare our results to those from a widely...
A hierarchical Bayesian GEV model for improving local and regional flood quantile estimates
Lima, Carlos H. R.; Lall, Upmanu; Troy, Tara; Devineni, Naresh
2016-10-01
We estimate local and regional Generalized Extreme Value (GEV) distribution parameters for flood frequency analysis in a multilevel, hierarchical Bayesian framework, to explicitly model and reduce uncertainties. As prior information for the model, we assume that the GEV location and scale parameters for each site come from independent log-normal distributions, whose mean parameter scales with the drainage area. From empirical and theoretical arguments, the shape parameter for each site is shrunk towards a common mean. Non-informative prior distributions are assumed for the hyperparameters and the MCMC method is used to sample from the joint posterior distribution. The model is tested using annual maximum series from 20 streamflow gauges located in an 83,000 km2 flood prone basin in Southeast Brazil. The results show a significant reduction of uncertainty estimates of flood quantile estimates over the traditional GEV model, particularly for sites with shorter records. For return periods within the range of the data (around 50 years), the Bayesian credible intervals for the flood quantiles tend to be narrower than the classical confidence limits based on the delta method. As the return period increases beyond the range of the data, the confidence limits from the delta method become unreliable and the Bayesian credible intervals provide a way to estimate satisfactory confidence bands for the flood quantiles considering parameter uncertainties and regional information. In order to evaluate the applicability of the proposed hierarchical Bayesian model for regional flood frequency analysis, we estimate flood quantiles for three randomly chosen out-of-sample sites and compare with classical estimates using the index flood method. The posterior distributions of the scaling law coefficients are used to define the predictive distributions of the GEV location and scale parameters for the out-of-sample sites given only their drainage areas and the posterior distribution of the
Lowman, L.; Barros, A. P.
2014-12-01
Computational modeling of surface erosion processes is inherently difficult because of the four-dimensional nature of the problem and the multiple temporal and spatial scales that govern individual mechanisms. Landscapes are modified via surface and fluvial erosion and exhumation, each of which takes place over a range of time scales. Traditional field measurements of erosion/exhumation rates are scale dependent, often valid for a single point-wise location or averaging over large aerial extents and periods with intense and mild erosion. We present a method of remotely estimating erosion rates using a Bayesian hierarchical model based upon the stream power erosion law (SPEL). A Bayesian approach allows for estimating erosion rates using the deterministic relationship given by the SPEL and data on channel slopes and precipitation at the basin and sub-basin scale. The spatial scale associated with this framework is the elevation class, where each class is characterized by distinct morphologic behavior observed through different modes in the distribution of basin outlet elevations. Interestingly, the distributions of first-order outlets are similar in shape and extent to the distribution of precipitation events (i.e. individual storms) over a 14-year period between 1998-2011. We demonstrate an application of the Bayesian hierarchical modeling framework for five basins and one intermontane basin located in the central Andes between 5S and 20S. Using remotely sensed data of current annual precipitation rates from the Tropical Rainfall Measuring Mission (TRMM) and topography from a high resolution (3 arc-seconds) digital elevation map (DEM), our erosion rate estimates are consistent with decadal-scale estimates based on landslide mapping and sediment flux observations and 1-2 orders of magnitude larger than most millennial and million year timescale estimates from thermochronology and cosmogenic nuclides.
Prion Amplification and Hierarchical Bayesian Modeling Refine Detection of Prion Infection
Wyckoff, A. Christy; Galloway, Nathan; Meyerett-Reid, Crystal; Powers, Jenny; Spraker, Terry; Monello, Ryan J.; Pulford, Bruce; Wild, Margaret; Antolin, Michael; Vercauteren, Kurt; Zabel, Mark
2015-02-01
Prions are unique infectious agents that replicate without a genome and cause neurodegenerative diseases that include chronic wasting disease (CWD) of cervids. Immunohistochemistry (IHC) is currently considered the gold standard for diagnosis of a prion infection but may be insensitive to early or sub-clinical CWD that are important to understanding CWD transmission and ecology. We assessed the potential of serial protein misfolding cyclic amplification (sPMCA) to improve detection of CWD prior to the onset of clinical signs. We analyzed tissue samples from free-ranging Rocky Mountain elk (Cervus elaphus nelsoni) and used hierarchical Bayesian analysis to estimate the specificity and sensitivity of IHC and sPMCA conditional on simultaneously estimated disease states. Sensitivity estimates were higher for sPMCA (99.51%, credible interval (CI) 97.15-100%) than IHC of obex (brain stem, 76.56%, CI 57.00-91.46%) or retropharyngeal lymph node (90.06%, CI 74.13-98.70%) tissues, or both (98.99%, CI 90.01-100%). Our hierarchical Bayesian model predicts the prevalence of prion infection in this elk population to be 18.90% (CI 15.50-32.72%), compared to previous estimates of 12.90%. Our data reveal a previously unidentified sub-clinical prion-positive portion of the elk population that could represent silent carriers capable of significantly impacting CWD ecology.
Probabilistic daily ILI syndromic surveillance with a spatio-temporal Bayesian hierarchical model.
Directory of Open Access Journals (Sweden)
Ta-Chien Chan
Full Text Available BACKGROUND: For daily syndromic surveillance to be effective, an efficient and sensible algorithm would be expected to detect aberrations in influenza illness, and alert public health workers prior to any impending epidemic. This detection or alert surely contains uncertainty, and thus should be evaluated with a proper probabilistic measure. However, traditional monitoring mechanisms simply provide a binary alert, failing to adequately address this uncertainty. METHODS AND FINDINGS: Based on the Bayesian posterior probability of influenza-like illness (ILI visits, the intensity of outbreak can be directly assessed. The numbers of daily emergency room ILI visits at five community hospitals in Taipei City during 2006-2007 were collected and fitted with a Bayesian hierarchical model containing meteorological factors such as temperature and vapor pressure, spatial interaction with conditional autoregressive structure, weekend and holiday effects, seasonality factors, and previous ILI visits. The proposed algorithm recommends an alert for action if the posterior probability is larger than 70%. External data from January to February of 2008 were retained for validation. The decision rule detects successfully the peak in the validation period. When comparing the posterior probability evaluation with the modified Cusum method, results show that the proposed method is able to detect the signals 1-2 days prior to the rise of ILI visits. CONCLUSIONS: This Bayesian hierarchical model not only constitutes a dynamic surveillance system but also constructs a stochastic evaluation of the need to call for alert. The monitoring mechanism provides earlier detection as well as a complementary tool for current surveillance programs.
2013-01-01
This paper proposes a hierarchical Bayesian framework for modeling the life cycle of marine exploited fish with a spatial perspective. The application was developed for a nursery-dependent fish species, the common sole (Solea solea), on the Eastern Channel population (Western Europe). The approach combined processes of different natures and various sources of observations within an integrated framework for life-cycle modeling: (1) outputs of an individual-based model for larval drift and surv...
Directory of Open Access Journals (Sweden)
David Lunn
Full Text Available The advantages of Bayesian statistical approaches, such as flexibility and the ability to acknowledge uncertainty in all parameters, have made them the prevailing method for analysing the spread of infectious diseases in human or animal populations. We introduce a Bayesian approach to experimental host-pathogen systems that shares these attractive features. Since uncertainty in all parameters is acknowledged, existing information can be accounted for through prior distributions, rather than through fixing some parameter values. The non-linear dynamics, multi-factorial design, multiple measurements of responses over time and sampling error that are typical features of experimental host-pathogen systems can also be naturally incorporated. We analyse the dynamics of the free-living protozoan Paramecium caudatum and its specialist bacterial parasite Holospora undulata. Our analysis provides strong evidence for a saturable infection function, and we were able to reproduce the two waves of infection apparent in the data by separating the initial inoculum from the parasites released after the first cycle of infection. In addition, the parameter estimates from the hierarchical model can be combined to infer variations in the parasite's basic reproductive ratio across experimental groups, enabling us to make predictions about the effect of resources and host genotype on the ability of the parasite to spread. Even though the high level of variability between replicates limited the resolution of the results, this Bayesian framework has strong potential to be used more widely in experimental ecology.
A spectral-spatial-dynamic hierarchical Bayesian (SSD-HB) model for estimating soybean yield
Kazama, Yoriko; Kujirai, Toshihiro
2014-10-01
A method called a "spectral-spatial-dynamic hierarchical-Bayesian (SSD-HB) model," which can deal with many parameters (such as spectral and weather information all together) by reducing the occurrence of multicollinearity, is proposed. Experiments conducted on soybean yields in Brazil fields with a RapidEye satellite image indicate that the proposed SSD-HB model can predict soybean yield with a higher degree of accuracy than other estimation methods commonly used in remote-sensing applications. In the case of the SSD-HB model, the mean absolute error between estimated yield of the target area and actual yield is 0.28 t/ha, compared to 0.34 t/ha when conventional PLS regression was applied, showing the potential effectiveness of the proposed model.
A Bayesian hierarchical nonhomogeneous hidden Markov model for multisite streamflow reconstructions
Bracken, C.; Rajagopalan, B.; Woodhouse, C.
2016-10-01
In many complex water supply systems, the next generation of water resources planning models will require simultaneous probabilistic streamflow inputs at multiple locations on an interconnected network. To make use of the valuable multicentury records provided by tree-ring data, reconstruction models must be able to produce appropriate multisite inputs. Existing streamflow reconstruction models typically focus on one site at a time, not addressing intersite dependencies and potentially misrepresenting uncertainty. To this end, we develop a model for multisite streamflow reconstruction with the ability to capture intersite correlations. The proposed model is a hierarchical Bayesian nonhomogeneous hidden Markov model (NHMM). A NHMM is fit to contemporary streamflow at each location using lognormal component distributions. Leading principal components of tree rings are used as covariates to model nonstationary transition probabilities and the parameters of the lognormal component distributions. Spatial dependence between sites is captured with a Gaussian elliptical copula. Parameters of the model are estimated in a fully Bayesian framework, in that marginal posterior distributions of all the parameters are obtained. The model is applied to reconstruct flows at 20 sites in the Upper Colorado River Basin (UCRB) from 1473 to 1906. Many previous reconstructions are available for this basin, making it ideal for testing this new method. The results show some improvements over regression-based methods in terms of validation statistics. Key advantages of the Bayesian NHMM over traditional approaches are a dynamic representation of uncertainty and the ability to make long multisite simulations that capture at-site statistics and spatial correlations between sites.
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.
Brochu, Eric; de Freitas, Nando
2010-01-01
We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences.
Merging information from multi-model flood projections in a hierarchical Bayesian framework
Le Vine, Nataliya
2016-04-01
Multi-model ensembles are becoming widely accepted for flood frequency change analysis. The use of multiple models results in large uncertainty around estimates of flood magnitudes, due to both uncertainty in model selection and natural variability of river flow. The challenge is therefore to extract the most meaningful signal from the multi-model predictions, accounting for both model quality and uncertainties in individual model estimates. The study demonstrates the potential of a recently proposed hierarchical Bayesian approach to combine information from multiple models. The approach facilitates explicit treatment of shared multi-model discrepancy as well as the probabilistic nature of the flood estimates, by treating the available models as a sample from a hypothetical complete (but unobserved) set of models. The advantages of the approach are: 1) to insure an adequate 'baseline' conditions with which to compare future changes; 2) to reduce flood estimate uncertainty; 3) to maximize use of statistical information in circumstances where multiple weak predictions individually lack power, but collectively provide meaningful information; 4) to adjust multi-model consistency criteria when model biases are large; and 5) to explicitly consider the influence of the (model performance) stationarity assumption. Moreover, the analysis indicates that reducing shared model discrepancy is the key to further reduction of uncertainty in the flood frequency analysis. The findings are of value regarding how conclusions about changing exposure to flooding are drawn, and to flood frequency change attribution studies.
Application of hierarchical Bayesian unmixing models in river sediment source apportionment
Blake, Will; Smith, Hugh; Navas, Ana; Bodé, Samuel; Goddard, Rupert; Zou Kuzyk, Zou; Lennard, Amy; Lobb, David; Owens, Phil; Palazon, Leticia; Petticrew, Ellen; Gaspar, Leticia; Stock, Brian; Boeckx, Pacsal; Semmens, Brice
2016-04-01
Fingerprinting and unmixing concepts are used widely across environmental disciplines for forensic evaluation of pollutant sources. In aquatic and marine systems, this includes tracking the source of organic and inorganic pollutants in water and linking problem sediment to soil erosion and land use sources. It is, however, the particular complexity of ecological systems that has driven creation of the most sophisticated mixing models, primarily to (i) evaluate diet composition in complex ecological food webs, (ii) inform population structure and (iii) explore animal movement. In the context of the new hierarchical Bayesian unmixing model, MIXSIAR, developed to characterise intra-population niche variation in ecological systems, we evaluate the linkage between ecological 'prey' and 'consumer' concepts and river basin sediment 'source' and sediment 'mixtures' to exemplify the value of ecological modelling tools to river basin science. Recent studies have outlined advantages presented by Bayesian unmixing approaches in handling complex source and mixture datasets while dealing appropriately with uncertainty in parameter probability distributions. MixSIAR is unique in that it allows individual fixed and random effects associated with mixture hierarchy, i.e. factors that might exert an influence on model outcome for mixture groups, to be explored within the source-receptor framework. This offers new and powerful ways of interpreting river basin apportionment data. In this contribution, key components of the model are evaluated in the context of common experimental designs for sediment fingerprinting studies namely simple, nested and distributed catchment sampling programmes. Illustrative examples using geochemical and compound specific stable isotope datasets are presented and used to discuss best practice with specific attention to (1) the tracer selection process, (2) incorporation of fixed effects relating to sample timeframe and sediment type in the modelling
Jin, Ick Hoon; Yuan, Ying; Bandyopadhyay, Dipankar
2016-01-01
Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, i.e., the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed, or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being non-missing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries, and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis-Hastings sampler. We compare and contrast our model performances to the standard non-spatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries. PMID:27807470
Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
DEFF Research Database (Denmark)
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Badiu, Mihai Alin;
2015-01-01
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued m......In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex...
Full Bayesian hierarchical light curve modeling of core-collapse supernova populations
Sanders, Nathan; Betancourt, Michael; Soderberg, Alicia Margarita
2016-06-01
While wide field surveys have yielded remarkable quantities of photometry of transient objects, including supernovae, light curves reconstructed from this data suffer from several characteristic problems. Because most transients are discovered near the detection limit, signal to noise is generally poor; because coverage is limited to the observing season, light curves are often incomplete; and because temporal sampling can be uneven across filters, these problems can be exacerbated at any one wavelength. While the prevailing approach of modeling individual light curves independently is successful at recovering inferences for the objects with the highest quality observations, it typically neglects a substantial portion of the data and can introduce systematic biases. Joint modeling of the light curves of transient populations enables direct inference on population-level characteristics as well as superior measurements for individual objects. We present a new hierarchical Bayesian model for supernova light curves, where information inferred from observations of every individual light curve in a sample is partially pooled across objects to constrain population-level hyperparameters. Using an efficient Hamiltonian Monte Carlo sampling technique, the model posterior can be explored to enable marginalization over weakly-identified hyperparameters through full Bayesian inference. We demonstrate our technique on the Pan-STARRS1 (PS1) Type IIP supernova light curve sample published by Sanders et al. (2015), consisting of nearly 20,000 individual photometric observations of more than 70 supernovae in five photometric filters. We discuss the Stan probabilistic programming language used to implement the model, computational challenges, and prospects for future work including generalization to multiple supernova types. We also discuss scientific results from the PS1 dataset including a new relation between the peak magnitude and decline rate of SNe IIP, a new perspective on the
Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models
Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas
2017-02-01
A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally
Modeling hypoxia in the Chesapeake Bay: Ensemble estimation using a Bayesian hierarchical model
Stow, Craig A.; Scavia, Donald
2009-02-01
Quantifying parameter and prediction uncertainty in a rigorous framework can be an important component of model skill assessment. Generally, models with lower uncertainty will be more useful for prediction and inference than models with higher uncertainty. Ensemble estimation, an idea with deep roots in the Bayesian literature, can be useful to reduce model uncertainty. It is based on the idea that simultaneously estimating common or similar parameters among models can result in more precise estimates. We demonstrate this approach using the Streeter-Phelps dissolved oxygen sag model fit to 29 years of data from Chesapeake Bay. Chesapeake Bay has a long history of bottom water hypoxia and several models are being used to assist management decision-making in this system. The Bayesian framework is particularly useful in a decision context because it can combine both expert-judgment and rigorous parameter estimation to yield model forecasts and a probabilistic estimate of the forecast uncertainty.
Hu, Yi; Ward, Michael P; Xia, Congcong; Li, Rui; Sun, Liqian; Lynn, Henry; Gao, Fenghua; Wang, Qizhi; Zhang, Shiqing; Xiong, Chenglong; Zhang, Zhijie; Jiang, Qingwu
2016-04-07
Schistosomiasis remains a major public health problem and causes substantial economic impact in east China, particularly along the Yangtze River Basin. Disease forecasting and surveillance can assist in the development and implementation of more effective intervention measures to control disease. In this study, we applied a Bayesian hierarchical spatio-temporal model to describe trends in schistosomiasis risk in Anhui Province, China, using annual parasitological and environmental data for the period 1997-2010. A computationally efficient approach-Integrated Nested Laplace Approximation-was used for model inference. A zero-inflated, negative binomial model best described the spatio-temporal dynamics of schistosomiasis risk. It predicted that the disease risk would generally be low and stable except for some specific, local areas during the period 2011-2014. High-risk counties were identified in the forecasting maps: three in which the risk remained high, and two in which risk would become high. The results indicated that schistosomiasis risk has been reduced to consistently low levels throughout much of this region of China; however, some counties were identified in which progress in schistosomiasis control was less than satisfactory. Whilst maintaining overall control, specific interventions in the future should focus on these refractive counties as part of a strategy to eliminate schistosomiasis from this region.
Indian Academy of Sciences (India)
Wayan Suparta; Gusrizal
2014-08-01
We implement a hierarchical Bayesian spatiotemporal (HBST) model to forecast the daily trapped particle flux distribution over the South Atlantic Anomaly (SAA) region. The National Oceanic and Atmospheric Administration (NOAA)-15 data from 1–30 March 2008 with particle energies as < 30 keV (mep0e1) and < 300 keV (mep0e3) for electrons and 80–240 keV (mep0p2) and < 6900 keV (mep0p6) for protons were used as the model input to forecast the flux values on 31 March 2008. Data were transformed into logarithmic values and gridded in a 5° × 5° longitude and latitude size to fulfill the modeling precondition. A Monte Carlo Markov chain (MCMC) was then performed to solve the HBST Gaussian Process (GP) model by using the Gibbs sampling method. The result for this model was interpolated by a Kriging technique to achieve the whole distribution figure over the SAA region. Statistical results of the root mean square error (RMSE), mean absolute percentage error (MAPE), and bias (BIAS) showed a good indicator of the HBST method. The statistical validation also indicated the high variability of particle flux values in the SAA core area. The visual validation showed a powerful combination of HBST-GP model with Kriging interpolation technique. The Kriging also produced a good quality of the distribution map of particle flux over the SAA region as indicated by its small variance value. This suggests that the model can be applied in the development of a Low Earth Orbit (LEO)-Equatorial satellite for monitoring trapped particle radiation hazard.
Huang, Susie Shih-Yin; Strathe, Anders Bjerring; Hung, Silas S O; Boston, Raymond C; Fadel, James G
2012-03-01
The biological function of selenium (Se) is determined by its form and concentration. Selenium is an essential micronutrient for all vertebrates, however, at environmental levels, it is a potent toxin. In the San Francisco Bay-Delta, Se pollution threatens top predatory fish, including white sturgeon. A multi-compartmental Bayesian hierarchical model was developed to estimate the fractional rates of absorption, disposition, and elimination of selenocompounds, in white sturgeon, from tissue measurements obtained in a previous study (Huang et al., 2012). This modeling methodology allows for a population based approach to estimate kinetic physiological parameters in white sturgeon. Briefly, thirty juvenile white sturgeon (five per treatment) were orally intubated with a control (no selenium) or a single dose of Se (500 μg Se/kg body weight) in the form of one inorganic (Selenite) or four organic selenocompounds: selenocystine (SeCys), l-selenomethionine (SeMet), Se-methylseleno-l-cysteine (MSeCys), or selenoyeast (SeYeast). Blood and urine Se were measured at intervals throughout the 48h post intubation period and eight tissues were sampled at 48 h. The model is composed of four state variables, conceptually the gut (Q1), blood (Q2), and tissue (Q3); and urine (Q0), all in units of μg Se. Six kinetics parameters were estimated: the fractional rates [1/h] of absorption, tissue disposition, tissue release, and urinary elimination (k12, k23, k32, and k20), the proportion of the absorbed dose eliminated through the urine (f20), and the distribution blood volume (V; percent body weight, BW). The parameter k12 was higher in sturgeon given the organic Se forms, in the descending order of MSeCys > SeMet > SeCys > Selenite > SeYeast. The parameters k23 and k32 followed similar patterns, and f20 was lowest in fish given MSeCys. Selenium form did not affect k20 or V. The parameter differences observed can be attributed to the different mechanisms of transmucosal transport
Wasson, Anton P.; Chiu, Grace S.; Zwart, Alexander B.; Binns, Timothy R.
2017-01-01
Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly “above ground,” little progress has been made “below ground”; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an “idealized” relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our
Wasson, Anton P; Chiu, Grace S; Zwart, Alexander B; Binns, Timothy R
2017-01-01
Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly "above ground," little progress has been made "below ground"; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an "idealized" relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our approach led
Kim, J.; Kwon, H. H.
2014-12-01
The existing regional frequency analysis has disadvantages in that it is difficult to consider geographical characteristics in estimating areal rainfall. In this regard, This study aims to develop a hierarchical Bayesian model based regional frequency analysis in that spatial patterns of the design rainfall with geographical information are explicitly incorporated. This study assumes that the parameters of Gumbel distribution are a function of geographical characteristics (e.g. altitude, latitude and longitude) within a general linear regression framework. Posterior distributions of the regression parameters are estimated by Bayesian Markov Chain Monte Calro (MCMC) method, and the identified functional relationship is used to spatially interpolate the parameters of the Gumbel distribution by using digital elevation models (DEM) as inputs. The proposed model is applied to derive design rainfalls over the entire Han-river watershed. It was found that the proposed Bayesian regional frequency analysis model showed similar results compared to L-moment based regional frequency analysis. In addition, the model showed an advantage in terms of quantifying uncertainty of the design rainfall and estimating the area rainfall considering geographical information. Acknowledgement: This research was supported by a grant (14AWMP-B079364-01) from Water Management Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government.
Rodhouse, T.J.; Irvine, K.M.; Vierling, K.T.; Vierling, L.A.
2011-01-01
Monitoring programs that evaluate restoration and inform adaptive management are important for addressing environmental degradation. These efforts may be well served by spatially explicit hierarchical approaches to modeling because of unavoidable spatial structure inherited from past land use patterns and other factors. We developed Bayesian hierarchical models to estimate trends from annual density counts observed in a spatially structured wetland forb (Camassia quamash [camas]) population following the cessation of grazing and mowing on the study area, and in a separate reference population of camas. The restoration site was bisected by roads and drainage ditches, resulting in distinct subpopulations ("zones") with different land use histories. We modeled this spatial structure by fitting zone-specific intercepts and slopes. We allowed spatial covariance parameters in the model to vary by zone, as in stratified kriging, accommodating anisotropy and improving computation and biological interpretation. Trend estimates provided evidence of a positive effect of passive restoration, and the strength of evidence was influenced by the amount of spatial structure in the model. Allowing trends to vary among zones and accounting for topographic heterogeneity increased precision of trend estimates. Accounting for spatial autocorrelation shifted parameter coefficients in ways that varied among zones depending on strength of statistical shrinkage, autocorrelation and topographic heterogeneity-a phenomenon not widely described. Spatially explicit estimates of trend from hierarchical models will generally be more useful to land managers than pooled regional estimates and provide more realistic assessments of uncertainty. The ability to grapple with historical contingency is an appealing benefit of this approach.
Mapping brucellosis increases relative to elk density using hierarchical Bayesian models
Cross, Paul C.; Heisey, Dennis M.; Scurlock, Brandon M.; Edwards, William H.; Brennan, Angela; Ebinger, Michael R.
2010-01-01
The relationship between host density and parasite transmission is central to the effectiveness of many disease management strategies. Few studies, however, have empirically estimated this relationship particularly in large mammals. We applied hierarchical Bayesian methods to a 19-year dataset of over 6400 brucellosis tests of adult female elk (Cervus elaphus) in northwestern Wyoming. Management captures that occurred from January to March were over two times more likely to be seropositive than hunted elk that were killed in September to December, while accounting for site and year effects. Areas with supplemental feeding grounds for elk had higher seroprevalence in 1991 than other regions, but by 2009 many areas distant from the feeding grounds were of comparable seroprevalence. The increases in brucellosis seroprevalence were correlated with elk densities at the elk management unit, or hunt area, scale (mean 2070 km2; range = [95–10237]). The data, however, could not differentiate among linear and non-linear effects of host density. Therefore, control efforts that focus on reducing elk densities at a broad spatial scale were only weakly supported. Additional research on how a few, large groups within a region may be driving disease dynamics is needed for more targeted and effective management interventions. Brucellosis appears to be expanding its range into new regions and elk populations, which is likely to further complicate the United States brucellosis eradication program. This study is an example of how the dynamics of host populations can affect their ability to serve as disease reservoirs.
Mapping brucellosis increases relative to elk density using hierarchical Bayesian models.
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Paul C Cross
Full Text Available The relationship between host density and parasite transmission is central to the effectiveness of many disease management strategies. Few studies, however, have empirically estimated this relationship particularly in large mammals. We applied hierarchical Bayesian methods to a 19-year dataset of over 6400 brucellosis tests of adult female elk (Cervus elaphus in northwestern Wyoming. Management captures that occurred from January to March were over two times more likely to be seropositive than hunted elk that were killed in September to December, while accounting for site and year effects. Areas with supplemental feeding grounds for elk had higher seroprevalence in 1991 than other regions, but by 2009 many areas distant from the feeding grounds were of comparable seroprevalence. The increases in brucellosis seroprevalence were correlated with elk densities at the elk management unit, or hunt area, scale (mean 2070 km(2; range = [95-10237]. The data, however, could not differentiate among linear and non-linear effects of host density. Therefore, control efforts that focus on reducing elk densities at a broad spatial scale were only weakly supported. Additional research on how a few, large groups within a region may be driving disease dynamics is needed for more targeted and effective management interventions. Brucellosis appears to be expanding its range into new regions and elk populations, which is likely to further complicate the United States brucellosis eradication program. This study is an example of how the dynamics of host populations can affect their ability to serve as disease reservoirs.
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Dongsheng Chen
2016-01-01
Full Text Available Accurate biomass estimations are important for assessing and monitoring forest carbon storage. Bayesian theory has been widely applied to tree biomass models. Recently, a hierarchical Bayesian approach has received increasing attention for improving biomass models. In this study, tree biomass data were obtained by sampling 310 trees from 209 permanent sample plots from larch plantations in six regions across China. Non-hierarchical and hierarchical Bayesian approaches were used to model allometric biomass equations. We found that the total, root, stem wood, stem bark, branch and foliage biomass model relationships were statistically significant (p-values < 0.001 for both the non-hierarchical and hierarchical Bayesian approaches, but the hierarchical Bayesian approach increased the goodness-of-fit statistics over the non-hierarchical Bayesian approach. The R2 values of the hierarchical approach were higher than those of the non-hierarchical approach by 0.008, 0.018, 0.020, 0.003, 0.088 and 0.116 for the total tree, root, stem wood, stem bark, branch and foliage models, respectively. The hierarchical Bayesian approach significantly improved the accuracy of the biomass model (except for the stem bark and can reflect regional differences by using random parameters to improve the regional scale model accuracy.
Yang, Yuqing; Chen, Ning; Chen, Ting
2017-01-25
The inference of associations between environmental factors and microbes and among microbes is critical to interpreting metagenomic data, but compositional bias, indirect associations resulting from common factors, and variance within metagenomic sequencing data limit the discovery of associations. To account for these problems, we propose metagenomic Lognormal-Dirichlet-Multinomial (mLDM), a hierarchical Bayesian model with sparsity constraints, to estimate absolute microbial abundance and simultaneously infer both conditionally dependent associations among microbes and direct associations between microbes and environmental factors. We empirically show the effectiveness of the mLDM model using synthetic data, data from the TARA Oceans project, and a colorectal cancer dataset. Finally, we apply mLDM to 16S sequencing data from the western English Channel and report several associations. Our model can be used on both natural environmental and human metagenomic datasets, promoting the understanding of associations in the microbial community.
Hierarchical Bayesian sparse image reconstruction with application to MRFM
Dobigeon, Nicolas; Tourneret, Jean-Yves
2008-01-01
This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g. by maximizing the estimated posterior distribution. In our fully Bayesian approach the posteriors of all the parameters are available. Thus our algorithm provides more information than other previously proposed sparse reconstr...
Grzegorczyk, Marco; Husmeier, Dirk
2013-01-01
To relax the homogeneity assumption of classical dynamic Bayesian networks (DBNs), various recent studies have combined DBNs with multiple changepoint processes. The underlying assumption is that the parameters associated with time series segments delimited by multiple changepoints are a priori inde
Semmens, Brice X; Ward, Eric J; Moore, Jonathan W; Darimont, Chris T
2009-07-09
Variability in resource use defines the width of a trophic niche occupied by a population. Intra-population variability in resource use may occur across hierarchical levels of population structure from individuals to subpopulations. Understanding how levels of population organization contribute to population niche width is critical to ecology and evolution. Here we describe a hierarchical stable isotope mixing model that can simultaneously estimate both the prey composition of a consumer diet and the diet variability among individuals and across levels of population organization. By explicitly estimating variance components for multiple scales, the model can deconstruct the niche width of a consumer population into relevant levels of population structure. We apply this new approach to stable isotope data from a population of gray wolves from coastal British Columbia, and show support for extensive intra-population niche variability among individuals, social groups, and geographically isolated subpopulations. The analytic method we describe improves mixing models by accounting for diet variability, and improves isotope niche width analysis by quantitatively assessing the contribution of levels of organization to the niche width of a population.
Hierarchical Bayesian inference in the visual cortex
Lee, Tai Sing; Mumford, David
2003-07-01
Traditional views of visual processing suggest that early visual neurons in areas V1 and V2 are static spatiotemporal filters that extract local features from a visual scene. The extracted information is then channeled through a feedforward chain of modules in successively higher visual areas for further analysis. Recent electrophysiological recordings from early visual neurons in awake behaving monkeys reveal that there are many levels of complexity in the information processing of the early visual cortex, as seen in the long-latency responses of its neurons. These new findings suggest that activity in the early visual cortex is tightly coupled and highly interactive with the rest of the visual system. They lead us to propose a new theoretical setting based on the mathematical framework of hierarchical Bayesian inference for reasoning about the visual system. In this framework, the recurrent feedforward/feedback loops in the cortex serve to integrate top-down contextual priors and bottom-up observations so as to implement concurrent probabilistic inference along the visual hierarchy. We suggest that the algorithms of particle filtering and Bayesian-belief propagation might model these interactive cortical computations. We review some recent neurophysiological evidences that support the plausibility of these ideas. 2003 Optical Society of America
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Auvinen Petri
2008-01-01
Full Text Available We propose a method for improving the quality of signal from DNA microarrays by using several scans at varying scanner sen-sitivities. A Bayesian latent intensity model is introduced for the analysis of such data. The method improves the accuracy at which expressions can be measured in all ranges and extends the dynamic range of measured gene expression at the high end. Our method is generic and can be applied to data from any organism, for imaging with any scanner that allows varying the laser power, and for extraction with any image analysis software. Results from a self-self hybridization data set illustrate an improved precision in the estimation of the expression of genes compared to what can be achieved by applying standard methods and using only a single scan.
Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model
Ellefsen, Karl J.; Smith, David
2016-01-01
Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples.
A BAYESIAN HIERARCHICAL SPATIAL POINT PROCESS MODEL FOR MULTI-TYPE NEUROIMAGING META-ANALYSIS.
Kang, Jian; Nichols, Thomas E; Wager, Tor D; Johnson, Timothy D
2014-09-01
Neuroimaging meta-analysis is an important tool for finding consistent effects over studies that each usually have 20 or fewer subjects. Interest in meta-analysis in brain mapping is also driven by a recent focus on so-called "reverse inference": where as traditional "forward inference" identifies the regions of the brain involved in a task, a reverse inference identifies the cognitive processes that a task engages. Such reverse inferences, however, requires a set of meta-analysis, one for each possible cognitive domain. However, existing methods for neuroimaging meta-analysis have significant limitations. Commonly used methods for neuroimaging meta-analysis are not model based, do not provide interpretable parameter estimates, and only produce null hypothesis inferences; further, they are generally designed for a single group of studies and cannot produce reverse inferences. In this work we address these limitations by adopting a non-parametric Bayesian approach for meta analysis data from multiple classes or types of studies. In particular, foci from each type of study are modeled as a cluster process driven by a random intensity function that is modeled as a kernel convolution of a gamma random field. The type-specific gamma random fields are linked and modeled as a realization of a common gamma random field, shared by all types, that induces correlation between study types and mimics the behavior of a univariate mixed effects model. We illustrate our model on simulation studies and a meta analysis of five emotions from 219 studies and check model fit by a posterior predictive assessment. In addition, we implement reverse inference by using the model to predict study type from a newly presented study. We evaluate this predictive performance via leave-one-out cross validation that is efficiently implemented using importance sampling techniques.
Molnar, S.; Dettmer, J.; Steininger, G.; Dosso, S. E.; Cassidy, J. F.
2013-12-01
This paper applies hierarchical, trans-dimensional Bayesian models for earth and residual-error parametrizations to the inversion of microtremor array dispersion data for shear-wave velocity (Vs) structure. The earth is parametrized in terms of flat-lying, homogeneous layers and residual errors are parametrized with a first-order autoregressive data-error model. The inversion accounts for the limited knowledge of the optimal earth and residual error model parametrization (e.g. the number of layers in the Vs profile) in the resulting Vs parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A trans-dimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the index) are considered in the results. In addition, serial residual-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate residual-error statistics, and have no requirement for computing the inverse or determinant of a covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the state space that spans multiple subspaces of different dimensions. The autoregressive process is restricted to first order and
Bayesian Hierarchical Model Characterization of Model Error in Ocean Data Assimilation and Forecasts
2012-09-28
potential benefits from allowing switching between different process models in this setting. This will be greatly facilitated by the emulator approach...of sea surface height (SSH), SST, and phytoplankton ( chlorophyll ) data from 1998, 1999, 2000, and 2001. We then used remotely sensed SeaWiFS ocean
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Fontez B.
2014-04-01
Full Text Available Back-calculation allows to increase available data on fish growth. The accuracy of back-calculation models is of paramount importance for growth analysis. Frequentist and Bayesian hierarchical approaches were used for regression between fish body size and scale size for the rare fish species Zingel asper. The Bayesian approach permits more reliable estimation of back-calculated size, taking into account biological information and cohort variability. This method greatly improves estimation of back-calculated length when sampling is uneven and/or small.
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J.-J. Boreux
2009-10-01
Full Text Available One basic premise of dendroclimatology is that tree rings can be viewed as climate proxies, i.e. rings are assumed to contain some hidden information about past climate. From a statistical perspective, this extraction problem can be understood as the search of a hidden variable which represents the common signal within a collection of tree-ring width series. Classical average-based techniques used in dendrochronology have been applied to estimate the mean behavior of this latent variable. Still, depending on tree species, regional factors and statistical methods, a precise quantification of uncertainties associated to the hidden variable distribution is difficult to assess. To model the error propagation throughout the extraction procedure, we propose and study a Bayesian hierarchical model that focuses on extracting an inter-annual high frequency signal. Our method is applied to black spruce (Picea mariana tree-rings recorded in Northern Quebec and compared to a classical average-based techniques used by dendrochronologists (Cook and Kairiukstis, 1992.
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J.-J. Boreux
2009-03-01
Full Text Available Dendrochronology, the scientific dating method based on the analysis of tree-ring growth patterns, has been frequently applied in climatology. The basic premise of dendroclimatology is that tree rings can be viewed as climate proxies, i.e. rings are assumed to contain some hidden information about past climate. From a statistical perspective, this extraction problem can be understood as the search of a hidden variable which represents the common signal within a collection of tree-ring width series. Classical average-based techniques used in dendrochronology have been, with different degrees of success (depending on tree species, regional factors and statistical methods, applied to estimate the mean behavior of this latent variable. Still, a precise quantification of uncertainties associated to the hidden variable distribution is difficult to assess. To model the error propagation throughout the extraction procedure, we propose and study a Bayesian hierarchical model that focuses on extracting an inter-annual high frequency signal. Our method is applied to black spruce (Picea mariana tree-rings recorded in northern Quebec and compared to a classical average-based techniques used by dendrochronologists.
Ishigami, Hideaki
2016-01-01
Relative age effect (RAE) in sports has been well documented. Recent studies investigate the effect of birthplace in addition to the RAE. The first objective of this study was to show the magnitude of the RAE in two major professional sports in Japan, baseball and soccer. Second, we examined the birthplace effect and compared its magnitude with that of the RAE. The effect sizes were estimated using a Bayesian hierarchical Poisson model with the number of players as dependent variable. The RAEs were 9.0% and 7.7% per month for soccer and baseball, respectively. These estimates imply that children born in the first month of a school year have about three times greater chance of becoming a professional player than those born in the last month of the year. Over half of the difference in likelihoods of becoming a professional player between birthplaces was accounted for by weather conditions, with the likelihood decreasing by 1% per snow day. An effect of population size was not detected in the data. By investigating different samples, we demonstrated that using quarterly data leads to underestimation and that the age range of sampled athletes should be set carefully.
Hierarchical Bayesian modeling and Markov chain Monte Carlo sampling for tuning-curve analysis.
Cronin, Beau; Stevenson, Ian H; Sur, Mriganka; Körding, Konrad P
2010-01-01
A central theme of systems neuroscience is to characterize the tuning of neural responses to sensory stimuli or the production of movement. Statistically, we often want to estimate the parameters of the tuning curve, such as preferred direction, as well as the associated degree of uncertainty, characterized by error bars. Here we present a new sampling-based, Bayesian method that allows the estimation of tuning-curve parameters, the estimation of error bars, and hypothesis testing. This method also provides a useful way of visualizing which tuning curves are compatible with the recorded data. We demonstrate the utility of this approach using recordings of orientation and direction tuning in primary visual cortex, direction of motion tuning in primary motor cortex, and simulated data.
Yu, Rongjie; Abdel-Aty, Mohamed
2014-01-01
Severe crashes are causing serious social and economic loss, and because of this, reducing crash injury severity has become one of the key objectives of the high speed facilities' (freeway and expressway) management. Traditional crash injury severity analysis utilized data mainly from crash reports concerning the crash occurrence information, drivers' characteristics and roadway geometric related variables. In this study, real-time traffic and weather data were introduced to analyze the crash injury severity. The space mean speeds captured by the Automatic Vehicle Identification (AVI) system on the two roadways were used as explanatory variables in this study; and data from a mountainous freeway (I-70 in Colorado) and an urban expressway (State Road 408 in Orlando) have been used to identify the analysis result's consistence. Binary probit (BP) models were estimated to classify the non-severe (property damage only) crashes and severe (injury and fatality) crashes. Firstly, Bayesian BP models' results were compared to the results from Maximum Likelihood Estimation BP models and it was concluded that Bayesian inference was superior with more significant variables. Then different levels of hierarchical Bayesian BP models were developed with random effects accounting for the unobserved heterogeneity at segment level and crash individual level, respectively. Modeling results from both studied locations demonstrate that large variations of speed prior to the crash occurrence would increase the likelihood of severe crash occurrence. Moreover, with considering unobserved heterogeneity in the Bayesian BP models, the model goodness-of-fit has improved substantially. Finally, possible future applications of the model results and the hierarchical Bayesian probit models were discussed.
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Salvador Dura-Bernal
Full Text Available Hierarchical generative models, such as Bayesian networks, and belief propagation have been shown to provide a theoretical framework that can account for perceptual processes, including feedforward recognition and feedback modulation. The framework explains both psychophysical and physiological experimental data and maps well onto the hierarchical distributed cortical anatomy. However, the complexity required to model cortical processes makes inference, even using approximate methods, very computationally expensive. Thus, existing object perception models based on this approach are typically limited to tree-structured networks with no loops, use small toy examples or fail to account for certain perceptual aspects such as invariance to transformations or feedback reconstruction. In this study we develop a Bayesian network with an architecture similar to that of HMAX, a biologically-inspired hierarchical model of object recognition, and use loopy belief propagation to approximate the model operations (selectivity and invariance. Crucially, the resulting Bayesian network extends the functionality of HMAX by including top-down recursive feedback. Thus, the proposed model not only achieves successful feedforward recognition invariant to noise, occlusions, and changes in position and size, but is also able to reproduce modulatory effects such as illusory contour completion and attention. Our novel and rigorous methodology covers key aspects such as learning using a layerwise greedy algorithm, combining feedback information from multiple parents and reducing the number of operations required. Overall, this work extends an established model of object recognition to include high-level feedback modulation, based on state-of-the-art probabilistic approaches. The methodology employed, consistent with evidence from the visual cortex, can be potentially generalized to build models of hierarchical perceptual organization that include top-down and bottom
Prediction of road accidents: A Bayesian hierarchical approach
DEFF Research Database (Denmark)
Deublein, Markus; Schubert, Matthias; Adey, Bryan T.;
2013-01-01
In this paper a novel methodology for the prediction of the occurrence of road accidents is presented. The methodology utilizes a combination of three statistical methods: (1) gamma-updating of the occurrence rates of injury accidents and injured road users, (2) hierarchical multivariate Poisson......-lognormal regression analysis taking into account correlations amongst multiple dependent model response variables and effects of discrete accident count data e.g. over-dispersion, and (3) Bayesian inference algorithms, which are applied by means of data mining techniques supported by Bayesian Probabilistic Networks...... in order to represent non-linearity between risk indicating and model response variables, as well as different types of uncertainties which might be present in the development of the specific models.Prior Bayesian Probabilistic Networks are first established by means of multivariate regression analysis...
Giovanini, Jack; Kroll, Andrew J; Jones, Jay E; Altman, Bob; Arnett, Edward B
2013-01-01
As human demand for ecosystem products increases, management intervention may become more frequent after environmental disturbances. Evaluations of ecological responses to cumulative effects of management interventions and natural disturbances provide critical decision-support tools for managers who strive to balance environmental conservation and economic development. We conducted an experiment to evaluate the effects of salvage logging on avian community composition in lodgepole pine (Pinus contorta) forests affected by beetle outbreaks in Oregon, USA, 1996-1998. Treatments consisted of the removal of lodgepole pine snags only, and live trees were not harvested. We used a bayesian hierarchical model to quantify occupancy dynamics for 27 breeding species, while accounting for variation in the detection process. We examined how magnitude and precision of treatment effects varied when incorporating prior information from a separate intervention study that occurred in a similar ecological system. Regardless of which prior we evaluated, we found no evidence that the harvest treatment had a negative impact on species richness, with an estimated average of 0.2-2.2 more species in harvested stands than unharvested stands. Estimated average similarity between control and treatment stands ranged from 0.82-0.87 (1 indicating complete similarity between a pair of stands) and suggested that treatment stands did not contain novel assemblies of species responding to the harvesting prescription. Estimated treatment effects were positive for twenty-four (90%) of the species, although the credible intervals contained 0 in all cases. These results suggest that, unlike most post-fire salvage logging prescriptions, selective harvesting after beetle outbreaks may meet multiple management objectives, including the maintenance of avian community richness comparable to what is found in unharvested stands. Our results provide managers with prescription alternatives to respond to severe
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Jack Giovanini
Full Text Available As human demand for ecosystem products increases, management intervention may become more frequent after environmental disturbances. Evaluations of ecological responses to cumulative effects of management interventions and natural disturbances provide critical decision-support tools for managers who strive to balance environmental conservation and economic development. We conducted an experiment to evaluate the effects of salvage logging on avian community composition in lodgepole pine (Pinus contorta forests affected by beetle outbreaks in Oregon, USA, 1996-1998. Treatments consisted of the removal of lodgepole pine snags only, and live trees were not harvested. We used a bayesian hierarchical model to quantify occupancy dynamics for 27 breeding species, while accounting for variation in the detection process. We examined how magnitude and precision of treatment effects varied when incorporating prior information from a separate intervention study that occurred in a similar ecological system. Regardless of which prior we evaluated, we found no evidence that the harvest treatment had a negative impact on species richness, with an estimated average of 0.2-2.2 more species in harvested stands than unharvested stands. Estimated average similarity between control and treatment stands ranged from 0.82-0.87 (1 indicating complete similarity between a pair of stands and suggested that treatment stands did not contain novel assemblies of species responding to the harvesting prescription. Estimated treatment effects were positive for twenty-four (90% of the species, although the credible intervals contained 0 in all cases. These results suggest that, unlike most post-fire salvage logging prescriptions, selective harvesting after beetle outbreaks may meet multiple management objectives, including the maintenance of avian community richness comparable to what is found in unharvested stands. Our results provide managers with prescription alternatives to
Song, Xin-Yuan; Lee, Sik-Yum
2008-01-01
Structural equation models are widely appreciated in behavioral, social, and psychological research to model relations between latent constructs and manifest variables, and to control for measurement errors. Most applications of structural equation models are based on fully observed data that are independently distributed. However, hierarchical…
Bayesian Data Analysis with the Bivariate Hierarchical Ornstein-Uhlenbeck Process Model.
Oravecz, Zita; Tuerlinckx, Francis; Vandekerckhove, Joachim
2016-01-01
In this paper, we propose a multilevel process modeling approach to describing individual differences in within-person changes over time. To characterize changes within an individual, repeated measures over time are modeled in terms of three person-specific parameters: a baseline level, intraindividual variation around the baseline, and regulatory mechanisms adjusting toward baseline. Variation due to measurement error is separated from meaningful intraindividual variation. The proposed model allows for the simultaneous analysis of longitudinal measurements of two linked variables (bivariate longitudinal modeling) and captures their relationship via two person-specific parameters. Relationships between explanatory variables and model parameters can be studied in a one-stage analysis, meaning that model parameters and regression coefficients are estimated simultaneously. Mathematical details of the approach, including a description of the core process model-the Ornstein-Uhlenbeck model-are provided. We also describe a user friendly, freely accessible software program that provides a straightforward graphical interface to carry out parameter estimation and inference. The proposed approach is illustrated by analyzing data collected via self-reports on affective states.
DEFF Research Database (Denmark)
Stahlhut, Carsten; Mørup, Morten; Winther, Ole;
2011-01-01
We present an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model representation is motivated by the many random contributions to the path from sources to measurements including the tissue conductivity distribution, the geometry of the cortical s...
A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins
Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predic...
A hierarchical Bayesian spatio-temporal model for extreme precipitation events
Ghosh, Souparno
2011-03-01
We propose a new approach to model a sequence of spatially distributed time series of extreme values. Unlike common practice, we incorporate spatial dependence directly in the likelihood and allow the temporal component to be captured at the second level of hierarchy. Inferences about the parameters and spatio-temporal predictions are obtained via MCMC technique. The model is fitted to a gridded precipitation data set collected over 99 years across the continental U.S. © 2010 John Wiley & Sons, Ltd..
Mandel, Kaisey; Scolnic, Daniel; Shariff, Hikmatali; Foley, Ryan; Kirshner, Robert
2017-01-01
Inferring peak optical absolute magnitudes of Type Ia supernovae (SN Ia) from distance-independent measures such as their light curve shapes and colors underpins the evidence for cosmic acceleration. SN Ia with broader, slower declining optical light curves are more luminous (“broader-brighter”) and those with redder colors are dimmer. But the “redder-dimmer” color-luminosity relation widely used in cosmological SN Ia analyses confounds its two separate physical origins. An intrinsic correlation arises from the physics of exploding white dwarfs, while interstellar dust in the host galaxy also makes SN Ia appear dimmer and redder. Conventional SN Ia cosmology analyses currently use a simplistic linear regression of magnitude versus color and light curve shape, which does not model intrinsic SN Ia variations and host galaxy dust as physically distinct effects, resulting in low color-magnitude slopes. We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colors as the convolution of an intrinsic SN Ia color-magnitude distribution and a host galaxy dust reddening-extinction distribution. If the intrinsic color-magnitude (MB vs. B-V) slope βint differs from the host galaxy dust law RB, this convolution results in a specific curve of mean extinguished absolute magnitude vs. apparent color. The derivative of this curve smoothly transitions from βint in the blue tail to RB in the red tail of the apparent color distribution. The conventional linear fit approximates this effective curve near the average apparent color, resulting in an apparent slope βapp between βint and RB. We incorporate these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze a dataset of SALT2 optical light curve fits of 277 nearby SN Ia at z < 0.10. The conventional linear fit obtains βapp ≈ 3. Our model finds a βint = 2.2 ± 0.3 and a distinct dust law of RB = 3.7 ± 0
MacNab, Ying C
2007-11-20
This paper presents a Bayesian disability-adjusted life year (DALY) methodology for spatial and spatiotemporal analyses of disease and/or injury burden. A Bayesian disease mapping model framework, which blends together spatial modelling, shared-component modelling (SCM), temporal modelling, ecological modelling, and non-linear modelling, is developed for small-area DALY estimation and inference. In particular, we develop a model framework that enables SCM as well as multivariate CAR modelling of non-fatal and fatal disease or injury rates and facilitates spline smoothing for non-linear modelling of temporal rate and risk trends. Using British Columbia (Canada) hospital admission-separation data and vital statistics mortality data on non-fatal and fatal road traffic injuries to male population age 20-39 for year 1991-2000 and for 84 local health areas and 16 health service delivery areas, spatial and spatiotemporal estimation and inference on years of life lost due to premature death, years lived with disability, and DALYs are presented. Fully Bayesian estimation and inference, with Markov chain Monte Carlo implementation, are illustrated. We present a methodological framework within which the DALY and the Bayesian disease mapping methodologies interface and intersect. Its development brings the relative importance of premature mortality and disability into the assessment of community health and health needs in order to provide reliable information and evidence for community-based public health surveillance and evaluation, disease and injury prevention, and resource provision.
Kim, Jang-Gyeong; Kwon, Hyun-Han; Kim, Dongkyun
2017-01-01
Poisson cluster stochastic rainfall generators (e.g., modified Bartlett-Lewis rectangular pulse, MBLRP) have been widely applied to generate synthetic sub-daily rainfall sequences. The MBLRP model reproduces the underlying distribution of the rainfall generating process. The existing optimization techniques are typically based on individual parameter estimates that treat each parameter as independent. However, parameter estimates sometimes compensate for the estimates of other parameters, which can cause high variability in the results if the covariance structure is not formally considered. Moreover, uncertainty associated with model parameters in the MBLRP rainfall generator is not usually addressed properly. Here, we develop a hierarchical Bayesian model (HBM)-based MBLRP model to jointly estimate parameters across weather stations and explicitly consider the covariance and uncertainty through a Bayesian framework. The model is tested using weather stations in South Korea. The HBM-based MBLRP model improves the identification of parameters with better reproduction of rainfall statistics at various temporal scales. Additionally, the spatial variability of the parameters across weather stations is substantially reduced compared to that of other methods.
Bayesian hierarchical models for network meta-analysis incorporating nonignorable missingness.
Zhang, Jing; Chu, Haitao; Hong, Hwanhee; Virnig, Beth A; Carlin, Bradley P
2015-07-28
Network meta-analysis expands the scope of a conventional pairwise meta-analysis to simultaneously compare multiple treatments, synthesizing both direct and indirect information and thus strengthening inference. Since most of trials only compare two treatments, a typical data set in a network meta-analysis managed as a trial-by-treatment matrix is extremely sparse, like an incomplete block structure with significant missing data. Zhang et al. proposed an arm-based method accounting for correlations among different treatments within the same trial and assuming that absent arms are missing at random. However, in randomized controlled trials, nonignorable missingness or missingness not at random may occur due to deliberate choices of treatments at the design stage. In addition, those undertaking a network meta-analysis may selectively choose treatments to include in the analysis, which may also lead to missingness not at random. In this paper, we extend our previous work to incorporate missingness not at random using selection models. The proposed method is then applied to two network meta-analyses and evaluated through extensive simulation studies. We also provide comprehensive comparisons of a commonly used contrast-based method and the arm-based method via simulations in a technical appendix under missing completely at random and missing at random.
Song, Hae-Ryoung; Lawson, Andrew; D'Agostino, Ralph B; Liese, Angela D
2011-03-01
Sparse count data violate assumptions of traditional Poisson models due to the excessive amount of zeros, and modeling sparse data becomes challenging. However, since aggregation to reduce sparseness may result in biased estimates of risk, solutions need to be found at the level of disaggregated data. We investigated different statistical approaches within a Bayesian hierarchical framework for modeling sparse data without aggregation of data. We compared our proposed models with the traditional Poisson model and the zero-inflated model based on simulated data. We applied statistical models to type 1 and type 2 diabetes in youth 10-19 years known as rare diseases, and compared models using the inference results and various model diagnostic tools. We showed that one of the models we proposed, a sparse Poisson convolution model, performed better than other models in the simulation and application based on the deviance information criterion (DIC) and the mean squared prediction error.
Directory of Open Access Journals (Sweden)
Ying Cao
Full Text Available Childhood acute lymphoblastic leukemia (ALL is a condition that arises from complex etiologies. The absence of consistent environmental risk factors and the presence of modest familial associations suggest ALL is a complex trait with an underlying genetic component. The identification of genetic factors associated with disease is complicated by complex genetic covariance structures and multiple testing issues. Both issues can be resolved with appropriate Bayesian variable selection methods. The present study was undertaken to extend our hierarchical Bayesian model for case-parent triads to incorporate single nucleotide polymorphisms (SNPs and incorporate the biological grouping of SNPs within genes. Based on previous evidence that genetic variation in the folate metabolic pathway influences ALL risk, we evaluated 128 tagging SNPs in 16 folate metabolic genes among 118 ALL case-parent triads recruited from the Texas Children's Cancer Center (Houston, TX between 2003 and 2010. We used stochastic search gene suggestion (SSGS in hierarchical Bayesian models to evaluate the association between folate metabolic SNPs and ALL. Using Bayes factors among these variants in childhood ALL case-parent triads, two SNPs were identified with a Bayes factor greater than 1. There was evidence that the minor alleles of NOS3 rs3918186 (OR = 2.16; 95% CI: 1.51-3.15 and SLC19A1 rs1051266 (OR = 2.07; 95% CI: 1.25-3.46 were positively associated with childhood ALL. Our findings are suggestive of the role of inherited genetic variation in the folate metabolic pathway on childhood ALL risk, and they also suggest the utility of Bayesian variable selection methods in the context of case-parent triads for evaluating the role of SNPs on disease risk.
Bayesian modeling using WinBUGS
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 ...
DEFF Research Database (Denmark)
Lin, Lin; Chan, Cliburn; Hadrup, Sine R
2013-01-01
Novel uses of automated flow cytometry technology for measuring levels of protein markers on thousands to millions of cells are promoting increasing need for relevant, customized Bayesian mixture modelling approaches in many areas of biomedical research and application. In studies of immune...... profiling in many biological areas, traditional flow cytometry measures relative levels of abundance of marker proteins using fluorescently labeled tags that identify specific markers by a single-color. One specific and important recent development in this area is the use of combinatorial marker assays...
Babcock, C. R.; Andersen, H. E.; Finley, A. O.; Cook, B.; Morton, D. C.
2015-12-01
Models using repeat LiDAR and field campaigns may be one mechanism to monitor carbon storage and flux in forested regions. Considering the ability of multi-temporal LiDAR to estimate growth, it is not surprising that there is great interest in developing forest carbon monitoring strategies that rely on repeated LiDAR acquisitions. Allowing for sparser field campaigns, LiDAR stands to make monitoring forest carbon cheaper and more efficient than field-only sampling procedures. Here, we look to the spatio-temporally data-rich Kenai Peninsula in Alaska to examine the potential for Bayesian spatio-temporal mapping of forest carbon storage and uncertainty. The framework explored here can predict forest carbon through space and time, while formally propagating uncertainty through to prediction. Bayesian spatio-temporal models are flexible frameworks allowing for forest growth processes to be formally integrated into the model. By incorporating a mechanism for growth---using temporally repeated field and LiDAR data---we can more fully exploit the information-rich inventory network to improve prediction accuracy. LiDAR data for the Kenai Peninsula has been collected on four different occasions---spatially coincident LiDAR strip samples in 2004, 09 and 14, along with a wall-to-wall collection in 2008. There were 436 plots measured twice between 2002 and 2014. LiDAR was acquired at least once over most inventory plots with many having LiDAR collected during 2, 3 or 4 different campaigns. Results from this research will impact how forests are inventoried. It is too expensive to monitor terrestrial carbon using field-only sampling strategies and currently proposed LiDAR model-based techniques lack the ability to properly utilize temporally repeated and misaligned data. Bayesian hierarchical spatio-temporal models offer a solution to these shortcomings and allow for formal predictive error assessment, which is useful for policy development and decision making.
Unsupervised Transient Light Curve Analysis Via Hierarchical Bayesian Inference
Sanders, Nathan; Soderberg, Alicia
2014-01-01
Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. We present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometr...
Lucka, Felix; Pursiainen, Sampsa; Burger, Martin; Wolters, Carsten H
2012-07-16
The estimation of the activity-related ion currents by measuring the induced electromagnetic fields at the head surface is a challenging and severely ill-posed inverse problem. This is especially true in the recovery of brain networks involving deep-lying sources by means of EEG/MEG recordings which is still a challenging task for any inverse method. Recently, hierarchical Bayesian modeling (HBM) emerged as a unifying framework for current density reconstruction (CDR) approaches comprising most established methods as well as offering promising new methods. Our work examines the performance of fully-Bayesian inference methods for HBM for source configurations consisting of few, focal sources when used with realistic, high-resolution finite element (FE) head models. The main foci of interest are the correct depth localization, a well-known source of systematic error of many CDR methods, and the separation of single sources in multiple-source scenarios. Both aspects are very important in the analysis of neurophysiological data and in clinical applications. For these tasks, HBM provides a promising framework and is able to improve upon established CDR methods such as minimum norm estimation (MNE) or sLORETA in many aspects. For challenging multiple-source scenarios where the established methods show crucial errors, promising results are attained. Additionally, we introduce Wasserstein distances as performance measures for the validation of inverse methods in complex source scenarios.
Bayesian hierarchical grouping: Perceptual grouping as mixture estimation.
Froyen, Vicky; Feldman, Jacob; Singh, Manish
2015-10-01
We propose a novel framework for perceptual grouping based on the idea of mixture models, called Bayesian hierarchical grouping (BHG). In BHG, we assume that the configuration of image elements is generated by a mixture of distinct objects, each of which generates image elements according to some generative assumptions. Grouping, in this framework, means estimating the number and the parameters of the mixture components that generated the image, including estimating which image elements are "owned" by which objects. We present a tractable implementation of the framework, based on the hierarchical clustering approach of Heller and Ghahramani (2005). We illustrate it with examples drawn from a number of classical perceptual grouping problems, including dot clustering, contour integration, and part decomposition. Our approach yields an intuitive hierarchical representation of image elements, giving an explicit decomposition of the image into mixture components, along with estimates of the probability of various candidate decompositions. We show that BHG accounts well for a diverse range of empirical data drawn from the literature. Because BHG provides a principled quantification of the plausibility of grouping interpretations over a wide range of grouping problems, we argue that it provides an appealing unifying account of the elusive Gestalt notion of Prägnanz.
Pham, Lisa M; Carvalho, Luis; Schaus, Scott; Kolaczyk, Eric D
Cellular response to a perturbation is the result of a dynamic system of biological variables linked in a complex network. A major challenge in drug and disease studies is identifying the key factors of a biological network that are essential in determining the cell's fate. Here our goal is the identification of perturbed pathways from high-throughput gene expression data. We develop a three-level hierarchical model, where (i) the first level captures the relationship between gene expression and biological pathways using confirmatory factor analysis, (ii) the second level models the behavior within an underlying network of pathways induced by an unknown perturbation using a conditional autoregressive model, and (iii) the third level is a spike-and-slab prior on the perturbations. We then identify perturbations through posterior-based variable selection. We illustrate our approach using gene transcription drug perturbation profiles from the DREAM7 drug sensitivity predication challenge data set. Our proposed method identified regulatory pathways that are known to play a causative role and that were not readily resolved using gene set enrichment analysis or exploratory factor models. Simulation results are presented assessing the performance of this model relative to a network-free variant and its robustness to inaccuracies in biological databases.
Poor-data and data-poor species stock assessment using a Bayesian hierarchical approach.
Jiao, Yan; Cortés, Enric; Andrews, Kate; Guo, Feng
2011-10-01
Appropriate inference for stocks or species with low-quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small-area, small-sample-size estimation problems because they allow poor-data species to borrow strength from species with good-quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor-data and data-poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70-80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state-space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species-specific data, because the poor-data species can borrow strength from the species with good data, making the estimation more stable and robust.
Eadie, Gwendolyn; Harris, William
2016-01-01
We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie, Harris, & Widrow (2015) and Eadie & Harris (2016) and builds upon the preliminary reports by Eadie et al (2015a,c). The method uses a distribution function $f(\\mathcal{E},L)$ to model the galaxy and kinematic data from satellite objects such as globular clusters to trace the Galaxy's gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie & Harris (2016), and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and in...
Lashkari, Danial; Sridharan, Ramesh; Vul, Edward; Hsieh, Po-Jang; Kanwisher, Nancy; Golland, Polina
2012-01-16
Functional MRI studies have uncovered a number of brain areas that demonstrate highly specific functional patterns. In the case of visual object recognition, small, focal regions have been characterized with selectivity for visual categories such as human faces. In this paper, we develop an algorithm that automatically learns patterns of functional specificity from fMRI data in a group of subjects. The method does not require spatial alignment of functional images from different subjects. The algorithm is based on a generative model that comprises two main layers. At the lower level, we express the functional brain response to each stimulus as a binary activation variable. At the next level, we define a prior over sets of activation variables in all subjects. We use a Hierarchical Dirichlet Process as the prior in order to learn the patterns of functional specificity shared across the group, which we call functional systems, and estimate the number of these systems. Inference based on our model enables automatic discovery and characterization of dominant and consistent functional systems. We apply the method to data from a visual fMRI study comprised of 69 distinct stimulus images. The discovered system activation profiles correspond to selectivity for a number of image categories such as faces, bodies, and scenes. Among systems found by our method, we identify new areas that are deactivated by face stimuli. In empirical comparisons with previously proposed exploratory methods, our results appear superior in capturing the structure in the space of visual categories of stimuli.
Swallow, Ben; Buckland, Stephen T; King, Ruth; Toms, Mike P
2016-03-01
The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zero-inflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about mean-variance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.
A Hierarchical Bayesian M/EEG Imaging Method Correcting for Incomplete Spatio-Temporal Priors
DEFF Research Database (Denmark)
Stahlhut, Carsten; Attias, Hagai T.; Sekihara, Kensuke;
2013-01-01
In this paper we present a hierarchical Bayesian model, to tackle the highly ill-posed problem that follows with MEG and EEG source imaging. Our model promotes spatiotemporal patterns through the use of both spatial and temporal basis functions. While in contrast to most previous spatio-temporal ...
Ma, Xiaoye; Chen, Yong; Cole, Stephen R; Chu, Haitao
2014-05-26
To account for between-study heterogeneity in meta-analysis of diagnostic accuracy studies, bivariate random effects models have been recommended to jointly model the sensitivities and specificities. As study design and population vary, the definition of disease status or severity could differ across studies. Consequently, sensitivity and specificity may be correlated with disease prevalence. To account for this dependence, a trivariate random effects model had been proposed. However, the proposed approach can only include cohort studies with information estimating study-specific disease prevalence. In addition, some diagnostic accuracy studies only select a subset of samples to be verified by the reference test. It is known that ignoring unverified subjects may lead to partial verification bias in the estimation of prevalence, sensitivities, and specificities in a single study. However, the impact of this bias on a meta-analysis has not been investigated. In this paper, we propose a novel hybrid Bayesian hierarchical model combining cohort and case-control studies and correcting partial verification bias at the same time. We investigate the performance of the proposed methods through a set of simulation studies. Two case studies on assessing the diagnostic accuracy of gadolinium-enhanced magnetic resonance imaging in detecting lymph node metastases and of adrenal fluorine-18 fluorodeoxyglucose positron emission tomography in characterizing adrenal masses are presented.
UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE
Energy Technology Data Exchange (ETDEWEB)
Sanders, N. E.; Soderberg, A. M. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Betancourt, M., E-mail: nsanders@cfa.harvard.edu [Department of Statistics, University of Warwick, Coventry CV4 7AL (United Kingdom)
2015-02-10
Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. We present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometric observations of 76 SNe, corresponding to a joint posterior distribution with 9176 parameters under our model. Our hierarchical model fits provide improved constraints on light curve parameters relevant to the physical properties of their progenitor stars relative to modeling individual light curves alone. Moreover, we directly evaluate the probability for occurrence rates of unseen light curve characteristics from the model hyperparameters, addressing observational biases in survey methodology. We view this modeling framework as an unsupervised machine learning technique with the ability to maximize scientific returns from data to be collected by future wide field transient searches like LSST.
Directory of Open Access Journals (Sweden)
Lewis G Coggins
Full Text Available Occupancy models using incidence data collected repeatedly at sites across the range of a population are increasingly employed to infer patterns and processes influencing population distribution and dynamics. While such work is common in terrestrial systems, fewer examples exist in marine applications. This disparity likely exists because the replicate samples required by these models to account for imperfect detection are often impractical to obtain when surveying aquatic organisms, particularly fishes. We employ simultaneous sampling using fish traps and novel underwater camera observations to generate the requisite replicate samples for occupancy models of red snapper, a reef fish species. Since the replicate samples are collected simultaneously by multiple sampling devices, many typical problems encountered when obtaining replicate observations are avoided. Our results suggest that augmenting traditional fish trap sampling with camera observations not only doubled the probability of detecting red snapper in reef habitats off the Southeast coast of the United States, but supplied the necessary observations to infer factors influencing population distribution and abundance while accounting for imperfect detection. We found that detection probabilities tended to be higher for camera traps than traditional fish traps. Furthermore, camera trap detections were influenced by the current direction and turbidity of the water, indicating that collecting data on these variables is important for future monitoring. These models indicate that the distribution and abundance of this species is more heavily influenced by latitude and depth than by micro-scale reef characteristics lending credence to previous characterizations of red snapper as a reef habitat generalist. This study demonstrates the utility of simultaneous sampling devices, including camera traps, in aquatic environments to inform occupancy models and account for imperfect detection when
Stewart, David R.; Long, James M.
2015-01-01
Species distribution models are useful tools to evaluate habitat relationships of fishes. We used hierarchical Bayesian multispecies mixture models to evaluate the relationships of both detection and abundance with habitat of reservoir fishes caught using tandem hoop nets. A total of 7,212 fish from 12 species were captured, and the majority of the catch was composed of Channel Catfish Ictalurus punctatus (46%), Bluegill Lepomis macrochirus(25%), and White Crappie Pomoxis annularis (14%). Detection estimates ranged from 8% to 69%, and modeling results suggested that fishes were primarily influenced by reservoir size and context, water clarity and temperature, and land-use types. Species were differentially abundant within and among habitat types, and some fishes were found to be more abundant in turbid, less impacted (e.g., by urbanization and agriculture) reservoirs with longer shoreline lengths; whereas, other species were found more often in clear, nutrient-rich impoundments that had generally shorter shoreline length and were surrounded by a higher percentage of agricultural land. Our results demonstrated that habitat and reservoir characteristics may differentially benefit species and assemblage structure. This study provides a useful framework for evaluating capture efficiency for not only hoop nets but other gear types used to sample fishes in reservoirs.
Spatial Hierarchical Bayesian Analysis of the Historical Extreme Streamflow
Najafi, M. R.; Moradkhani, H.
2012-04-01
Analysis of the climate change impact on extreme hydro-climatic events is crucial for future hydrologic/hydraulic designs and water resources decision making. The purpose of this study is to investigate the changes of the extreme value distribution parameters with respect to time to reflect upon the impact of climate change. We develop a statistical model using the observed streamflow data of the Columbia River Basin in USA to estimate the changes of high flows as a function of time as well as other variables. Generalized Pareto Distribution (GPD) is used to model the upper 95% flows during December through March for 31 gauge stations. In the process layer of the model the covariates including time, latitude, longitude, elevation and basin area are considered to assess the sensitivity of the model to each variable. Markov Chain Monte Carlo (MCMC) method is used to estimate the parameters. The Spatial Hierarchical Bayesian technique models the GPD parameters spatially and borrows strength from other locations by pooling data together, while providing an explicit estimation of the uncertainties in all stages of modeling.
Using hierarchical Bayesian methods to examine the tools of decision-making
Directory of Open Access Journals (Sweden)
Michael D. Lee
2011-12-01
Full Text Available Hierarchical Bayesian methods offer a principled and comprehensive way to relate psychological models to data. Here we use them to model the patterns of information search, stopping and deciding in a simulated binary comparison judgment task. The simulation involves 20 subjects making 100 forced choice comparisons about the relative magnitudes of two objects (which of two German cities has more inhabitants. Two worked-examples show how hierarchical models can be developed to account for and explain the diversity of both search and stopping rules seen across the simulated individuals. We discuss how the results provide insight into current debates in the literature on heuristic decision making and argue that they demonstrate the power and flexibility of hierarchical Bayesian methods in modeling human decision-making.
Seichter, Felicia; Vogt, Josef; Radermacher, Peter; Mizaikoff, Boris
2017-01-25
The calibration of analytical systems is time-consuming and the effort for daily calibration routines should therefore be minimized, while maintaining the analytical accuracy and precision. The 'calibration transfer' approach proposes to combine calibration data already recorded with actual calibrations measurements. However, this strategy was developed for the multivariate, linear analysis of spectroscopic data, and thus, cannot be applied to sensors with a single response channel and/or a non-linear relationship between signal and desired analytical concentration. To fill this gap for a non-linear calibration equation, we assume that the coefficients for the equation, collected over several calibration runs, are normally distributed. Considering that coefficients of an actual calibration are a sample of this distribution, only a few standards are needed for a complete calibration data set. The resulting calibration transfer approach is demonstrated for a fluorescence oxygen sensor and implemented as a hierarchical Bayesian model, combined with a Lagrange Multipliers technique and Monte-Carlo Markov-Chain sampling. The latter provides realistic estimates for coefficients and prediction together with accurate error bounds by simulating known measurement errors and system fluctuations. Performance criteria for validation and optimal selection of a reduced set of calibration samples were developed and lead to a setup which maintains the analytical performance of a full calibration. Strategies for a rapid determination of problems occurring in a daily calibration routine, are proposed, thereby opening the possibility of correcting the problem just in time.
Hierarchical topic modeling with nested hierarchical Dirichlet process
Institute of Scientific and Technical Information of China (English)
Yi-qun DING; Shan-ping LI; Zhen ZHANG; Bin SHEN
2009-01-01
This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonparametric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as welt as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more free-grained topic relationships compared to the hierarchical latent Dirichlet allocation model.
Model Diagnostics for Bayesian Networks
Sinharay, Sandip
2006-01-01
Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…
Finley, Andrew O.; Banerjee, Sudipto; Cook, Bruce D.; Bradford, John B.
2013-01-01
In this paper we detail a multivariate spatial regression model that couples LiDAR, hyperspectral and forest inventory data to predict forest outcome variables at a high spatial resolution. The proposed model is used to analyze forest inventory data collected on the US Forest Service Penobscot Experimental Forest (PEF), ME, USA. In addition to helping meet the regression model's assumptions, results from the PEF analysis suggest that the addition of multivariate spatial random effects improves model fit and predictive ability, compared with two commonly applied modeling approaches. This improvement results from explicitly modeling the covariation among forest outcome variables and spatial dependence among observations through the random effects. Direct application of such multivariate models to even moderately large datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation. We apply a spatial dimension reduction technique to help overcome this computational hurdle without sacrificing richness in modeling.
A hierarchical Bayesian framework for force field selection in molecular dynamics simulations.
Wu, S; Angelikopoulos, P; Papadimitriou, C; Moser, R; Koumoutsakos, P
2016-02-13
We present a hierarchical Bayesian framework for the selection of force fields in molecular dynamics (MD) simulations. The framework associates the variability of the optimal parameters of the MD potentials under different environmental conditions with the corresponding variability in experimental data. The high computational cost associated with the hierarchical Bayesian framework is reduced by orders of magnitude through a parallelized Transitional Markov Chain Monte Carlo method combined with the Laplace Asymptotic Approximation. The suitability of the hierarchical approach is demonstrated by performing MD simulations with prescribed parameters to obtain data for transport coefficients under different conditions, which are then used to infer and evaluate the parameters of the MD model. We demonstrate the selection of MD models based on experimental data and verify that the hierarchical model can accurately quantify the uncertainty across experiments; improve the posterior probability density function estimation of the parameters, thus, improve predictions on future experiments; identify the most plausible force field to describe the underlying structure of a given dataset. The framework and associated software are applicable to a wide range of nanoscale simulations associated with experimental data with a hierarchical structure.
Mandel, Kaisey S; Shariff, Hikmatali; Foley, Ryan J; Kirshner, Robert P
2016-01-01
Conventional Type Ia supernova (SN Ia) cosmology analyses currently use a simplistic linear regression of magnitude versus color and light curve shape, which does not model intrinsic SN Ia variations and host galaxy dust as physically distinct effects, resulting in low color-magnitude slopes. We construct a probabilistic generative model for the distribution of dusty extinguished absolute magnitudes and apparent colors as a convolution of the intrinsic SN Ia color-magnitude distribution and the host galaxy dust reddening-extinction distribution. If the intrinsic color-magnitude (M_B vs. B-V) slope beta_int differs from the host galaxy dust law R_B, this convolution results in a specific curve of mean extinguished absolute magnitude vs. apparent color. The derivative of this curve smoothly transitions from beta_int in the blue tail to R_B in the red tail of the apparent color distribution. The conventional linear fit approximates this effective curve at this transition near the average apparent color, resultin...
Directory of Open Access Journals (Sweden)
Guillaume Marrelec
Full Text Available The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity, provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering.
基于DNA微阵列数据分析的分级Bayes模型%A Bayesian Hierarchical Model for DNA Microarray Data
Institute of Scientific and Technical Information of China (English)
刘妍岩; 杨丹
2009-01-01
In DNA microarray analysis, there is often interest in isolating a few genes that best discriminate between tissue types. In particular, it is critical to develop suitable models to explain the patterns of DNA expression for these different types of tissues. Toward this goal, we propose a methodology for the analysis of high-density oligonucleotide arrays.The log-transformed data are assumed to follow a mixture normal distribution based on the characteristic of gene itself. The variation in the data can reasonably be thought to arise from the effects of genes, tissue types, and their interactions. We introduce a hierarchical Bayesian priors for the parameters and propose a model selection criterion for identifying subsets of genes that show different expression levels between normal and tumor types. In addition, we develop Markov chain Monte Carlo algorithms for sampling from the posterior distribution of parameters and for computing criterion. The proposed methodology is evaluated via simulations studies.%如何分离出少量区别不同组织类型的特异性基因是DNA微阵列数据分析中的主要问题,特别是构建恰当的统计模型来刻画这些不同组织类型的DNA表达形式尤为重要.为此,基于基因DNA微阵列数据的特点,我们假定对数变换后的微阵列数据服从混合正态分布.我们采用分级Bayesian先验刻画不同基因的相关性,利用分级Bayesian方法构建模型,给出了刻画不同组织基因表达的差异的一个标准,用MCMC迭代计算该标准.模拟计算表明我们的模型具有较好的识别能力.
Eadie, Gwendolyn M.; Springford, Aaron; Harris, William E.
2017-02-01
We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie et al. and Eadie and Harris and builds upon the preliminary reports by Eadie et al. The method uses a distribution function f({ E },L) to model the Galaxy and kinematic data from satellite objects, such as globular clusters (GCs), to trace the Galaxy’s gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie and Harris and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within 125 kpc of 4.8× {10}11{M}ȯ with a 95% Bayesian credible region of (4.0{--}5.8)× {10}11{M}ȯ . Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements.
The Infinite Hierarchical Factor Regression Model
Rai, Piyush
2009-01-01
We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.
Tools to estimate PM2.5 mass have expanded in recent years, and now include: 1) stationary monitor readings, 2) Community Multi-Scale Air Quality (CMAQ) model estimates, 3) Hierarchical Bayesian (HB) estimates from combined stationary monitor readings and CMAQ model output; and, ...
Collaborative Hierarchical Sparse Modeling
Sprechmann, Pablo; Sapiro, Guillermo; Eldar, Yonina C
2010-01-01
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the sparsity-inducing property of the Lasso model, at the individual feature level, with the block-sparsity property of the group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the hierarchical Lasso, which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level but not necessarily at the lower one. Signals then share the same active groups, or classes, but not necessarily the same active set. This is very well suited for applications such as source separation. An efficient optimization procedure, which guarantees convergence to the global opt...
Risk Assessment for Mobile Systems Through a Multilayered Hierarchical Bayesian Network.
Li, Shancang; Tryfonas, Theo; Russell, Gordon; Andriotis, Panagiotis
2016-08-01
Mobile systems are facing a number of application vulnerabilities that can be combined together and utilized to penetrate systems with devastating impact. When assessing the overall security of a mobile system, it is important to assess the security risks posed by each mobile applications (apps), thus gaining a stronger understanding of any vulnerabilities present. This paper aims at developing a three-layer framework that assesses the potential risks which apps introduce within the Android mobile systems. A Bayesian risk graphical model is proposed to evaluate risk propagation in a layered risk architecture. By integrating static analysis, dynamic analysis, and behavior analysis in a hierarchical framework, the risks and their propagation through each layer are well modeled by the Bayesian risk graph, which can quantitatively analyze risks faced to both apps and mobile systems. The proposed hierarchical Bayesian risk graph model offers a novel way to investigate the security risks in mobile environment and enables users and administrators to evaluate the potential risks. This strategy allows to strengthen both app security as well as the security of the entire system.
Improved Estimates of the Milky Way's Disk Scale Length From Hierarchical Bayesian Techniques
Licquia, Timothy C
2016-01-01
The exponential scale length ($L_d$) of the Milky Way's (MW's) disk is a critical parameter for describing the global physical size of our Galaxy, important both for interpreting other Galactic measurements and helping us to understand how our Galaxy fits into extragalactic contexts. Unfortunately, current estimates span a wide range of values and often are statistically incompatible with one another. Here, we aim to determine an improved, aggregate estimate for $L_d$ by utilizing a hierarchical Bayesian (HB) meta-analysis technique that accounts for the possibility that any one measurement has not properly accounted for all statistical or systematic errors. Within this machinery we explore a variety of ways of modeling the nature of problematic measurements, and then use a Bayesian model averaging technique to derive net posterior distributions that incorporate any model-selection uncertainty. Our meta-analysis combines 29 different (15 visible and 14 infrared) photometric measurements of $L_d$ available in ...
Congdon, Peter
2014-01-01
This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBU
Learning emergent behaviours for a hierarchical Bayesian framework for active robotic perception.
Ferreira, João Filipe; Tsiourti, Christiana; Dias, Jorge
2012-08-01
In this research work, we contribute with a behaviour learning process for a hierarchical Bayesian framework for multimodal active perception, devised to be emergent, scalable and adaptive. This framework is composed by models built upon a common spatial configuration for encoding perception and action that is naturally fitting for the integration of readings from multiple sensors, using a Bayesian approach devised in previous work. The proposed learning process is shown to reproduce goal-dependent human-like active perception behaviours by learning model parameters (referred to as "attentional sets") for different free-viewing and active search tasks. Learning was performed by presenting several 3D audiovisual virtual scenarios using a head-mounted display, while logging the spatial distribution of fixations of the subject (in 2D, on left and right images, and in 3D space), data which are consequently used as the training set for the framework. As a consequence, the hierarchical Bayesian framework adequately implements high-level behaviour resulting from low-level interaction of simpler building blocks by using the attentional sets learned for each task, and is able to change these attentional sets "on the fly," allowing the implementation of goal-dependent behaviours (i.e., top-down influences).
Mustac, M.; Kim, S.; Tkalcic, H.; Rhie, J.; Chen, Y.; Ford, S. R.; Sebastian, N.
2015-12-01
Conventional approaches to inverse problems suffer from non-linearity and non-uniqueness in estimations of seismic structures and source properties. Estimated results and associated uncertainties are often biased by applied regularizations and additional constraints, which are commonly introduced to solve such problems. Bayesian methods, however, provide statistically meaningful estimations of models and their uncertainties constrained by data information. In addition, hierarchical and trans-dimensional (trans-D) techniques are inherently implemented in the Bayesian framework to account for involved error statistics and model parameterizations, and, in turn, allow more rigorous estimations of the same. Here, we apply Bayesian methods throughout the entire inference process to estimate seismic structures and source properties in Northeast Asia including east China, the Korean peninsula, and the Japanese islands. Ambient noise analysis is first performed to obtain a base three-dimensional (3-D) heterogeneity model using continuous broadband waveforms from more than 300 stations. As for the tomography of surface wave group and phase velocities in the 5-70 s band, we adopt a hierarchical and trans-D Bayesian inversion method using Voronoi partition. The 3-D heterogeneity model is further improved by joint inversions of teleseismic receiver functions and dispersion data using a newly developed high-efficiency Bayesian technique. The obtained model is subsequently used to prepare 3-D structural Green's functions for the source characterization. A hierarchical Bayesian method for point source inversion using regional complete waveform data is applied to selected events from the region. The seismic structure and source characteristics with rigorously estimated uncertainties from the novel Bayesian methods provide enhanced monitoring and discrimination of seismic events in northeast Asia.
Determining the Bayesian optimal sampling strategy in a hierarchical system.
Energy Technology Data Exchange (ETDEWEB)
Grace, Matthew D.; Ringland, James T.; Boggs, Paul T.; Pebay, Philippe Pierre
2010-09-01
Consider a classic hierarchy tree as a basic model of a 'system-of-systems' network, where each node represents a component system (which may itself consist of a set of sub-systems). For this general composite system, we present a technique for computing the optimal testing strategy, which is based on Bayesian decision analysis. In previous work, we developed a Bayesian approach for computing the distribution of the reliability of a system-of-systems structure that uses test data and prior information. This allows for the determination of both an estimate of the reliability and a quantification of confidence in the estimate. Improving the accuracy of the reliability estimate and increasing the corresponding confidence require the collection of additional data. However, testing all possible sub-systems may not be cost-effective, feasible, or even necessary to achieve an improvement in the reliability estimate. To address this sampling issue, we formulate a Bayesian methodology that systematically determines the optimal sampling strategy under specified constraints and costs that will maximally improve the reliability estimate of the composite system, e.g., by reducing the variance of the reliability distribution. This methodology involves calculating the 'Bayes risk of a decision rule' for each available sampling strategy, where risk quantifies the relative effect that each sampling strategy could have on the reliability estimate. A general numerical algorithm is developed and tested using an example multicomponent system. The results show that the procedure scales linearly with the number of components available for testing.
Gelman, Andrew; Stern, Hal S; Dunson, David B; Vehtari, Aki; Rubin, Donald B
2013-01-01
FUNDAMENTALS OF BAYESIAN INFERENCEProbability and InferenceSingle-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian ApproachesHierarchical ModelsFUNDAMENTALS OF BAYESIAN DATA ANALYSISModel Checking Evaluating, Comparing, and Expanding ModelsModeling Accounting for Data Collection Decision AnalysisADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional ApproximationsREGRESSION MODELS Introduction to Regression Models Hierarchical Linear
A hierarchical Bayesian-MAP approach to inverse problems in imaging
Raj, Raghu G.
2016-07-01
We present a novel approach to inverse problems in imaging based on a hierarchical Bayesian-MAP (HB-MAP) formulation. In this paper we specifically focus on the difficult and basic inverse problem of multi-sensor (tomographic) imaging wherein the source object of interest is viewed from multiple directions by independent sensors. Given the measurements recorded by these sensors, the problem is to reconstruct the image (of the object) with a high degree of fidelity. We employ a probabilistic graphical modeling extension of the compound Gaussian distribution as a global image prior into a hierarchical Bayesian inference procedure. Since the prior employed by our HB-MAP algorithm is general enough to subsume a wide class of priors including those typically employed in compressive sensing (CS) algorithms, HB-MAP algorithm offers a vehicle to extend the capabilities of current CS algorithms to include truly global priors. After rigorously deriving the regression algorithm for solving our inverse problem from first principles, we demonstrate the performance of the HB-MAP algorithm on Monte Carlo trials and on real empirical data (natural scenes). In all cases we find that our algorithm outperforms previous approaches in the literature including filtered back-projection and a variety of state-of-the-art CS algorithms. We conclude with directions of future research emanating from this work.
Modeling hierarchical structures - Hierarchical Linear Modeling using MPlus
Jelonek, M
2006-01-01
The aim of this paper is to present the technique (and its linkage with physics) of overcoming problems connected to modeling social structures, which are typically hierarchical. Hierarchical Linear Models provide a conceptual and statistical mechanism for drawing conclusions regarding the influence of phenomena at different levels of analysis. In the social sciences it is used to analyze many problems such as educational, organizational or market dilemma. This paper introduces the logic of modeling hierarchical linear equations and estimation based on MPlus software. I present my own model to illustrate the impact of different factors on school acceptation level.
Dries, M; Koopmans, L V E
2016-01-01
Recent studies based on the integrated light of distant galaxies suggest that the initial mass function (IMF) might not be universal. Variations of the IMF with galaxy type and/or formation time may have important consequences for our understanding of galaxy evolution. We have developed a new stellar population synthesis (SPS) code specifically designed to reconstruct the IMF. We implement a novel approach combining regularization with hierarchical Bayesian inference. Within this approach we use a parametrized IMF prior to regulate a direct inference of the IMF. This direct inference gives more freedom to the IMF and allows the model to deviate from parametrized models when demanded by the data. We use Markov Chain Monte Carlo sampling techniques to reconstruct the best parameters for the IMF prior, the age, and the metallicity of a single stellar population. We present our code and apply our model to a number of mock single stellar populations with different ages, metallicities, and IMFs. When systematic unc...
Dries, M.; Trager, S. C.; Koopmans, L. V. E.
2016-11-01
Recent studies based on the integrated light of distant galaxies suggest that the initial mass function (IMF) might not be universal. Variations of the IMF with galaxy type and/or formation time may have important consequences for our understanding of galaxy evolution. We have developed a new stellar population synthesis (SPS) code specifically designed to reconstruct the IMF. We implement a novel approach combining regularization with hierarchical Bayesian inference. Within this approach, we use a parametrized IMF prior to regulate a direct inference of the IMF. This direct inference gives more freedom to the IMF and allows the model to deviate from parametrized models when demanded by the data. We use Markov chain Monte Carlo sampling techniques to reconstruct the best parameters for the IMF prior, the age and the metallicity of a single stellar population. We present our code and apply our model to a number of mock single stellar populations with different ages, metallicities and IMFs. When systematic uncertainties are not significant, we are able to reconstruct the input parameters that were used to create the mock populations. Our results show that if systematic uncertainties do play a role, this may introduce a bias on the results. Therefore, it is important to objectively compare different ingredients of SPS models. Through its Bayesian framework, our model is well suited for this.
Sánchez Gil, M. Carmen; Berihuete, Angel; Alfaro, Emilio J.; Pérez, Enrique; Sarro, Luis M.
2015-09-01
One of the fundamental goals of modern Astronomy is to estimate the physical parameters of galaxies from images in different spectral bands. We present a hierarchical Bayesian model for obtaining age maps from images in the Ha line (taken with Taurus Tunable Filter (TTF)), ultraviolet band (far UV or FUV, from GALEX) and infrared bands (24, 70 and 160 microns (μm), from Spitzer). As shown in [1], we present the burst ages for young stellar populations in the nearby and nearly face on galaxy M74. As it is shown in the previous work, the Hα to FUV flux ratio gives a good relative indicator of very recent star formation history (SFH). As a nascent star-forming region evolves, the Ha line emission declines earlier than the UV continuum, leading to a decrease in the HαFUV ratio. Through a specific star-forming galaxy model (Starburst 99, SB99), we can obtain the corresponding theoretical ratio Hα / FUV to compare with our observed flux ratios, and thus to estimate the ages of the observed regions. Due to the nature of the problem, it is necessary to propose a model of high complexity to take into account the mean uncertainties, and the interrelationship between parameters when the Hα / FUV flux ratio mentioned above is obtained. To address the complexity of the model, we propose a Bayesian hierarchical model, where a joint probability distribution is defined to determine the parameters (age, metallicity, IMF), from the observed data, in this case the observed flux ratios Hα / FUV. The joint distribution of the parameters is described through an i.i.d. (independent and identically distributed random variables), generated through MCMC (Markov Chain Monte Carlo) techniques.
DEFF Research Database (Denmark)
Jensen, Finn Verner; Nielsen, Thomas Dyhre
2016-01-01
and edges. The nodes represent variables, which may be either discrete or continuous. An edge between two nodes A and B indicates a direct influence between the state of A and the state of B, which in some domains can also be interpreted as a causal relation. The wide-spread use of Bayesian networks...
Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system.
Huang, Yangxin; Liu, Dacheng; Wu, Hulin
2006-06-01
HIV dynamics studies have significantly contributed to the understanding of HIV infection and antiviral treatment strategies. But most studies are limited to short-term viral dynamics due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. In this article, a mechanism-based dynamic model is proposed for characterizing long-term viral dynamics with antiretroviral therapy, described by a set of nonlinear differential equations without closed-form solutions. In this model we directly incorporate drug concentration, adherence, and drug susceptibility into a function of treatment efficacy, defined as an inhibition rate of virus replication. We investigate a Bayesian approach under the framework of hierarchical Bayesian (mixed-effects) models for estimating unknown dynamic parameters. In particular, interest focuses on estimating individual dynamic parameters. The proposed methods not only help to alleviate the difficulty in parameter identifiability, but also flexibly deal with sparse and unbalanced longitudinal data from individual subjects. For illustration purposes, we present one simulation example to implement the proposed approach and apply the methodology to a data set from an AIDS clinical trial. The basic concept of the longitudinal HIV dynamic systems and the proposed methodologies are generally applicable to any other biomedical dynamic systems.
Improving water quality assessments through a hierarchical Bayesian analysis of variability.
Gronewold, Andrew D; Borsuk, Mark E
2010-10-15
Water quality measurement error and variability, while well-documented in laboratory-scale studies, is rarely acknowledged or explicitly resolved in most model-based water body assessments, including those conducted in compliance with the United States Environmental Protection Agency (USEPA) Total Maximum Daily Load (TMDL) program. Consequently, proposed pollutant loading reductions in TMDLs and similar water quality management programs may be biased, resulting in either slower-than-expected rates of water quality restoration and designated use reinstatement or, in some cases, overly conservative management decisions. To address this problem, we present a hierarchical Bayesian approach for relating actual in situ or model-predicted pollutant concentrations to multiple sampling and analysis procedures, each with distinct sources of variability. We apply this method to recently approved TMDLs to investigate whether appropriate accounting for measurement error and variability will lead to different management decisions. We find that required pollutant loading reductions may in fact vary depending not only on how measurement variability is addressed but also on which water quality analysis procedure is used to assess standard compliance. As a general strategy, our Bayesian approach to quantifying variability may represent an alternative to the common practice of addressing all forms of uncertainty through an arbitrary margin of safety (MOS).
What are hierarchical models and how do we analyze them?
Royle, Andy
2016-01-01
In this chapter we provide a basic definition of hierarchical models and introduce the two canonical hierarchical models in this book: site occupancy and N-mixture models. The former is a hierarchical extension of logistic regression and the latter is a hierarchical extension of Poisson regression. We introduce basic concepts of probability modeling and statistical inference including likelihood and Bayesian perspectives. We go through the mechanics of maximizing the likelihood and characterizing the posterior distribution by Markov chain Monte Carlo (MCMC) methods. We give a general perspective on topics such as model selection and assessment of model fit, although we demonstrate these topics in practice in later chapters (especially Chapters 5, 6, 7, and 10 Chapter 5 Chapter 6 Chapter 7 Chapter 10)
Bayesian hierarchical clustering for studying cancer gene expression data with unknown statistics.
Directory of Open Access Journals (Sweden)
Korsuk Sirinukunwattana
Full Text Available Clustering analysis is an important tool in studying gene expression data. The Bayesian hierarchical clustering (BHC algorithm can automatically infer the number of clusters and uses Bayesian model selection to improve clustering quality. In this paper, we present an extension of the BHC algorithm. Our Gaussian BHC (GBHC algorithm represents data as a mixture of Gaussian distributions. It uses normal-gamma distribution as a conjugate prior on the mean and precision of each of the Gaussian components. We tested GBHC over 11 cancer and 3 synthetic datasets. The results on cancer datasets show that in sample clustering, GBHC on average produces a clustering partition that is more concordant with the ground truth than those obtained from other commonly used algorithms. Furthermore, GBHC frequently infers the number of clusters that is often close to the ground truth. In gene clustering, GBHC also produces a clustering partition that is more biologically plausible than several other state-of-the-art methods. This suggests GBHC as an alternative tool for studying gene expression data. The implementation of GBHC is available at https://sites.google.com/site/gaussianbhc/
Busschaert, P; Geeraerd, A H; Uyttendaele, M; Van Impe, J F
2011-06-01
Microbiological contamination data often is censored because of the presence of non-detects or because measurement outcomes are known only to be smaller than, greater than, or between certain boundary values imposed by the laboratory procedures. Therefore, it is not straightforward to fit distributions that summarize contamination data for use in quantitative microbiological risk assessment, especially when variability and uncertainty are to be characterized separately. In this paper, distributions are fit using Bayesian analysis, and results are compared to results obtained with a methodology based on maximum likelihood estimation and the non-parametric bootstrap method. The Bayesian model is also extended hierarchically to estimate the effects of the individual elements of a covariate such as, for example, on a national level, the food processing company where the analyzed food samples were processed, or, on an international level, the geographical origin of contamination data. Including this extra information allows a risk assessor to differentiate between several scenario's and increase the specificity of the estimate of risk of illness, or compare different scenario's to each other. Furthermore, inference is made on the predictive importance of several different covariates while taking into account uncertainty, allowing to indicate which covariates are influential factors determining contamination.
Bayesian Model Averaging for Propensity Score Analysis
Kaplan, David; Chen, Jianshen
2013-01-01
The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…
Robust Bayesian Regularized Estimation Based on t Regression Model
Directory of Open Access Journals (Sweden)
Zean Li
2015-01-01
Full Text Available The t distribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable selection method based on Bayesian adaptive Lasso t regression. A Gibbs sampler is developed based on the Bayesian hierarchical model framework, where we treat the t distribution as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients. We also consider the Bayesian t regression with adaptive group Lasso and obtain the Gibbs sampler from the posterior distributions. Both simulation studies and real data example show that our method performs well compared with other existing methods when the error distribution has heavy tails and/or outliers.
Bayesian stable isotope mixing models
In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixtur...
Bayesian Evidence and Model Selection
Knuth, Kevin H; Malakar, Nabin K; Mubeen, Asim M; Placek, Ben
2014-01-01
In this paper we review the concept of the Bayesian evidence and its application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical techniques. Application to several practical examples within the context of signal processing are discussed.
Bayesian model reduction and empirical Bayes for group (DCM) studies.
Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter
2016-03-01
This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.
A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference
Muir, J. B.; Tkalčić, H.
2015-11-01
The problem of decomposing irregular data on the sphere into a set of spherical harmonics is common in many fields of geosciences where it is necessary to build a quantitative understanding of a globally varying field. For example, in global seismology, a compressional or shear wave speed that emerges from tomographic images is used to interpret current state and composition of the mantle, and in geomagnetism, secular variation of magnetic field intensity measured at the surface is studied to better understand the changes in the Earth's core. Optimization methods are widely used for spherical harmonic analysis of irregular data, but they typically do not treat the dependence of the uncertainty estimates on the imposed regularization. This can cause significant difficulties in interpretation, especially when the best-fit model requires more variables as a result of underestimating data noise. Here, with the above limitations in mind, the problem of spherical harmonic expansion of irregular data is treated within the hierarchical Bayesian framework. The hierarchical approach significantly simplifies the problem by removing the need for regularization terms and user-supplied noise estimates. The use of the corrected Akaike Information Criterion for picking the optimal maximum degree of spherical harmonic expansion and the resulting spherical harmonic analyses are first illustrated on a noisy synthetic data set. Subsequently, the method is applied to two global data sets sensitive to the Earth's inner core and lowermost mantle, consisting of PKPab-df and PcP-P differential traveltime residuals relative to a spherically symmetric Earth model. The posterior probability distributions for each spherical harmonic coefficient are calculated via Markov Chain Monte Carlo sampling; the uncertainty obtained for the coefficients thus reflects the noise present in the real data and the imperfections in the spherical harmonic expansion.
Tashiro, Tohru
2013-01-01
We propose a new model about diffusion of a product which includes a memory of how many adopters or advertisements a non-adopter met, where (non-)adopters mean people (not) possessing the product. This effect is lacking in the Bass model. As an application, we utilize the model to fit the iPod sales data, and so the better agreement is obtained than the Bass model.
Tashiro, Tohru
2014-03-01
We propose a new model about diffusion of a product which includes a memory of how many adopters or advertisements a non-adopter met, where (non-)adopters mean people (not) possessing the product. This effect is lacking in the Bass model. As an application, we utilize the model to fit the iPod sales data, and so the better agreement is obtained than the Bass model.
Shetty, Rahul; Bigiel, Frank
2012-01-01
We develop a Bayesian linear regression method which rigorously treats measurement uncertainties, and accounts for hierarchical data structure for investigating the relationship between the star formation rate and gas surface density. The method simultaneously estimates the intercept, slope, and scatter about the regression line of each individual subject (e.g. a galaxy) and the population (e.g. an ensemble of galaxies). Using synthetic datasets, we demonstrate that the Bayesian method accurately recovers the parameters of both the individuals and the population, especially when compared to commonly employed least squares methods, such as the bisector. We apply the Bayesian method to estimate the Kennicutt-Schmidt (KS) parameters of a sample of spiral galaxies compiled by Bigiel et al. (2008). We find significant variation in the KS parameters, indicating that no single KS relationship holds for all galaxies. This suggests that the relationship between molecular gas and star formation differs between galaxies...
Borsboom, D.; Haig, B.D.
2013-01-01
Unlike most other statistical frameworks, Bayesian statistical inference is wedded to a particular approach in the philosophy of science (see Howson & Urbach, 2006); this approach is called Bayesianism. Rather than being concerned with model fitting, this position in the philosophy of science primar
Hierarchical model of matching
Pedrycz, Witold; Roventa, Eugene
1992-01-01
The issue of matching two fuzzy sets becomes an essential design aspect of many algorithms including fuzzy controllers, pattern classifiers, knowledge-based systems, etc. This paper introduces a new model of matching. Its principal features involve the following: (1) matching carried out with respect to the grades of membership of fuzzy sets as well as some functionals defined on them (like energy, entropy,transom); (2) concepts of hierarchies in the matching model leading to a straightforward distinction between 'local' and 'global' levels of matching; and (3) a distributed character of the model realized as a logic-based neural network.
Alsing, Justin; Jaffe, Andrew H
2016-01-01
We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the CFHTLenS weak lensing survey - the first application of this method to data. In the first approach, we sample the joint posterior distribution of the shear maps and power spectra by Gibbs sampling, with minimal model assumptions. In the second approach, we sample the joint posterior of the shear maps and cosmological parameters, providing a new, accurate and principled approach to cosmological parameter inference from cosmic shear data. As a first demonstration on data we perform a 2-bin tomographic analysis to constrain cosmological parameters and investigate the possibility of photometric redshift bias in the CFHTLenS data. Under the baseline $\\Lambda$CDM model we constrain $S_8 = \\sigma_8(\\Omega_\\mathrm{m}/0.3)^{0.5} = 0.67 ^{\\scriptscriptstyle+ 0.03 }_{\\scriptscriptstyle- 0.03 }$ $(68\\%)$, consistent with previous CFHTLenS analysis but in tension with Planck. Adding neutrino m...
Gil, M Carmen Sánchez; Alfaro, Emilio J; Pérez, Enrique; Sarro, Luis M
2015-01-01
One of the fundamental goals of modern Astronomy is to estimate the physical parameters of galaxies from images in different spectral bands. We present a hierarchical Bayesian model for obtaining age maps from images in the \\Ha\\ line (taken with Taurus Tunable Filter (TTF)), ultraviolet band (far UV or FUV, from GALEX) and infrared bands (24, 70 and 160 microns ($\\mu$m), from Spitzer). As shown in S\\'anchez-Gil et al. (2011), we present the burst ages for young stellar populations in the nearby and nearly face on galaxy M74. As it is shown in the previous work, the \\Ha\\ to FUV flux ratio gives a good relative indicator of very recent star formation history (SFH). As a nascent star-forming region evolves, the \\Ha\\ line emission declines earlier than the UV continuum, leading to a decrease in the \\Ha\\/FUV ratio. Through a specific star-forming galaxy model (Starburst 99, SB99), we can obtain the corresponding theoretical ratio \\Ha\\ / FUV to compare with our observed flux ratios, and thus to estimate the ages of...
Mandel, Kaisey S; Kirshner, Robert P
2014-01-01
We investigate the correlations between the peak intrinsic colors of Type Ia supernovae (SN Ia) and their expansion velocities at maximum light, measured from the Si II 6355 A spectral feature. We construct a new hierarchical Bayesian regression model and Gibbs sampler to estimate the dependence of the intrinsic colors of a SN Ia on its ejecta velocity, while accounting for the random effects of intrinsic scatter, measurement error, and reddening by host galaxy dust. The method is applied to the apparent color data from BVRI light curves and Si II velocity data for 79 nearby SN Ia. Comparison of the apparent color distributions of high velocity (HV) and normal velocity (NV) supernovae reveals significant discrepancies in B-V and B-R, but not other colors. Hence, they are likely due to intrinsic color differences originating in the B-band, rather than dust reddening. The mean intrinsic B-V and B-R color differences between HV and NV groups are 0.06 +/- 0.02 and 0.09 +/- 0.02 mag, respectively. Under a linear m...
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.
Jomelli, Vincent; Pavlova, Irina; Eckert, Nicolas; Grancher, Delphine; Brunstein, Daniel
2015-12-01
How can debris flow occurrences be modelled at regional scale and take both environmental and climatic conditions into account? And, of the two, which has the most influence on debris flow activity? In this paper, we try to answer these questions with an innovative Bayesian hierarchical probabilistic model that simultaneously accounts for how debris flows respond to environmental and climatic variables. In it, full decomposition of space and time effects in occurrence probabilities is assumed, revealing an environmental and a climatic trend shared by all years/catchments, respectively, clearly distinguished from residual "random" effects. The resulting regional and annual occurrence probabilities evaluated as functions of the covariates make it possible to weight the respective contribution of the different terms and, more generally, to check the model performances at different spatio-temporal scales. After suitable validation, the model can be used to make predictions at undocumented sites and could be used in further studies for predictions under future climate conditions. Also, the Bayesian paradigm easily copes with missing data, thus making it possible to account for events that may have been missed during surveys. As a case study, we extract 124 debris flow event triggered between 1970 and 2005 in 27 catchments located in the French Alps from the French national natural hazard survey and model their variability of occurrence considering environmental and climatic predictors at the same time. We document the environmental characteristics of each debris flow catchment (morphometry, lithology, land cover, and the presence of permafrost). We also compute 15 climate variables including mean temperature and precipitation between May and October and the number of rainy days with daily cumulative rainfall greater than 10/15/20/25/30/40 mm day- 1. Application of our model shows that the combination of environmental and climatic predictors explained 77% of the overall
Nonparametric Bayesian Modeling of Complex Networks
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Mørup, Morten
2013-01-01
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...... for complex networks can be derived and point out relevant literature....
Modeling Diagnostic Assessments with Bayesian Networks
Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego
2007-01-01
This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…
Directory of Open Access Journals (Sweden)
Rasheda Arman Chowdhury
Full Text Available Localizing the generators of epileptic activity in the brain using Electro-EncephaloGraphy (EEG or Magneto-EncephaloGraphy (MEG signals is of particular interest during the pre-surgical investigation of epilepsy. Epileptic discharges can be detectable from background brain activity, provided they are associated with spatially extended generators. Using realistic simulations of epileptic activity, this study evaluates the ability of distributed source localization methods to accurately estimate the location of the generators and their sensitivity to the spatial extent of such generators when using MEG data. Source localization methods based on two types of realistic models have been investigated: (i brain activity may be modeled using cortical parcels and (ii brain activity is assumed to be locally smooth within each parcel. A Data Driven Parcellization (DDP method was used to segment the cortical surface into non-overlapping parcels and diffusion-based spatial priors were used to model local spatial smoothness within parcels. These models were implemented within the Maximum Entropy on the Mean (MEM and the Hierarchical Bayesian (HB source localization frameworks. We proposed new methods in this context and compared them with other standard ones using Monte Carlo simulations of realistic MEG data involving sources of several spatial extents and depths. Detection accuracy of each method was quantified using Receiver Operating Characteristic (ROC analysis and localization error metrics. Our results showed that methods implemented within the MEM framework were sensitive to all spatial extents of the sources ranging from 3 cm(2 to 30 cm(2, whatever were the number and size of the parcels defining the model. To reach a similar level of accuracy within the HB framework, a model using parcels larger than the size of the sources should be considered.
Bayesian Age-Period-Cohort Modeling and Prediction - BAMP
Directory of Open Access Journals (Sweden)
Volker J. Schmid
2007-10-01
Full Text Available The software package BAMP provides a method of analyzing incidence or mortality data on the Lexis diagram, using a Bayesian version of an age-period-cohort model. A hierarchical model is assumed with a binomial model in the first-stage. As smoothing priors for the age, period and cohort parameters random walks of first and second order, with and without an additional unstructured component are available. Unstructured heterogeneity can also be included in the model. In order to evaluate the model fit, posterior deviance, DIC and predictive deviances are computed. By projecting the random walk prior into the future, future death rates can be predicted.
Weber, Stephanie A; Insaf, Tabassum Z; Hall, Eric S; Talbot, Thomas O; Huff, Amy K
2016-11-01
An enhanced research paradigm is presented to address the spatial and temporal gaps in fine particulate matter (PM2.5) measurements and generate realistic and representative concentration fields for use in epidemiological studies of human exposure to ambient air particulate concentrations. The general approach for research designed to analyze health impacts of exposure to PM2.5 is to use concentration data from the nearest ground-based air quality monitor(s), which typically have missing data on the temporal and spatial scales due to filter sampling schedules and monitor placement, respectively. To circumvent these data gaps, this research project uses a Hierarchical Bayesian Model (HBM) to generate estimates of PM2.5 in areas with and without air quality monitors by combining PM2.5 concentrations measured by monitors, PM2.5 concentration estimates derived from satellite aerosol optical depth (AOD) data, and Community-Multiscale Air Quality (CMAQ) model predictions of PM2.5 concentrations. This methodology represents a substantial step forward in the approach for developing representative PM2.5 concentration datasets to correlate with inpatient hospitalizations and emergency room visits data for asthma and inpatient hospitalizations for myocardial infarction (MI) and heart failure (HF) using case-crossover analysis. There were two key objective of this current study. First was to show that the inputs to the HBM could be expanded to include AOD data in addition to data from PM2.5 monitors and predictions from CMAQ. The second objective was to determine if inclusion of AOD surfaces in HBM model algorithms results in PM2.5 air pollutant concentration surfaces which more accurately predict hospital admittance and emergency room visits for MI, asthma, and HF. This study focuses on the New York City, NY metropolitan and surrounding areas during the 2004-2006 time period, in order to compare the health outcome impacts with those from previous studies and focus on any
Multicollinearity in hierarchical linear models.
Yu, Han; Jiang, Shanhe; Land, Kenneth C
2015-09-01
This study investigates an ill-posed problem (multicollinearity) in Hierarchical Linear Models from both the data and the model perspectives. We propose an intuitive, effective approach to diagnosing the presence of multicollinearity and its remedies in this class of models. A simulation study demonstrates the impacts of multicollinearity on coefficient estimates, associated standard errors, and variance components at various levels of multicollinearity for finite sample sizes typical in social science studies. We further investigate the role multicollinearity plays at each level for estimation of coefficient parameters in terms of shrinkage. Based on these analyses, we recommend a top-down method for assessing multicollinearity in HLMs that first examines the contextual predictors (Level-2 in a two-level model) and then the individual predictors (Level-1) and uses the results for data collection, research problem redefinition, model re-specification, variable selection and estimation of a final model.
Bayesian methods for estimating the reliability in complex hierarchical networks (interim report).
Energy Technology Data Exchange (ETDEWEB)
Marzouk, Youssef M.; Zurn, Rena M.; Boggs, Paul T.; Diegert, Kathleen V. (Sandia National Laboratories, Albuquerque, NM); Red-Horse, John Robert (Sandia National Laboratories, Albuquerque, NM); Pebay, Philippe Pierre
2007-05-01
Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitment to maintaining the integrity of the nuclear weapons stockpile. In this report, we undertake a key element in that process: development of an analytical framework for determining the reliability of the stockpile in a realistic environment of time-variance, inherent uncertainty, and sparse available information. This framework is probabilistic in nature and is founded on a novel combination of classical and computational Bayesian analysis, Bayesian networks, and polynomial chaos expansions. We note that, while the focus of the effort is stockpile-related, it is applicable to any reasonably-structured hierarchical system, including systems with feedback.
Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys
Leistedt, Boris; Peiris, Hiranya V
2016-01-01
Accurately characterizing the redshift distributions of galaxies is essential for analysing deep photometric surveys and testing cosmological models. We present a technique to simultaneously infer redshift distributions and individual redshifts from photometric galaxy catalogues. Our model constructs a piecewise constant representation (effectively a histogram) of the distribution of galaxy types and redshifts, the parameters of which are efficiently inferred from noisy photometric flux measurements. This approach can be seen as a generalization of template-fitting photometric redshift methods and relies on a library of spectral templates to relate the photometric fluxes of individual galaxies to their redshifts. We illustrate this technique on simulated galaxy survey data, and demonstrate that it delivers correct posterior distributions on the underlying type and redshift distributions, as well as on the individual types and redshifts of galaxies. We show that even with uninformative priors, large photometri...
Hierarchical spatiotemporal matrix models for characterizing invasions.
Hooten, Mevin B; Wikle, Christopher K; Dorazio, Robert M; Royle, J Andrew
2007-06-01
The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing.
A hierarchical model for spatial capture-recapture data
Royle, J. Andrew; Young, K.V.
2008-01-01
Estimating density is a fundamental objective of many animal population studies. Application of methods for estimating population size from ostensibly closed populations is widespread, but ineffective for estimating absolute density because most populations are subject to short-term movements or so-called temporary emigration. This phenomenon invalidates the resulting estimates because the effective sample area is unknown. A number of methods involving the adjustment of estimates based on heuristic considerations are in widespread use. In this paper, a hierarchical model of spatially indexed capture recapture data is proposed for sampling based on area searches of spatial sample units subject to uniform sampling intensity. The hierarchical model contains explicit models for the distribution of individuals and their movements, in addition to an observation model that is conditional on the location of individuals during sampling. Bayesian analysis of the hierarchical model is achieved by the use of data augmentation, which allows for a straightforward implementation in the freely available software WinBUGS. We present results of a simulation study that was carried out to evaluate the operating characteristics of the Bayesian estimator under variable densities and movement patterns of individuals. An application of the model is presented for survey data on the flat-tailed horned lizard (Phrynosoma mcallii) in Arizona, USA.
Siwek, M; Finocchiaro, R; Curik, I; Portolano, B
2011-02-01
Genetic structure and relationship amongst the main goat populations in Sicily (Girgentana, Derivata di Siria, Maltese and Messinese) were analysed using information from 19 microsatellite markers genotyped on 173 individuals. A posterior Bayesian approach implemented in the program STRUCTURE revealed a hierarchical structure with two clusters at the first level (Girgentana vs. Messinese, Derivata di Siria and Maltese), explaining 4.8% of variation (amovaФ(ST) estimate). Seven clusters nested within these first two clusters (further differentiations of Girgentana, Derivata di Siria and Maltese), explaining 8.5% of variation (amovaФ(SC) estimate). The analyses and methods applied in this study indicate their power to detect subtle population structure.
Energy Technology Data Exchange (ETDEWEB)
Mandel, Kaisey S.; Kirshner, Robert P. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Foley, Ryan J., E-mail: kmandel@cfa.harvard.edu [Astronomy Department, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801 (United States)
2014-12-20
We investigate the statistical dependence of the peak intrinsic colors of Type Ia supernovae (SNe Ia) on their expansion velocities at maximum light, measured from the Si II λ6355 spectral feature. We construct a new hierarchical Bayesian regression model, accounting for the random effects of intrinsic scatter, measurement error, and reddening by host galaxy dust, and implement a Gibbs sampler and deviance information criteria to estimate the correlation. The method is applied to the apparent colors from BVRI light curves and Si II velocity data for 79 nearby SNe Ia. The apparent color distributions of high-velocity (HV) and normal velocity (NV) supernovae exhibit significant discrepancies for B – V and B – R, but not other colors. Hence, they are likely due to intrinsic color differences originating in the B band, rather than dust reddening. The mean intrinsic B – V and B – R color differences between HV and NV groups are 0.06 ± 0.02 and 0.09 ± 0.02 mag, respectively. A linear model finds significant slopes of –0.021 ± 0.006 and –0.030 ± 0.009 mag (10{sup 3} km s{sup –1}){sup –1} for intrinsic B – V and B – R colors versus velocity, respectively. Because the ejecta velocity distribution is skewed toward high velocities, these effects imply non-Gaussian intrinsic color distributions with skewness up to +0.3. Accounting for the intrinsic-color-velocity correlation results in corrections to A{sub V} extinction estimates as large as –0.12 mag for HV SNe Ia and +0.06 mag for NV events. Velocity measurements from SN Ia spectra have the potential to diminish systematic errors from the confounding of intrinsic colors and dust reddening affecting supernova distances.
Bayesian inference for OPC modeling
Burbine, Andrew; Sturtevant, John; Fryer, David; Smith, Bruce W.
2016-03-01
The use of optical proximity correction (OPC) demands increasingly accurate models of the photolithographic process. Model building and inference techniques in the data science community have seen great strides in the past two decades which make better use of available information. This paper aims to demonstrate the predictive power of Bayesian inference as a method for parameter selection in lithographic models by quantifying the uncertainty associated with model inputs and wafer data. Specifically, the method combines the model builder's prior information about each modelling assumption with the maximization of each observation's likelihood as a Student's t-distributed random variable. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, a model's parameter space is explored to find the most credible parameter values. During parameter exploration, the parameters' posterior distributions are generated by applying Bayes' rule, using a likelihood function and the a priori knowledge supplied. The MCMC algorithm used, an affine invariant ensemble sampler (AIES), is implemented by initializing many walkers which semiindependently explore the space. The convergence of these walkers to global maxima of the likelihood volume determine the parameter values' highest density intervals (HDI) to reveal champion models. We show that this method of parameter selection provides insights into the data that traditional methods do not and outline continued experiments to vet the method.
Bayesian Calibration of Microsimulation Models.
Rutter, Carolyn M; Miglioretti, Diana L; Savarino, James E
2009-12-01
Microsimulation models that describe disease processes synthesize information from multiple sources and can be used to estimate the effects of screening and treatment on cancer incidence and mortality at a population level. These models are characterized by simulation of individual event histories for an idealized population of interest. Microsimulation models are complex and invariably include parameters that are not well informed by existing data. Therefore, a key component of model development is the choice of parameter values. Microsimulation model parameter values are selected to reproduce expected or known results though the process of model calibration. Calibration may be done by perturbing model parameters one at a time or by using a search algorithm. As an alternative, we propose a Bayesian method to calibrate microsimulation models that uses Markov chain Monte Carlo. We show that this approach converges to the target distribution and use a simulation study to demonstrate its finite-sample performance. Although computationally intensive, this approach has several advantages over previously proposed methods, including the use of statistical criteria to select parameter values, simultaneous calibration of multiple parameters to multiple data sources, incorporation of information via prior distributions, description of parameter identifiability, and the ability to obtain interval estimates of model parameters. We develop a microsimulation model for colorectal cancer and use our proposed method to calibrate model parameters. The microsimulation model provides a good fit to the calibration data. We find evidence that some parameters are identified primarily through prior distributions. Our results underscore the need to incorporate multiple sources of variability (i.e., due to calibration data, unknown parameters, and estimated parameters and predicted values) when calibrating and applying microsimulation models.
Nonparametric Bayesian inference of the microcanonical stochastic block model
Peixoto, Tiago P
2016-01-01
A principled approach to characterize the hidden modular structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: 1. Deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, that not only remove limitations that seriously degrade the inference on large networks, but also reveal s...
GPstuff: Bayesian Modeling with Gaussian Processes
Vanhatalo, J.; Riihimaki, J.; Hartikainen, J.; Jylänki, P.P.; Tolvanen, V.; Vehtari, A.
2013-01-01
The GPstuff toolbox is a versatile collection of Gaussian process models and computational tools required for Bayesian inference. The tools include, among others, various inference methods, sparse approximations and model assessment methods.
DEFF Research Database (Denmark)
Mantzouni, Irene; Sørensen, Helle; O'Hara, Robert B.;
2010-01-01
and Beverton and Holt stock–recruitment (SR) models were extended by applying hierarchical methods, mixed-effects models, and Bayesian inference to incorporate the influence of these ecosystem factors on model parameters representing cod maximum reproductive rate and carrying capacity. We identified...
Aksoy, Ozan; Weesie, Jeroen
2014-05-01
In this paper, using a within-subjects design, we estimate the utility weights that subjects attach to the outcome of their interaction partners in four decision situations: (1) binary Dictator Games (DG), second player's role in the sequential Prisoner's Dilemma (PD) after the first player (2) cooperated and (3) defected, and (4) first player's role in the sequential Prisoner's Dilemma game. We find that the average weights in these four decision situations have the following order: (1)>(2)>(4)>(3). Moreover, the average weight is positive in (1) but negative in (2), (3), and (4). Our findings indicate the existence of strong negative and small positive reciprocity for the average subject, but there is also high interpersonal variation in the weights in these four nodes. We conclude that the PD frame makes subjects more competitive than the DG frame. Using hierarchical Bayesian modeling, we simultaneously analyze beliefs of subjects about others' utility weights in the same four decision situations. We compare several alternative theoretical models on beliefs, e.g., rational beliefs (Bayesian-Nash equilibrium) and a consensus model. Our results on beliefs strongly support the consensus effect and refute rational beliefs: there is a strong relationship between own preferences and beliefs and this relationship is relatively stable across the four decision situations.
spTimer: Spatio-Temporal Bayesian Modeling Using R
Directory of Open Access Journals (Sweden)
Khandoker Shuvo Bakar
2015-02-01
Full Text Available Hierarchical Bayesian modeling of large point-referenced space-time data is increasingly becoming feasible in many environmental applications due to the recent advances in both statistical methodology and computation power. Implementation of these methods using the Markov chain Monte Carlo (MCMC computational techniques, however, requires development of problem-specific and user-written computer code, possibly in a low-level language. This programming requirement is hindering the widespread use of the Bayesian model-based methods among practitioners and, hence there is an urgent need to develop high-level software that can analyze large data sets rich in both space and time. This paper develops the package spTimer for hierarchical Bayesian modeling of stylized environmental space-time monitoring data as a contributed software package in the R language that is fast becoming a very popular statistical computing platform. The package is able to fit, spatially and temporally predict large amounts of space-time data using three recently developed Bayesian models. The user is given control over many options regarding covariance function selection, distance calculation, prior selection and tuning of the implemented MCMC algorithms, although suitable defaults are provided. The package has many other attractive features such as on the fly transformations and an ability to spatially predict temporally aggregated summaries on the original scale, which saves the problem of storage when using MCMC methods for large datasets. A simulation example, with more than a million observations, and a real life data example are used to validate the underlying code and to illustrate the software capabilities.
A Model of Hierarchical Key Assignment Scheme
Institute of Scientific and Technical Information of China (English)
ZHANG Zhigang; ZHAO Jing; XU Maozhi
2006-01-01
A model of the hierarchical key assignment scheme is approached in this paper, which can be used with any cryptography algorithm. Besides, the optimal dynamic control property of a hierarchical key assignment scheme will be defined in this paper. Also, our scheme model will meet this property.
Bayesian modeling of ChIP-chip data using latent variables.
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
Bayesian Uncertainty Analyses Via Deterministic Model
Krzysztofowicz, R.
2001-05-01
Rational decision-making requires that the total uncertainty about a variate of interest (a predictand) be quantified in terms of a probability distribution, conditional on all available information and knowledge. Suppose the state-of-knowledge is embodied in a deterministic model, which is imperfect and outputs only an estimate of the predictand. Fundamentals are presented of three Bayesian approaches to producing a probability distribution of the predictand via any deterministic model. The Bayesian Processor of Output (BPO) quantifies the total uncertainty in terms of a posterior distribution, conditional on model output. The Bayesian Processor of Ensemble (BPE) quantifies the total uncertainty in terms of a posterior distribution, conditional on an ensemble of model output. The Bayesian Forecasting System (BFS) decomposes the total uncertainty into input uncertainty and model uncertainty, which are characterized independently and then integrated into a predictive distribution.
Bayesian models a statistical primer for ecologists
Hobbs, N Thompson
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 probabili
A Bayesian model of context-sensitive value attribution.
Rigoli, Francesco; Friston, Karl J; Martinelli, Cristina; Selaković, Mirjana; Shergill, Sukhwinder S; Dolan, Raymond J
2016-06-22
Substantial evidence indicates that incentive value depends on an anticipation of rewards within a given context. However, the computations underlying this context sensitivity remain unknown. To address this question, we introduce a normative (Bayesian) account of how rewards map to incentive values. This assumes that the brain inverts a model of how rewards are generated. Key features of our account include (i) an influence of prior beliefs about the context in which rewards are delivered (weighted by their reliability in a Bayes-optimal fashion), (ii) the notion that incentive values correspond to precision-weighted prediction errors, (iii) and contextual information unfolding at different hierarchical levels. This formulation implies that incentive value is intrinsically context-dependent. We provide empirical support for this model by showing that incentive value is influenced by context variability and by hierarchically nested contexts. The perspective we introduce generates new empirical predictions that might help explaining psychopathologies, such as addiction.
Directory of Open Access Journals (Sweden)
Ram K Raghavan
Full Text Available This study aims to examine the spatio-temporal dynamics of Rocky Mountain spotted fever (RMSF prevalence in four contiguous states of Midwestern United States, and to determine the impact of environmental and socio-economic factors associated with this disease. Bayesian hierarchical models were used to quantify space and time only trends and spatio-temporal interaction effect in the case reports submitted to the state health departments in the region. Various socio-economic, environmental and climatic covariates screened a priori in a bivariate procedure were added to a main-effects Bayesian model in progressive steps to evaluate important drivers of RMSF space-time patterns in the region. Our results show a steady increase in RMSF incidence over the study period to newer geographic areas, and the posterior probabilities of county-specific trends indicate clustering of high risk counties in the central and southern parts of the study region. At the spatial scale of a county, the prevalence levels of RMSF is influenced by poverty status, average relative humidity, and average land surface temperature (>35°C in the region, and the relevance of these factors in the context of climate-change impacts on tick-borne diseases are discussed.
Hierarchical hybrid testability modeling and evaluation method based on information fusion
Institute of Scientific and Technical Information of China (English)
Xishan Zhang; Kaoli Huang; Pengcheng Yan; Guangyao Lian
2015-01-01
In order to meet the demand of testability analysis and evaluation for complex equipment under a smal sample test in the equipment life cycle, the hierarchical hybrid testability model-ing and evaluation method (HHTME), which combines the testabi-lity structure model (TSM) with the testability Bayesian networks model (TBNM), is presented. Firstly, the testability network topo-logy of complex equipment is built by using the hierarchical hybrid testability modeling method. Secondly, the prior conditional prob-ability distribution between network nodes is determined through expert experience. Then the Bayesian method is used to update the conditional probability distribution, according to history test information, virtual simulation information and similar product in-formation. Final y, the learned hierarchical hybrid testability model (HHTM) is used to estimate the testability of equipment. Compared with the results of other modeling methods, the relative deviation of the HHTM is only 0.52%, and the evaluation result is the most accurate.
Bayesian Modeling of a Human MMORPG Player
Synnaeve, Gabriel
2010-01-01
This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.
Bayesian Modeling of a Human MMORPG Player
Synnaeve, Gabriel; Bessière, Pierre
2011-03-01
This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.
HIERARCHICAL OPTIMIZATION MODEL ON GEONETWORK
Directory of Open Access Journals (Sweden)
Z. Zha
2012-07-01
Full Text Available In existing construction experience of Spatial Data Infrastructure (SDI, GeoNetwork, as the geographical information integrated solution, is an effective way of building SDI. During GeoNetwork serving as an internet application, several shortcomings are exposed. The first one is that the time consuming of data loading has been considerately increasing with the growth of metadata count. Consequently, the efficiency of query and search service becomes lower. Another problem is that stability and robustness are both ruined since huge amount of metadata. The final flaw is that the requirements of multi-user concurrent accessing based on massive data are not effectively satisfied on the internet. A novel approach, Hierarchical Optimization Model (HOM, is presented to solve the incapability of GeoNetwork working with massive data in this paper. HOM optimizes the GeoNetwork from these aspects: internal procedure, external deployment strategies, etc. This model builds an efficient index for accessing huge metadata and supporting concurrent processes. In this way, the services based on GeoNetwork can maintain stable while running massive metadata. As an experiment, we deployed more than 30 GeoNetwork nodes, and harvest nearly 1.1 million metadata. From the contrast between the HOM-improved software and the original one, the model makes indexing and retrieval processes more quickly and keeps the speed stable on metadata amount increasing. It also shows stable on multi-user concurrent accessing to system services, the experiment achieved good results and proved that our optimization model is efficient and reliable.
Multi-Fraction Bayesian Sediment Transport Model
Directory of Open Access Journals (Sweden)
Mark L. Schmelter
2015-09-01
Full Text Available A Bayesian approach to sediment transport modeling can provide a strong basis for evaluating and propagating model uncertainty, which can be useful in transport applications. Previous work in developing and applying Bayesian sediment transport models used a single grain size fraction or characterized the transport of mixed-size sediment with a single characteristic grain size. Although this approach is common in sediment transport modeling, it precludes the possibility of capturing processes that cause mixed-size sediments to sort and, thereby, alter the grain size available for transport and the transport rates themselves. This paper extends development of a Bayesian transport model from one to k fractional dimensions. The model uses an existing transport function as its deterministic core and is applied to the dataset used to originally develop the function. The Bayesian multi-fraction model is able to infer the posterior distributions for essential model parameters and replicates predictive distributions of both bulk and fractional transport. Further, the inferred posterior distributions are used to evaluate parametric and other sources of variability in relations representing mixed-size interactions in the original model. Successful OPEN ACCESS J. Mar. Sci. Eng. 2015, 3 1067 development of the model demonstrates that Bayesian methods can be used to provide a robust and rigorous basis for quantifying uncertainty in mixed-size sediment transport. Such a method has heretofore been unavailable and allows for the propagation of uncertainty in sediment transport applications.
Directory of Open Access Journals (Sweden)
Björn J. Döring
2013-12-01
Full Text Available A synthetic aperture radar (SAR system requires external absolute calibration so that radiometric measurements can be exploited in numerous scientific and commercial applications. Besides estimating a calibration factor, metrological standards also demand the derivation of a respective calibration uncertainty. This uncertainty is currently not systematically determined. Here for the first time it is proposed to use hierarchical modeling and Bayesian statistics as a consistent method for handling and analyzing the hierarchical data typically acquired during external calibration campaigns. Through the use of Markov chain Monte Carlo simulations, a joint posterior probability can be conveniently derived from measurement data despite the necessary grouping of data samples. The applicability of the method is demonstrated through a case study: The radar reflectivity of DLR’s new C-band Kalibri transponder is derived through a series of RADARSAT-2 acquisitions and a comparison with reference point targets (corner reflectors. The systematic derivation of calibration uncertainties is seen as an important step toward traceable radiometric calibration of synthetic aperture radars.
Hierarchical modeling and analysis for spatial data
Banerjee, Sudipto; Gelfand, Alan E
2003-01-01
Among the many uses of hierarchical modeling, their application to the statistical analysis of spatial and spatio-temporal data from areas such as epidemiology And environmental science has proven particularly fruitful. Yet to date, the few books that address the subject have been either too narrowly focused on specific aspects of spatial analysis, or written at a level often inaccessible to those lacking a strong background in mathematical statistics.Hierarchical Modeling and Analysis for Spatial Data is the first accessible, self-contained treatment of hierarchical methods, modeling, and dat
Bayesian Data-Model Fit Assessment for Structural Equation Modeling
Levy, Roy
2011-01-01
Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…
A Model for Slicing JAVA Programs Hierarchically
Institute of Scientific and Technical Information of China (English)
Bi-Xin Li; Xiao-Cong Fan; Jun Pang; Jian-Jun Zhao
2004-01-01
Program slicing can be effectively used to debug, test, analyze, understand and maintain objectoriented software. In this paper, a new slicing model is proposed to slice Java programs based on their inherent hierarchical feature. The main idea of hierarchical slicing is to slice programs in a stepwise way, from package level, to class level, method level, and finally up to statement level. The stepwise slicing algorithm and the related graph reachability algorithms are presented, the architecture of the Java program Analyzing Tool (JATO) based on hierarchical slicing model is provided, the applications and a small case study are also discussed.
Bayesian modeling of unknown diseases for biosurveillance.
Shen, Yanna; Cooper, Gregory F
2009-11-14
This paper investigates Bayesian modeling of unknown causes of events in the context of disease-outbreak detection. We introduce a Bayesian approach that models and detects both (1) known diseases (e.g., influenza and anthrax) by using informative prior probabilities and (2) unknown diseases (e.g., a new, highly contagious respiratory virus that has never been seen before) by using relatively non-informative prior probabilities. We report the results of simulation experiments which support that this modeling method can improve the detection of new disease outbreaks in a population. A key contribution of this paper is that it introduces a Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has broad applicability in medical informatics, where the space of known causes of outcomes of interest is seldom complete.
Distributed Bayesian Networks for User Modeling
DEFF Research Database (Denmark)
Tedesco, Roberto; Dolog, Peter; Nejdl, Wolfgang
2006-01-01
by such adaptive applications are often partial fragments of an overall user model. The fragments have then to be collected and merged into a global user profile. In this paper we investigate and present algorithms able to cope with distributed, fragmented user models – based on Bayesian Networks – in the context...... of Web-based eLearning platforms. The scenario we are tackling assumes learners who use several systems over time, which are able to create partial Bayesian Networks for user models based on the local system context. In particular, we focus on how to merge these partial user models. Our merge mechanism...... efficiently combines distributed learner models without the need to exchange internal structure of local Bayesian networks, nor local evidence between the involved platforms....
Conservation Laws in the Hierarchical Model
Beijeren, H. van; Gallavotti, G.; Knops, H.
1974-01-01
An exposition of the renormalization-group equations for the hierarchical model is given. Attention is drawn to some properties of the spin distribution functions which are conserved under the action of the renormalization group.
A Bayesian Analysis of Spectral ARMA Model
Directory of Open Access Journals (Sweden)
Manoel I. Silvestre Bezerra
2012-01-01
Full Text Available Bezerra et al. (2008 proposed a new method, based on Yule-Walker equations, to estimate the ARMA spectral model. In this paper, a Bayesian approach is developed for this model by using the noninformative prior proposed by Jeffreys (1967. The Bayesian computations, simulation via Markov Monte Carlo (MCMC is carried out and characteristics of marginal posterior distributions such as Bayes estimator and confidence interval for the parameters of the ARMA model are derived. Both methods are also compared with the traditional least squares and maximum likelihood approaches and a numerical illustration with two examples of the ARMA model is presented to evaluate the performance of the procedures.
Bayesian Modeling of ChIP-chip Data Through a High-Order Ising Model
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.
Bayesian semiparametric dynamic Nelson-Siegel model
C. Cakmakli
2011-01-01
This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model where the density of the yield curve factors and thereby the density of the yields are estimated along with other model parameters. This is accomplished by modeling the error distributions of the factors according to a Diric
Posterior Predictive Model Checking in Bayesian Networks
Crawford, Aaron
2014-01-01
This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex…
Bayesian calibration of car-following models
Van Hinsbergen, C.P.IJ.; Van Lint, H.W.C.; Hoogendoorn, S.P.; Van Zuylen, H.J.
2010-01-01
Recent research has revealed that there exist large inter-driver differences in car-following behavior such that different car-following models may apply to different drivers. This study applies Bayesian techniques to the calibration of car-following models, where prior distributions on each model p
Bayesian modeling of flexible cognitive control.
Jiang, Jiefeng; Heller, Katherine; Egner, Tobias
2014-10-01
"Cognitive control" describes endogenous guidance of behavior in situations where routine stimulus-response associations are suboptimal for achieving a desired goal. The computational and neural mechanisms underlying this capacity remain poorly understood. We examine recent advances stemming from the application of a Bayesian learner perspective that provides optimal prediction for control processes. In reviewing the application of Bayesian models to cognitive control, we note that an important limitation in current models is a lack of a plausible mechanism for the flexible adjustment of control over conflict levels changing at varying temporal scales. We then show that flexible cognitive control can be achieved by a Bayesian model with a volatility-driven learning mechanism that modulates dynamically the relative dependence on recent and remote experiences in its prediction of future control demand. We conclude that the emergent Bayesian perspective on computational mechanisms of cognitive control holds considerable promise, especially if future studies can identify neural substrates of the variables encoded by these models, and determine the nature (Bayesian or otherwise) of their neural implementation.
Bayesian modeling of flexible cognitive control
Jiang, Jiefeng; Heller, Katherine; Egner, Tobias
2014-01-01
“Cognitive control” describes endogenous guidance of behavior in situations where routine stimulus-response associations are suboptimal for achieving a desired goal. The computational and neural mechanisms underlying this capacity remain poorly understood. We examine recent advances stemming from the application of a Bayesian learner perspective that provides optimal prediction for control processes. In reviewing the application of Bayesian models to cognitive control, we note that an important limitation in current models is a lack of a plausible mechanism for the flexible adjustment of control over conflict levels changing at varying temporal scales. We then show that flexible cognitive control can be achieved by a Bayesian model with a volatility-driven learning mechanism that modulates dynamically the relative dependence on recent and remote experiences in its prediction of future control demand. We conclude that the emergent Bayesian perspective on computational mechanisms of cognitive control holds considerable promise, especially if future studies can identify neural substrates of the variables encoded by these models, and determine the nature (Bayesian or otherwise) of their neural implementation. PMID:24929218
Hierarchical animal movement models for population-level inference
Hooten, Mevin B.; Buderman, Frances E.; Brost, Brian M.; Hanks, Ephraim M.; Ivans, Jacob S.
2016-01-01
New methods for modeling animal movement based on telemetry data are developed regularly. With advances in telemetry capabilities, animal movement models are becoming increasingly sophisticated. Despite a need for population-level inference, animal movement models are still predominantly developed for individual-level inference. Most efforts to upscale the inference to the population level are either post hoc or complicated enough that only the developer can implement the model. Hierarchical Bayesian models provide an ideal platform for the development of population-level animal movement models but can be challenging to fit due to computational limitations or extensive tuning required. We propose a two-stage procedure for fitting hierarchical animal movement models to telemetry data. The two-stage approach is statistically rigorous and allows one to fit individual-level movement models separately, then resample them using a secondary MCMC algorithm. The primary advantages of the two-stage approach are that the first stage is easily parallelizable and the second stage is completely unsupervised, allowing for an automated fitting procedure in many cases. We demonstrate the two-stage procedure with two applications of animal movement models. The first application involves a spatial point process approach to modeling telemetry data, and the second involves a more complicated continuous-time discrete-space animal movement model. We fit these models to simulated data and real telemetry data arising from a population of monitored Canada lynx in Colorado, USA.
Analysis hierarchical model for discrete event systems
Ciortea, E. M.
2015-11-01
The This paper presents the hierarchical model based on discrete event network for robotic systems. Based on the hierarchical approach, Petri network is analysed as a network of the highest conceptual level and the lowest level of local control. For modelling and control of complex robotic systems using extended Petri nets. Such a system is structured, controlled and analysed in this paper by using Visual Object Net ++ package that is relatively simple and easy to use, and the results are shown as representations easy to interpret. The hierarchical structure of the robotic system is implemented on computers analysed using specialized programs. Implementation of hierarchical model discrete event systems, as a real-time operating system on a computer network connected via a serial bus is possible, where each computer is dedicated to local and Petri model of a subsystem global robotic system. Since Petri models are simplified to apply general computers, analysis, modelling, complex manufacturing systems control can be achieved using Petri nets. Discrete event systems is a pragmatic tool for modelling industrial systems. For system modelling using Petri nets because we have our system where discrete event. To highlight the auxiliary time Petri model using transport stream divided into hierarchical levels and sections are analysed successively. Proposed robotic system simulation using timed Petri, offers the opportunity to view the robotic time. Application of goods or robotic and transmission times obtained by measuring spot is obtained graphics showing the average time for transport activity, using the parameters sets of finished products. individually.
Bayesian Approach to Neuro-Rough Models for Modelling HIV
Marwala, Tshilidzi
2007-01-01
This paper proposes a new neuro-rough model for modelling the risk of HIV from demographic data. The model is formulated using Bayesian framework and trained using Markov Chain Monte Carlo method and Metropolis criterion. When the model was tested to estimate the risk of HIV infection given the demographic data it was found to give the accuracy of 62% as opposed to 58% obtained from a Bayesian formulated rough set model trained using Markov chain Monte Carlo method and 62% obtained from a Bayesian formulated multi-layered perceptron (MLP) model trained using hybrid Monte. The proposed model is able to combine the accuracy of the Bayesian MLP model and the transparency of Bayesian rough set model.
Survey of Bayesian Models for Modelling of Stochastic Temporal Processes
Energy Technology Data Exchange (ETDEWEB)
Ng, B
2006-10-12
This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.
Walter, William D.; Smith, Rick; Vanderklok, Mike; VerCauterren, Kurt C.
2014-01-01
Bovine tuberculosis is a bacterial disease caused by Mycobacterium bovis in livestock and wildlife with hosts that include Eurasian badgers (Meles meles), brushtail possum (Trichosurus vulpecula), and white-tailed deer (Odocoileus virginianus). Risk-assessment efforts in Michigan have been initiated on farms to minimize interactions of cattle with wildlife hosts but research onM. bovis on cattle farms has not investigated the spatial context of disease epidemiology. To incorporate spatially explicit data, initial likelihood of infection probabilities for cattle farms tested for M. bovis, prevalence of M. bovis in white-tailed deer, deer density, and environmental variables for each farm were modeled in a Bayesian hierarchical framework. We used geo-referenced locations of 762 cattle farms that have been tested for M. bovis, white-tailed deer prevalence, and several environmental variables that may lead to long-term survival and viability of M. bovis on farms and surrounding habitats (i.e., soil type, habitat type). Bayesian hierarchical analyses identified deer prevalence and proportion of sandy soil within our sampling grid as the most supported model. Analysis of cattle farms tested for M. bovisidentified that for every 1% increase in sandy soil resulted in an increase in odds of infection by 4%. Our analysis revealed that the influence of prevalence of M. bovis in white-tailed deer was still a concern even after considerable efforts to prevent cattle interactions with white-tailed deer through on-farm mitigation and reduction in the deer population. Cattle farms test positive for M. bovis annually in our study area suggesting that the potential for an environmental source either on farms or in the surrounding landscape may contributing to new or re-infections with M. bovis. Our research provides an initial assessment of potential environmental factors that could be incorporated into additional modeling efforts as more knowledge of deer herd
Energy Technology Data Exchange (ETDEWEB)
Kelly, Brandon C.; Goodman, Alyssa A. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Shetty, Rahul [Zentrum fuer Astronomie der Universitaet Heidelberg, Institut fuer Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg (Germany); Stutz, Amelia M.; Launhardt, Ralf [Max Planck Institut fuer Astronomie, Koenigstuhl 17, 69117 Heidelberg (Germany); Kauffmann, Jens [NASA JPL, 4800 Oak Grove Drive, Pasadena, CA 91109 (United States)
2012-06-10
We present a hierarchical Bayesian method for fitting infrared spectral energy distributions (SEDs) of dust emission to observed fluxes. Under the standard assumption of optically thin single temperature (T) sources, the dust SED as represented by a power-law-modified blackbody is subject to a strong degeneracy between T and the spectral index {beta}. The traditional non-hierarchical approaches, typically based on {chi}{sup 2} minimization, are severely limited by this degeneracy, as it produces an artificial anti-correlation between T and {beta} even with modest levels of observational noise. The hierarchical Bayesian method rigorously and self-consistently treats measurement uncertainties, including calibration and noise, resulting in more precise SED fits. As a result, the Bayesian fits do not produce any spurious anti-correlations between the SED parameters due to measurement uncertainty. We demonstrate that the Bayesian method is substantially more accurate than the {chi}{sup 2} fit in recovering the SED parameters, as well as the correlations between them. As an illustration, we apply our method to Herschel and submillimeter ground-based observations of the star-forming Bok globule CB244. This source is a small, nearby molecular cloud containing a single low-mass protostar and a starless core. We find that T and {beta} are weakly positively correlated-in contradiction with the {chi}{sup 2} fits, which indicate a T-{beta} anti-correlation from the same data set. Additionally, in comparison to the {chi}{sup 2} fits the Bayesian SED parameter estimates exhibit a reduced range in values.
Bayesian state space models for dynamic genetic network construction across multiple tissues.
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.
Snyder, Carolyn W.
2016-09-01
Statistical challenges often preclude comparisons among different sea surface temperature (SST) reconstructions over the past million years. Inadequate consideration of uncertainty can result in misinterpretation, overconfidence, and biased conclusions. Here I apply Bayesian hierarchical regressions to analyze local SST responsiveness to climate changes for 54 SST reconstructions from across the globe over the past million years. I develop methods to account for multiple sources of uncertainty, including the quantification of uncertainty introduced from absolute dating into interrecord comparisons. The estimates of local SST responsiveness explain 64% (62% to 77%, 95% interval) of the total variation within each SST reconstruction with a single number. There is remarkable agreement between SST proxy methods, with the exception of Mg/Ca proxy methods estimating muted responses at high latitudes. The Indian Ocean exhibits a muted response in comparison to other oceans. I find a stable estimate of the proposed "universal curve" of change in local SST responsiveness to climate changes as a function of sin2(latitude) over the past 400,000 years: SST change at 45°N/S is larger than the average tropical response by a factor of 1.9 (1.5 to 2.6, 95% interval) and explains 50% (35% to 58%, 95% interval) of the total variation between each SST reconstruction. These uncertainty and statistical methods are well suited for application across paleoclimate and environmental data series intercomparisons.
Semiparametric Quantile Modelling of Hierarchical Data
Institute of Scientific and Technical Information of China (English)
Mao Zai TIAN; Man Lai TANG; Ping Shing CHAN
2009-01-01
The classic hierarchical linear model formulation provides a considerable flexibility for modelling the random effects structure and a powerful tool for analyzing nested data that arise in various areas such as biology, economics and education. However, it assumes the within-group errors to be independently and identically distributed (i.i.d.) and models at all levels to be linear. Most importantly, traditional hierarchical models (just like other ordinary mean regression methods) cannot characterize the entire conditional distribution of a dependent variable given a set of covariates and fail to yield robust estimators. In this article, we relax the aforementioned and normality assumptions, and develop a so-called Hierarchical Semiparametric Quantile Regression Models in which the within-group errors could be heteroscedastic and models at some levels are allowed to be nonparametric. We present the ideas with a 2-level model. The level-l model is specified as a nonparametric model whereas level-2 model is set as a parametric model. Under the proposed semiparametric setting the vector of partial derivatives of the nonparametric function in level-1 becomes the response variable vector in level 2. The proposed method allows us to model the fixed effects in the innermost level (i.e., level 2) as a function of the covariates instead of a constant effect. We outline some mild regularity conditions required for convergence and asymptotic normality for our estimators. We illustrate our methodology with a real hierarchical data set from a laboratory study and some simulation studies.
The Hierarchical Dirichlet Process Hidden Semi-Markov Model
Johnson, Matthew J
2012-01-01
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi- Markovianity, which has been developed in the parametric setting to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration HDP-HSMM and develop posterior sampling algorithms for efficient inference in both the direct-assignment and weak-limit approximation settings. We demonstrate the utility of the model and our inference methods on synthetic data as well as experiments on a speaker diarization problem and an example of learning the patterns in Morse code.
Bayesian Spatial Modelling with R-INLA
Finn Lindgren; Håvard Rue
2015-01-01
The principles behind the interface to continuous domain spatial models in the R- INLA software package for R are described. The integrated nested Laplace approximation (INLA) approach proposed by Rue, Martino, and Chopin (2009) is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized) linear mixed to spatial and spatio-temporal models. Combined with the stochastic...
Hierarchical linear regression models for conditional quantiles
Institute of Scientific and Technical Information of China (English)
TIAN Maozai; CHEN Gemai
2006-01-01
The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models,but it cannot deal effectively with the data with a hierarchical structure.In practice,the existence of such data hierarchies is neither accidental nor ignorable,it is a common phenomenon.To ignore this hierarchical data structure risks overlooking the importance of group effects,and may also render many of the traditional statistical analysis techniques used for studying data relationships invalid.On the other hand,the hierarchical models take a hierarchical data structure into account and have also many applications in statistics,ranging from overdispersion to constructing min-max estimators.However,the hierarchical models are virtually the mean regression,therefore,they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional covariates.Furthermore,the estimated coefficient vector (marginal effects)is sensitive to an outlier observation on the dependent variable.In this article,a new approach,which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models,is developed.On the theoretical front,we also consider the asymptotic properties of the new method,obtaining the simple conditions for an n1/2-convergence and an asymptotic normality.We also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.
Modelling crime linkage with Bayesian networks
J. de Zoete; M. Sjerps; D. Lagnado; N. Fenton
2015-01-01
When two or more crimes show specific similarities, such as a very distinct modus operandi, the probability that they were committed by the same offender becomes of interest. This probability depends on the degree of similarity and distinctiveness. We show how Bayesian networks can be used to model
Bayesian modelling of geostatistical malaria risk data
Directory of Open Access Journals (Sweden)
L. Gosoniu
2006-11-01
Full Text Available Bayesian geostatistical models applied to malaria risk data quantify the environment-disease relations, identify significant environmental predictors of malaria transmission and provide model-based predictions of malaria risk together with their precision. These models are often based on the stationarity assumption which implies that spatial correlation is a function of distance between locations and independent of location. We relax this assumption and analyse malaria survey data in Mali using a Bayesian non-stationary model. Model fit and predictions are based on Markov chain Monte Carlo simulation methods. Model validation compares the predictive ability of the non-stationary model with the stationary analogue. Results indicate that the stationarity assumption is important because it influences the significance of environmental factors and the corresponding malaria risk maps.
Bayesian modelling of geostatistical malaria risk data.
Gosoniu, L; Vounatsou, P; Sogoba, N; Smith, T
2006-11-01
Bayesian geostatistical models applied to malaria risk data quantify the environment-disease relations, identify significant environmental predictors of malaria transmission and provide model-based predictions of malaria risk together with their precision. These models are often based on the stationarity assumption which implies that spatial correlation is a function of distance between locations and independent of location. We relax this assumption and analyse malaria survey data in Mali using a Bayesian non-stationary model. Model fit and predictions are based on Markov chain Monte Carlo simulation methods. Model validation compares the predictive ability of the non-stationary model with the stationary analogue. Results indicate that the stationarity assumption is important because it influences the significance of environmental factors and the corresponding malaria risk maps.
A Bayesian nonparametric meta-analysis model.
Karabatsos, George; Talbott, Elizabeth; Walker, Stephen G
2015-03-01
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall effect size, such models may be adequate, but for prediction, they surely are not if the effect-size distribution exhibits non-normal behavior. To address this issue, we propose a Bayesian nonparametric meta-analysis model, which can describe a wider range of effect-size distributions, including unimodal symmetric distributions, as well as skewed and more multimodal distributions. We demonstrate our model through the analysis of real meta-analytic data arising from behavioral-genetic research. We compare the predictive performance of the Bayesian nonparametric model against various conventional and more modern normal fixed-effects and random-effects models.
A hierarchical community occurrence model for North Carolina stream fish
Midway, S.R.; Wagner, Tyler; Tracy, B.H.
2016-01-01
The southeastern USA is home to one of the richest—and most imperiled and threatened—freshwater fish assemblages in North America. For many of these rare and threatened species, conservation efforts are often limited by a lack of data. Drawing on a unique and extensive data set spanning over 20 years, we modeled occurrence probabilities of 126 stream fish species sampled throughout North Carolina, many of which occur more broadly in the southeastern USA. Specifically, we developed species-specific occurrence probabilities from hierarchical Bayesian multispecies models that were based on common land use and land cover covariates. We also used index of biotic integrity tolerance classifications as a second level in the model hierarchy; we identify this level as informative for our work, but it is flexible for future model applications. Based on the partial-pooling property of the models, we were able to generate occurrence probabilities for many imperiled and data-poor species in addition to highlighting a considerable amount of occurrence heterogeneity that supports species-specific investigations whenever possible. Our results provide critical species-level information on many threatened and imperiled species as well as information that may assist with re-evaluation of existing management strategies, such as the use of surrogate species. Finally, we highlight the use of a relatively simple hierarchical model that can easily be generalized for similar situations in which conventional models fail to provide reliable estimates for data-poor groups.
Bayesian Multiscale Modeling of Closed Curves in Point Clouds.
Gu, Kelvin; Pati, Debdeep; Dunson, David B
2014-10-01
Modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy, to the classification of organisms based on their structural information. In low-contrast images or sparse and noisy point clouds, there is often insufficient data to recover local segments of the boundary in isolation. Thus, it becomes critical to model the entire boundary in the form of a closed curve. To achieve this, we develop a Bayesian hierarchical model that expresses highly diverse 2D objects in the form of closed curves. The model is based on a novel multiscale deformation process. By relating multiple objects through a hierarchical formulation, we can successfully recover missing boundaries by borrowing structural information from similar objects at the appropriate scale. Furthermore, the model's latent parameters help interpret the population, indicating dimensions of significant structural variability and also specifying a 'central curve' that summarizes the collection. Theoretical properties of our prior are studied in specific cases and efficient Markov chain Monte Carlo methods are developed, evaluated through simulation examples and applied to panorex teeth images for modeling teeth contours and also to a brain tumor contour detection problem.
Link, William; Sauer, John R.
2016-01-01
The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.
Link, William A; Sauer, John R
2016-07-01
The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.
Bayesian Model comparison of Higgs couplings
Bergstrom, Johannes
2014-01-01
We investigate the possibility of contributions from physics beyond the Standard Model (SM) to the Higgs couplings, in the light of the LHC data. The work is performed within an interim framework where the magnitude of the Higgs production and decay rates are rescaled though Higgs coupling scale factors. We perform Bayesian parameter inference on these scale factors, concluding that there is good compatibility with the SM. Furthermore, we carry out Bayesian model comparison on all models where any combination of scale factors can differ from their SM values and find that typically models with fewer free couplings are strongly favoured. We consider the evidence that each coupling individually equals the SM value, making the minimal assumptions on the other couplings. Finally, we make a comparison of the SM against a single "not-SM" model, and find that there is moderate to strong evidence for the SM.
Bayesian inference for pulsar timing models
Vigeland, Sarah J
2013-01-01
The extremely regular, periodic radio emission from millisecond pulsars make them useful tools for studying neutron star astrophysics, general relativity, and low-frequency gravitational waves. These studies require that the observed pulse time of arrivals are fit to complicated timing models that describe numerous effects such as the astrometry of the source, the evolution of the pulsar's spin, the presence of a binary companion, and the propagation of the pulses through the interstellar medium. In this paper, we discuss the benefits of using Bayesian inference to obtain these timing solutions. These include the validation of linearized least-squares model fits when they are correct, and the proper characterization of parameter uncertainties when they are not; the incorporation of prior parameter information and of models of correlated noise; and the Bayesian comparison of alternative timing models. We describe our computational setup, which combines the timing models of tempo2 with the nested-sampling integ...
Hierarchic Models of Turbulence, Superfluidity and Superconductivity
Kaivarainen, A
2000-01-01
New models of Turbulence, Superfluidity and Superconductivity, based on new Hierarchic theory, general for liquids and solids (physics/0102086), have been proposed. CONTENTS: 1 Turbulence. General description; 2 Mesoscopic mechanism of turbulence; 3 Superfluidity. General description; 4 Mesoscopic scenario of fluidity; 5 Superfluidity as a hierarchic self-organization process; 6 Superfluidity in 3He; 7 Superconductivity: General properties of metals and semiconductors; Plasma oscillations; Cyclotron resonance; Electroconductivity; 8. Microscopic theory of superconductivity (BCS); 9. Mesoscopic scenario of superconductivity: Interpretation of experimental data in the framework of mesoscopic model of superconductivity.
Institute of Scientific and Technical Information of China (English)
何永强; 宫玉荣; 朱予聪
2015-01-01
提出了运用贝叶斯理论和层次模型对传感器网络节点故障进行预测的方法，结合传感器网络各节点处理信息的时序关系，用定性分析将时间信息融合到节点中分析故障传播机制和故障预测。根据节点的历史信息和当前运行情况，预测和确定节点的故障概率；利用参数学习和概率推理，预测上层节点的故障概率。通过仿真实验并与其他预测方法进行比较分析，验证了该方法的可靠性和精确性，为传感器网络节点的故障预测提供了新的思路和方法。%This paper presents the method for sensor network node failure prediction with the relationship between timing and level using Bayesian model methods. The method combines processing information in each node sensor network and uses qualitative analysis to integrate time information into the node to analyze the fault propagation mechanism and failure prediction. According to the probabili-ty of failure history information of node and the current operating conditions,nodes failure probabilities are forecasted and determined. Using the parameters of learning and probabilistic reasoning,the probability of failure of the upper node is predicted. Through simula-tion analysis and comparative analysis with other forecasting methods,the accuracy and precision of the method for sensor network node failure prediction is verified,providing new ideas and methods for nodes failure detection.
Strategic games on a hierarchical network model
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Among complex network models, the hierarchical network model is the one most close to such real networks as world trade web, metabolic network, WWW, actor network, and so on. It has not only the property of power-law degree distribution, but growth based on growth and preferential attachment, showing the scale-free degree distribution property. In this paper, we study the evolution of cooperation on a hierarchical network model, adopting the prisoner's dilemma (PD) game and snowdrift game (SG) as metaphors of the interplay between connected nodes. BA model provides a unifying framework for the emergence of cooperation. But interestingly, we found that on hierarchical model, there is no sign of cooperation for PD game, while the frequency of cooperation decreases as the common benefit decreases for SG. By comparing the scaling clustering coefficient properties of the hierarchical network model with that of BA model, we found that the former amplifies the effect of hubs. Considering different performances of PD game and SG on complex network, we also found that common benefit leads to cooperation in the evolution. Thus our study may shed light on the emergence of cooperation in both natural and social environments.
Structure learning for Bayesian networks as models of biological networks.
Larjo, Antti; Shmulevich, Ilya; Lähdesmäki, Harri
2013-01-01
Bayesian networks are probabilistic graphical models suitable for modeling several kinds of biological systems. In many cases, the structure of a Bayesian network represents causal molecular mechanisms or statistical associations of the underlying system. Bayesian networks have been applied, for example, for inferring the structure of many biological networks from experimental data. We present some recent progress in learning the structure of static and dynamic Bayesian networks from data.
Bayesian network modelling of upper gastrointestinal bleeding
Aisha, Nazziwa; Shohaimi, Shamarina; Adam, Mohd Bakri
2013-09-01
Bayesian networks are graphical probabilistic models that represent causal and other relationships between domain variables. In the context of medical decision making, these models have been explored to help in medical diagnosis and prognosis. In this paper, we discuss the Bayesian network formalism in building medical support systems and we learn a tree augmented naive Bayes Network (TAN) from gastrointestinal bleeding data. The accuracy of the TAN in classifying the source of gastrointestinal bleeding into upper or lower source is obtained. The TAN achieves a high classification accuracy of 86% and an area under curve of 92%. A sensitivity analysis of the model shows relatively high levels of entropy reduction for color of the stool, history of gastrointestinal bleeding, consistency and the ratio of blood urea nitrogen to creatinine. The TAN facilitates the identification of the source of GIB and requires further validation.
Designing and testing inflationary models with Bayesian networks
Energy Technology Data Exchange (ETDEWEB)
Price, Layne C. [Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics; Auckland Univ. (New Zealand). Dept. of Physics; Peiris, Hiranya V. [Univ. College London (United Kingdom). Dept. of Physics and Astronomy; Frazer, Jonathan [DESY Hamburg (Germany). Theory Group; Univ. of the Basque Country, Bilbao (Spain). Dept. of Theoretical Physics; Basque Foundation for Science, Bilbao (Spain). IKERBASQUE; Easther, Richard [Auckland Univ. (New Zealand). Dept. of Physics
2015-11-15
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N{sub f}-quadratic inflation as an illustrative example, finding that the number of e-folds N{sub *} between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.
Designing and testing inflationary models with Bayesian networks
Price, Layne C; Frazer, Jonathan; Easther, Richard
2015-01-01
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use $N_f$--quadratic inflation as an illustrative example, finding that the number of $e$-folds $N_*$ between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.
Managing Clustered Data Using Hierarchical Linear Modeling
Warne, Russell T.; Li, Yan; McKyer, E. Lisako J.; Condie, Rachel; Diep, Cassandra S.; Murano, Peter S.
2012-01-01
Researchers in nutrition research often use cluster or multistage sampling to gather participants for their studies. These sampling methods often produce violations of the assumption of data independence that most traditional statistics share. Hierarchical linear modeling is a statistical method that can overcome violations of the independence…
A Bayesian Generative Model for Learning Semantic Hierarchies
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Roni eMittelman
2014-05-01
Full Text Available Building fine-grained visual recognition systems that are capable of recognizing tens of thousands of categories, has received much attention in recent years. The well known semantic hierarchical structure of categories and concepts, has been shown to provide a key prior which allows for optimal predictions. The hierarchical organization of various domains and concepts has been subject to extensive research, and led to the development of the WordNet domains hierarchy [18], which was also used to organize the images in the ImageNet [11] dataset, in which the category count approaches the human capacity. Still, for the human visual system, the form of the hierarchy must be discovered with minimal use of supervision or innate knowledge. In this work, we propose a new Bayesian generative model for learning such domain hierarchies, based on semantic input. Our model is motivated by the super-subordinate organization of domain labels and concepts that characterizes WordNet, and accounts for several important challenges: maintaining context information when progressing deeper into the hierarchy, learning a coherent semantic concept for each node, and modeling uncertainty in the perception process.
Bayesian Recurrent Neural Network for Language Modeling.
Chien, Jen-Tzung; Ku, Yuan-Chu
2016-02-01
A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.
Bayesian Network Based XP Process Modelling
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Mohamed Abouelela
2010-07-01
Full Text Available A Bayesian Network based mathematical model has been used for modelling Extreme Programmingsoftware development process. The model is capable of predicting the expected finish time and theexpected defect rate for each XP release. Therefore, it can be used to determine the success/failure of anyXP Project. The model takes into account the effect of three XP practices, namely: Pair Programming,Test Driven Development and Onsite Customer practices. The model’s predictions were validated againsttwo case studies. Results show the precision of our model especially in predicting the project finish time.
A Bayesian Model of Biases in Artificial Language Learning: The Case of a Word-Order Universal
Culbertson, Jennifer; Smolensky, Paul
2012-01-01
In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language-learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners' input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized…
Bayesian nonparametric duration model with censorship
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Joseph Hakizamungu
2007-10-01
Full Text Available This paper is concerned with nonparametric i.i.d. durations models censored observations and we establish by a simple and unified approach the general structure of a bayesian nonparametric estimator for a survival function S. For Dirichlet prior distributions, we describe completely the structure of the posterior distribution of the survival function. These results are essentially supported by prior and posterior independence properties.
Hierarchical models in the brain.
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Karl Friston
2008-11-01
Full Text Available This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain.
Bayesian structural equation modeling in sport and exercise psychology.
Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus
2015-08-01
Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.
Hierarchical model of vulnerabilities for emotional disorders.
Norton, Peter J; Mehta, Paras D
2007-01-01
Clark and Watson's (1991) tripartite model of anxiety and depression has had a dramatic impact on our understanding of the dispositional variables underlying emotional disorders. More recently, calls have been made to examine not simply the influence of negative affectivity (NA) but also mediating factors that might better explain how NA influences anxious and depressive syndromes (e.g. Taylor, 1998; Watson, 2005). Extending preliminary projects, this study evaluated two hierarchical models of NA, mediating factors of anxiety sensitivity and intolerance of uncertainty, and specific emotional manifestations. Data provided a very good fit to a model elaborated from preliminary studies, lending further support to hierarchical models of emotional vulnerabilities. Implications for classification and diagnosis are discussed.
Bayesian Inference of a Multivariate Regression Model
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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.
Hierarchical Climate Modeling for Cosmoclimatology
Ohfuchi, Wataru
2010-05-01
It has been reported that there are correlations among solar activity, amount of galactic cosmic ray, amount of low clouds and surface air temperature (Svensmark and Friis-Chistensen, 1997). These correlations seem to exist for current climate change, Little Ice Age, and geological time scale climate changes. Some hypothetic mechanisms have been argued for the correlations but it still needs quantitative studies to understand the mechanism. In order to decrease uncertainties, only first principles or laws very close to first principles should be used. Our group at Japan Agency for Marine-Earth Science and Technology has started modeling effort to tackle this problem. We are constructing models from galactic cosmic ray inducing ionization, to aerosol formation, to cloud formation, to global climate. In this talk, we introduce our modeling activities. For aerosol formation, we use molecular dynamics. For cloud formation, we use a new cloud microphysics model called "super droplet method". We also try to couple a nonhydrostatic atmospheric regional cloud resolving model and a hydrostatic atmospheric general circulation model.
Joint hierarchical models for sparsely sampled high-dimensional LiDAR and forest variables
Finley, Andrew O.; Banerjee, Sudipto; Zhou, Yuzhen; Cook, Bruce D; Babcock, Chad
2016-01-01
Recent advancements in remote sensing technology, specifically Light Detection and Ranging (LiDAR) sensors, provide the data needed to quantify forest characteristics at a fine spatial resolution over large geographic domains. From an inferential standpoint, there is interest in prediction and interpolation of the often sparsely sampled and spatially misaligned LiDAR signals and forest variables. We propose a fully process-based Bayesian hierarchical model for above ground biomass (AGB) and L...
Contending non-double-couple source components with hierarchical Bayesian moment tensor inversion
Mustac, M.; Tkalcic, H.
2015-12-01
Seismic moment tensors can aid the discrimination between earthquakes and explosions. However, the isotropic component can be found in a large number of earthquakes simply as a consequence of earthquake location, poorly modeled structure or noise in the data. Recently, we have developed a method for moment tensor inversion, capable of retrieving parameter uncertainties together with their optimal values, using probabilistic Bayesian inference. It has been applied to data from a complex volcanic environment in the Long Valley Caldera (LVC), California, and confirmed a large isotropic source component. We now extend the application to two different environments where the existence of non-double-couple source components is likely. The method includes notable treatment of the noise, utilizing pre-event noise to estimate the noise covariance matrix. This is extended throughout the inversion, where noise variance is a "hyperparameter" that determines the level of data fit. On top of that, different noise parameters for each station are used as weights, naturally penalizing stations with noisy data. In the LVC case, this means increasing the amount of information from two stations at moderate distances, which results in a 1 km deeper estimate for the source location. This causes a change in the non-double-couple components in the inversions assuming a simple diagonal or exponential covariance matrix, but not in the inversion assuming a more complicated, attenuated cosine covariance matrix. Combining a sophisticated noise treatment with a powerful Bayesian inversion technique can give meaningful uncertainty estimates for long-period (20-50 s) data, provided an appropriate regional structure model.
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Mario A Pardo
Full Text Available We inferred the population densities of blue whales (Balaenoptera musculus and short-beaked common dolphins (Delphinus delphis in the Northeast Pacific Ocean as functions of the water-column's physical structure by implementing hierarchical models in a Bayesian framework. This approach allowed us to propagate the uncertainty of the field observations into the inference of species-habitat relationships and to generate spatially explicit population density predictions with reduced effects of sampling heterogeneity. Our hypothesis was that the large-scale spatial distributions of these two cetacean species respond primarily to ecological processes resulting from shoaling and outcropping of the pycnocline in regions of wind-forced upwelling and eddy-like circulation. Physically, these processes affect the thermodynamic balance of the water column, decreasing its volume and thus the height of the absolute dynamic topography (ADT. Biologically, they lead to elevated primary productivity and persistent aggregation of low-trophic-level prey. Unlike other remotely sensed variables, ADT provides information about the structure of the entire water column and it is also routinely measured at high spatial-temporal resolution by satellite altimeters with uniform global coverage. Our models provide spatially explicit population density predictions for both species, even in areas where the pycnocline shoals but does not outcrop (e.g. the Costa Rica Dome and the North Equatorial Countercurrent thermocline ridge. Interannual variations in distribution during El Niño anomalies suggest that the population density of both species decreases dramatically in the Equatorial Cold Tongue and the Costa Rica Dome, and that their distributions retract to particular areas that remain productive, such as the more oceanic waters in the central California Current System, the northern Gulf of California, the North Equatorial Countercurrent thermocline ridge, and the more
Pardo, Mario A; Gerrodette, Tim; Beier, Emilio; Gendron, Diane; Forney, Karin A; Chivers, Susan J; Barlow, Jay; Palacios, Daniel M
2015-01-01
We inferred the population densities of blue whales (Balaenoptera musculus) and short-beaked common dolphins (Delphinus delphis) in the Northeast Pacific Ocean as functions of the water-column's physical structure by implementing hierarchical models in a Bayesian framework. This approach allowed us to propagate the uncertainty of the field observations into the inference of species-habitat relationships and to generate spatially explicit population density predictions with reduced effects of sampling heterogeneity. Our hypothesis was that the large-scale spatial distributions of these two cetacean species respond primarily to ecological processes resulting from shoaling and outcropping of the pycnocline in regions of wind-forced upwelling and eddy-like circulation. Physically, these processes affect the thermodynamic balance of the water column, decreasing its volume and thus the height of the absolute dynamic topography (ADT). Biologically, they lead to elevated primary productivity and persistent aggregation of low-trophic-level prey. Unlike other remotely sensed variables, ADT provides information about the structure of the entire water column and it is also routinely measured at high spatial-temporal resolution by satellite altimeters with uniform global coverage. Our models provide spatially explicit population density predictions for both species, even in areas where the pycnocline shoals but does not outcrop (e.g. the Costa Rica Dome and the North Equatorial Countercurrent thermocline ridge). Interannual variations in distribution during El Niño anomalies suggest that the population density of both species decreases dramatically in the Equatorial Cold Tongue and the Costa Rica Dome, and that their distributions retract to particular areas that remain productive, such as the more oceanic waters in the central California Current System, the northern Gulf of California, the North Equatorial Countercurrent thermocline ridge, and the more southern portion of the
Bayesian variable selection for latent class models.
Ghosh, Joyee; Herring, Amy H; Siega-Riz, Anna Maria
2011-09-01
In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.
Bayesian model selection in Gaussian regression
Abramovich, Felix
2009-01-01
We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized least squares estimation with a complexity penalty associated with a prior on the model size. We investigate the optimality properties of the resulting estimator. We establish the oracle inequality and specify conditions on the prior that imply its asymptotic minimaxity within a wide range of sparse and dense settings for "nearly-orthogonal" and "multicollinear" designs.
Bayesian mixture models for partially verified data
DEFF Research Database (Denmark)
Kostoulas, Polychronis; Browne, William J.; Nielsen, Søren Saxmose;
2013-01-01
for some individuals, in order to minimize this loss in the discriminatory power. The distribution of the continuous antibody response against MAP has been obtained for healthy, MAP-infected and MAP-infectious cows of different age groups. The overall power of the milk-ELISA to discriminate between healthy......Bayesian mixture models can be used to discriminate between the distributions of continuous test responses for different infection stages. These models are particularly useful in case of chronic infections with a long latent period, like Mycobacterium avium subsp. paratuberculosis (MAP) infection...
A hierarchical nest survival model integrating incomplete temporally varying covariates
Converse, Sarah J.; Royle, J. Andrew; Adler, Peter H.; Urbanek, Richard P.; Barzan, Jeb A.
2013-01-01
Nest success is a critical determinant of the dynamics of avian populations, and nest survival modeling has played a key role in advancing avian ecology and management. Beginning with the development of daily nest survival models, and proceeding through subsequent extensions, the capacity for modeling the effects of hypothesized factors on nest survival has expanded greatly. We extend nest survival models further by introducing an approach to deal with incompletely observed, temporally varying covariates using a hierarchical model. Hierarchical modeling offers a way to separate process and observational components of demographic models to obtain estimates of the parameters of primary interest, and to evaluate structural effects of ecological and management interest. We built a hierarchical model for daily nest survival to analyze nest data from reintroduced whooping cranes (Grus americana) in the Eastern Migratory Population. This reintroduction effort has been beset by poor reproduction, apparently due primarily to nest abandonment by breeding birds. We used the model to assess support for the hypothesis that nest abandonment is caused by harassment from biting insects. We obtained indices of blood-feeding insect populations based on the spatially interpolated counts of insects captured in carbon dioxide traps. However, insect trapping was not conducted daily, and so we had incomplete information on a temporally variable covariate of interest. We therefore supplemented our nest survival model with a parallel model for estimating the values of the missing insect covariates. We used Bayesian model selection to identify the best predictors of daily nest survival. Our results suggest that the black fly Simulium annulus may be negatively affecting nest survival of reintroduced whooping cranes, with decreasing nest survival as abundance of S. annulus increases. The modeling framework we have developed will be applied in the future to a larger data set to evaluate the
Hierarchical mixture models for assessing fingerprint individuality
Dass, Sarat C.; Li, Mingfei
2009-01-01
The study of fingerprint individuality aims to determine to what extent a fingerprint uniquely identifies an individual. Recent court cases have highlighted the need for measures of fingerprint individuality when a person is identified based on fingerprint evidence. The main challenge in studies of fingerprint individuality is to adequately capture the variability of fingerprint features in a population. In this paper hierarchical mixture models are introduced to infer the extent of individua...
Zhang, Zhidong
2016-01-01
This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model,…
A Bayesian Shrinkage Approach for AMMI Models.
da Silva, Carlos Pereira; de Oliveira, Luciano Antonio; Nuvunga, Joel Jorge; Pamplona, Andrezza Kéllen Alves; Balestre, Marcio
2015-01-01
Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05) in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct posterior
A Bayesian Shrinkage Approach for AMMI Models.
Directory of Open Access Journals (Sweden)
Carlos Pereira da Silva
Full Text Available Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI model, are widely applicable to genotype-by-environment interaction (GEI studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05 in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct
Semantic Image Segmentation with Contextual Hierarchical Models.
Seyedhosseini, Mojtaba; Tasdizen, Tolga
2016-05-01
Semantic segmentation is the problem of assigning an object label to each pixel. It unifies the image segmentation and object recognition problems. The importance of using contextual information in semantic segmentation frameworks has been widely realized in the field. We propose a contextual framework, called contextual hierarchical model (CHM), which learns contextual information in a hierarchical framework for semantic segmentation. At each level of the hierarchy, a classifier is trained based on downsampled input images and outputs of previous levels. Our model then incorporates the resulting multi-resolution contextual information into a classifier to segment the input image at original resolution. This training strategy allows for optimization of a joint posterior probability at multiple resolutions through the hierarchy. Contextual hierarchical model is purely based on the input image patches and does not make use of any fragments or shape examples. Hence, it is applicable to a variety of problems such as object segmentation and edge detection. We demonstrate that CHM performs at par with state-of-the-art on Stanford background and Weizmann horse datasets. It also outperforms state-of-the-art edge detection methods on NYU depth dataset and achieves state-of-the-art on Berkeley segmentation dataset (BSDS 500).
An accessible method for implementing hierarchical models with spatio-temporal abundance data
Ross, Beth E.; Hooten, Melvin B.; Koons, David N.
2012-01-01
A common goal in ecology and wildlife management is to determine the causes of variation in population dynamics over long periods of time and across large spatial scales. Many assumptions must nevertheless be overcome to make appropriate inference about spatio-temporal variation in population dynamics, such as autocorrelation among data points, excess zeros, and observation error in count data. To address these issues, many scientists and statisticians have recommended the use of Bayesian hierarchical models. Unfortunately, hierarchical statistical models remain somewhat difficult to use because of the necessary quantitative background needed to implement them, or because of the computational demands of using Markov Chain Monte Carlo algorithms to estimate parameters. Fortunately, new tools have recently been developed that make it more feasible for wildlife biologists to fit sophisticated hierarchical Bayesian models (i.e., Integrated Nested Laplace Approximation, ‘INLA’). We present a case study using two important game species in North America, the lesser and greater scaup, to demonstrate how INLA can be used to estimate the parameters in a hierarchical model that decouples observation error from process variation, and accounts for unknown sources of excess zeros as well as spatial and temporal dependence in the data. Ultimately, our goal was to make unbiased inference about spatial variation in population trends over time.
Directory of Open Access Journals (Sweden)
Robert W Burn
Full Text Available Elephant poaching and the ivory trade remain high on the agenda at meetings of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES. Well-informed debates require robust estimates of trends, the spatial distribution of poaching, and drivers of poaching. We present an analysis of trends and drivers of an indicator of elephant poaching of all elephant species. The site-based monitoring system known as Monitoring the Illegal Killing of Elephants (MIKE, set up by the 10(th Conference of the Parties of CITES in 1997, produces carcass encounter data reported mainly by anti-poaching patrols. Data analyzed were site by year totals of 6,337 carcasses from 66 sites in Africa and Asia from 2002-2009. Analysis of these observational data is a serious challenge to traditional statistical methods because of the opportunistic and non-random nature of patrols, and the heterogeneity across sites. Adopting a bayesian hierarchical modeling approach, we used the proportion of carcasses that were illegally killed (PIKE as a poaching index, to estimate the trend and the effects of site- and country-level factors associated with poaching. Important drivers of illegal killing that emerged at country level were poor governance and low levels of human development, and at site level, forest cover and area of the site in regions where human population density is low. After a drop from 2002, PIKE remained fairly constant from 2003 until 2006, after which it increased until 2008. The results for 2009 indicate a decline. Sites with PIKE ranging from the lowest to the highest were identified. The results of the analysis provide a sound information base for scientific evidence-based decision making in the CITES process.
Burn, Robert W; Underwood, Fiona M; Blanc, Julian
2011-01-01
Elephant poaching and the ivory trade remain high on the agenda at meetings of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES). Well-informed debates require robust estimates of trends, the spatial distribution of poaching, and drivers of poaching. We present an analysis of trends and drivers of an indicator of elephant poaching of all elephant species. The site-based monitoring system known as Monitoring the Illegal Killing of Elephants (MIKE), set up by the 10(th) Conference of the Parties of CITES in 1997, produces carcass encounter data reported mainly by anti-poaching patrols. Data analyzed were site by year totals of 6,337 carcasses from 66 sites in Africa and Asia from 2002-2009. Analysis of these observational data is a serious challenge to traditional statistical methods because of the opportunistic and non-random nature of patrols, and the heterogeneity across sites. Adopting a bayesian hierarchical modeling approach, we used the proportion of carcasses that were illegally killed (PIKE) as a poaching index, to estimate the trend and the effects of site- and country-level factors associated with poaching. Important drivers of illegal killing that emerged at country level were poor governance and low levels of human development, and at site level, forest cover and area of the site in regions where human population density is low. After a drop from 2002, PIKE remained fairly constant from 2003 until 2006, after which it increased until 2008. The results for 2009 indicate a decline. Sites with PIKE ranging from the lowest to the highest were identified. The results of the analysis provide a sound information base for scientific evidence-based decision making in the CITES process.
Model uncertainty and Bayesian model averaging in vector autoregressive processes
R.W. Strachan (Rodney); H.K. van Dijk (Herman)
2006-01-01
textabstractEconomic forecasts and policy decisions are often informed by empirical analysis based on econometric models. However, inference based upon a single model, when several viable models exist, limits its usefulness. Taking account of model uncertainty, a Bayesian model averaging procedure i
Nonparametric Bayesian inference of the microcanonical stochastic block model
Peixoto, Tiago P.
2017-01-01
A principled approach to characterize the hidden modular structure of networks is to formulate generative models and then infer their parameters from data. When the desired structure is composed of modules or "communities," a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints, i.e., the generated networks are not allowed to violate the patterns imposed by the model. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: (1) deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, which not only remove limitations that seriously degrade the inference on large networks but also reveal structures at multiple scales; (2) a very efficient inference algorithm that scales well not only for networks with a large number of nodes and edges but also with an unlimited number of modules. We show also how this approach can be used to sample modular hierarchies from the posterior distribution, as well as to perform model selection. We discuss and analyze the differences between sampling from the posterior and simply finding the single parameter estimate that maximizes it. Furthermore, we expose a direct equivalence between our microcanonical approach and alternative derivations based on the canonical SBM.
Bayesian Spatial Modelling with R-INLA
Directory of Open Access Journals (Sweden)
Finn Lindgren
2015-02-01
Full Text Available The principles behind the interface to continuous domain spatial models in the R- INLA software package for R are described. The integrated nested Laplace approximation (INLA approach proposed by Rue, Martino, and Chopin (2009 is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging from (generalized linear mixed to spatial and spatio-temporal models. Combined with the stochastic partial differential equation approach (SPDE, Lindgren, Rue, and Lindstrm 2011, one can accommodate all kinds of geographically referenced data, including areal and geostatistical ones, as well as spatial point process data. The implementation interface covers stationary spatial mod- els, non-stationary spatial models, and also spatio-temporal models, and is applicable in epidemiology, ecology, environmental risk assessment, as well as general geostatistics.
Bayesian Discovery of Linear Acyclic Causal Models
Hoyer, Patrik O
2012-01-01
Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accur...
Ogle, Kiona; Ryan, Edmund; Dijkstra, Feike A.; Pendall, Elise
2016-12-01
Nonsteady state chambers are often employed to measure soil CO2 fluxes. CO2 concentrations (C) in the headspace are sampled at different times (t), and fluxes (f) are calculated from regressions of C versus t based on a limited number of observations. Variability in the data can lead to poor fits and unreliable f estimates; groups with too few observations or poor fits are often discarded, resulting in "missing" f values. We solve these problems by fitting linear (steady state) and nonlinear (nonsteady state, diffusion based) models of C versus t, within a hierarchical Bayesian framework. Data are from the Prairie Heating and CO2 Enrichment study that manipulated atmospheric CO2, temperature, soil moisture, and vegetation. CO2 was collected from static chambers biweekly during five growing seasons, resulting in >12,000 samples and >3100 groups and associated fluxes. We compare f estimates based on nonhierarchical and hierarchical Bayesian (B versus HB) versions of the linear and diffusion-based (L versus D) models, resulting in four different models (BL, BD, HBL, and HBD). Three models fit the data exceptionally well (R2 ≥ 0.98), but the BD model was inferior (R2 = 0.87). The nonhierarchical models (BL and BD) produced highly uncertain f estimates (wide 95% credible intervals), whereas the hierarchical models (HBL and HBD) produced very precise estimates. Of the hierarchical versions, the linear model (HBL) underestimated f by 33% relative to the nonsteady state model (HBD). The hierarchical models offer improvements upon traditional nonhierarchical approaches to estimating f, and we provide example code for the models.
Royle, J. Andrew; Dorazio, Robert M.
2008-01-01
A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics.
A Bayesian Model for Discovering Typological Implications
Daumé, Hal
2009-01-01
A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such implications are typically discovered by painstaking hand analysis over a small sample of languages. We propose a computational model for assisting at this process. Our model is able to discover both well-known implications as well as some novel implications that deserve further study. Moreover, through a careful application of hierarchical analysis, we are able to cope with the well-known sampling problem: languages are not independent.
Wang, Li; Gac, Nicolas; Mohammad-Djafari, Ali
2015-01-01
In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is estimated thanks to the prior model of the volume but also the hyper parameters of this prior. This additional complexity in the reconstruction methods when applied to large volumes (from 5123 to 81923 voxels) results in an increasing computational cost. To reduce it, the hierarchical Bayesian methods investigated in this paper lead to an algorithm acceleration by Variational Bayesian Approximation (VBA) [1] and hardware acceleration thanks to projection and back-projection operators paralleled on many core processors like GPU [2]. In this paper, we will consider a Student-t prior on the gradient of the image implemented in a hierarchical way [3, 4, 1]. Operators H (forward or projection) and Ht (adjoint or back-projection) implanted in multi-GPU [2] have been used in this study. Different methods will be evalued on synthetic volume "Shepp and Logan" in terms of quality and time of reconstruction. We used several simple regularizations of order 1 and order 2. Other prior models also exists [5]. Sometimes for a discrete image, we can do the segmentation and reconstruction at the same time, then the reconstruction can be done with less projections.
Hopes and Cautions in Implementing Bayesian Structural Equation Modeling
MacCallum, Robert C.; Edwards, Michael C.; Cai, Li
2012-01-01
Muthen and Asparouhov (2012) have proposed and demonstrated an approach to model specification and estimation in structural equation modeling (SEM) using Bayesian methods. Their contribution builds on previous work in this area by (a) focusing on the translation of conventional SEM models into a Bayesian framework wherein parameters fixed at zero…
Jones, Matt; Love, Bradley C
2011-08-01
The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology - namely, Behaviorism and evolutionary psychology - that set aside mechanistic explanations or make use of optimality assumptions. Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls
Three Layer Hierarchical Model for Chord
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Waqas A. Imtiaz
2012-12-01
Full Text Available Increasing popularity of decentralized Peer-to-Peer (P2P architecture emphasizes on the need to come across an overlay structure that can provide efficient content discovery mechanism, accommodate high churn rate and adapt to failures in the presence of heterogeneity among the peers. Traditional p2p systems incorporate distributed client-server communication, which finds the peer efficiently that store a desires data item, with minimum delay and reduced overhead. However traditional models are not able to solve the problems relating scalability and high churn rates. Hierarchical model were introduced to provide better fault isolation, effective bandwidth utilization, a superior adaptation to the underlying physical network and a reduction of the lookup path length as additional advantages. It is more efficient and easier to manage than traditional p2p networks. This paper discusses a further step in p2p hierarchy via 3-layers hierarchical model with distributed database architecture in different layer, each of which is connected through its root. The peers are divided into three categories according to their physical stability and strength. They are Ultra Super-peer, Super-peer and Ordinary Peer and we assign these peers to first, second and third level of hierarchy respectively. Peers in a group in lower layer have their own local database which hold as associated super-peer in middle layer and access the database among the peers through user queries. In our 3-layer hierarchical model for DHT algorithms, we used an advanced Chord algorithm with optimized finger table which can remove the redundant entry in the finger table in upper layer that influences the system to reduce the lookup latency. Our research work finally resulted that our model really provides faster search since the network lookup latency is decreased by reducing the number of hops. The peers in such network then can contribute with improve functionality and can perform well in
Entropic Priors and Bayesian Model Selection
Brewer, Brendon J
2009-01-01
We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured, weakening the usual Bayesian "Occam's Razor". This is illustrated with a simple example involving what Jaynes called a "sure thing" hypothesis. Jaynes' resolution of the situation involved introducing a large number of alternative "sure thing" hypotheses that were possible before we observed the data. However, in more complex situations, it may not be possible to explicitly enumerate large numbers of alternatives. The entropic priors formalism produces the desired result without modifying the hypothesis space or requiring explicit enumeration of alternatives; all that is required is a good model for the prior predictive distribution for the data. This idea is illustrated with a simple rigged-lottery example, and we outline how this idea may help to resolve a recent debate amongst ...
Bayesian Estimation of a Mixture Model
Directory of Open Access Journals (Sweden)
Ilhem Merah
2015-05-01
Full Text Available We present the properties of a bathtub curve reliability model having both a sufficient adaptability and a minimal number of parameters introduced by Idée and Pierrat (2010. This one is a mixture of a Gamma distribution G(2, (1/θ and a new distribution L(θ. We are interesting by Bayesian estimation of the parameters and survival function of this model with a squared-error loss function and non-informative prior using the approximations of Lindley (1980 and Tierney and Kadane (1986. Using a statistical sample of 60 failure data relative to a technical device, we illustrate the results derived. Based on a simulation study, comparisons are made between these two methods and the maximum likelihood method of this two parameters model.
Effect on Prediction when Modeling Covariates in Bayesian Nonparametric Models.
Cruz-Marcelo, Alejandro; Rosner, Gary L; Müller, Peter; Stewart, Clinton F
2013-04-01
In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparametric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. Limited attention, however, has been directed to the following two aspects. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.
MERGING DIGITAL SURFACE MODELS IMPLEMENTING BAYESIAN APPROACHES
Directory of Open Access Journals (Sweden)
H. Sadeq
2016-06-01
Full Text Available In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades. It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
Merging Digital Surface Models Implementing Bayesian Approaches
Sadeq, H.; Drummond, J.; Li, Z.
2016-06-01
In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades). It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
Universality: Accurate Checks in Dyson's Hierarchical Model
Godina, J. J.; Meurice, Y.; Oktay, M. B.
2003-06-01
In this talk we present high-accuracy calculations of the susceptibility near βc for Dyson's hierarchical model in D = 3. Using linear fitting, we estimate the leading (γ) and subleading (Δ) exponents. Independent estimates are obtained by calculating the first two eigenvalues of the linearized renormalization group transformation. We found γ = 1.29914073 ± 10 -8 and, Δ = 0.4259469 ± 10-7 independently of the choice of local integration measure (Ising or Landau-Ginzburg). After a suitable rescaling, the approximate fixed points for a large class of local measure coincide accurately with a fixed point constructed by Koch and Wittwer.
Cressie, Noel; Calder, Catherine A; Clark, James S; Ver Hoef, Jay M; Wikle, Christopher K
2009-04-01
Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.
Improving randomness characterization through Bayesian model selection
R., Rafael Díaz-H; Martínez, Alí M Angulo; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Castillo, Isaac Pérez
2016-01-01
Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We...
Modeling Social Annotation: a Bayesian Approach
Plangprasopchok, Anon
2008-01-01
Collaborative tagging systems, such as del.icio.us, CiteULike, and others, allow users to annotate objects, e.g., Web pages or scientific papers, with descriptive labels called tags. The social annotations, contributed by thousands of users, can potentially be used to infer categorical knowledge, classify documents or recommend new relevant information. Traditional text inference methods do not make best use of socially-generated data, since they do not take into account variations in individual users' perspectives and vocabulary. In a previous work, we introduced a simple probabilistic model that takes interests of individual annotators into account in order to find hidden topics of annotated objects. Unfortunately, our proposed approach had a number of shortcomings, including overfitting, local maxima and the requirement to specify values for some parameters. In this paper we address these shortcomings in two ways. First, we extend the model to a fully Bayesian framework. Second, we describe an infinite ver...
3-Layered Bayesian Model Using in Text Classification
Directory of Open Access Journals (Sweden)
Chang Jiayu
2013-01-01
Full Text Available Naive Bayesian is one of quite effective classification methods in all of the text disaggregated models. Usually, the computed result will be large deviation from normal, with the reason of attribute relevance and so on. This study embarked from the degree of correlation, defined the node’s degree as well as the relations between nodes, proposed a 3-layered Bayesian Model. According to the conditional probability recurrence formula, the theory support of the 3-layered Bayesian Model is obtained. According to the theory analysis and the empirical datum contrast to the Naive Bayesian, the model has better attribute collection and classify. It can be also promoted to the Multi-layer Bayesian Model using in text classification.
Loss Function Based Ranking in Two-Stage, Hierarchical Models
Lin, Rongheng; Louis, Thomas A.; Paddock, Susan M.; Ridgeway, Greg
2009-01-01
Performance evaluations of health services providers burgeons. Similarly, analyzing spatially related health information, ranking teachers and schools, and identification of differentially expressed genes are increasing in prevalence and importance. Goals include valid and efficient ranking of units for profiling and league tables, identification of excellent and poor performers, the most differentially expressed genes, and determining “exceedances” (how many and which unit-specific true parameters exceed a threshold). These data and inferential goals require a hierarchical, Bayesian model that accounts for nesting relations and identifies both population values and random effects for unit-specific parameters. Furthermore, the Bayesian approach coupled with optimizing a loss function provides a framework for computing non-standard inferences such as ranks and histograms. Estimated ranks that minimize Squared Error Loss (SEL) between the true and estimated ranks have been investigated. The posterior mean ranks minimize SEL and are “general purpose,” relevant to a broad spectrum of ranking goals. However, other loss functions and optimizing ranks that are tuned to application-specific goals require identification and evaluation. For example, when the goal is to identify the relatively good (e.g., in the upper 10%) or relatively poor performers, a loss function that penalizes classification errors produces estimates that minimize the error rate. We construct loss functions that address this and other goals, developing a unified framework that facilitates generating candidate estimates, comparing approaches and producing data analytic performance summaries. We compare performance for a fully parametric, hierarchical model with Gaussian sampling distribution under Gaussian and a mixture of Gaussians prior distributions. We illustrate approaches via analysis of standardized mortality ratio data from the United States Renal Data System. Results show that SEL
A hierarchical model for ordinal matrix factorization
DEFF Research Database (Denmark)
Paquet, Ulrich; Thomson, Blaise; Winther, Ole
2012-01-01
This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based...... on Gibbs sampling and one based on variational Bayes. Importantly, these algorithms may be implemented in the factorization of very large matrices with missing entries. The model is evaluated on a collaborative filtering task, where users have rated a collection of movies and the system is asked to predict...... their ratings for other movies. The Netflix data set is used for evaluation, which consists of around 100 million ratings. Using root mean-squared error (RMSE) as an evaluation metric, results show that the suggested model outperforms alternative factorization techniques. Results also show how Gibbs sampling...
Modelling crime linkage with Bayesian networks.
de Zoete, Jacob; Sjerps, Marjan; Lagnado, David; Fenton, Norman
2015-05-01
When two or more crimes show specific similarities, such as a very distinct modus operandi, the probability that they were committed by the same offender becomes of interest. This probability depends on the degree of similarity and distinctiveness. We show how Bayesian networks can be used to model different evidential structures that can occur when linking crimes, and how they assist in understanding the complex underlying dependencies. That is, how evidence that is obtained in one case can be used in another and vice versa. The flip side of this is that the intuitive decision to "unlink" a case in which exculpatory evidence is obtained leads to serious overestimation of the strength of the remaining cases.
Gene function classification using Bayesian models with hierarchy-based priors
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Neal Radford M
2006-10-01
Full Text Available Abstract Background We investigate whether annotation of gene function can be improved using a classification scheme that is aware that functional classes are organized in a hierarchy. The classifiers look at phylogenic descriptors, sequence based attributes, and predicted secondary structure. We discuss three Bayesian models and compare their performance in terms of predictive accuracy. These models are the ordinary multinomial logit (MNL model, a hierarchical model based on a set of nested MNL models, and an MNL model with a prior that introduces correlations between the parameters for classes that are nearby in the hierarchy. We also provide a new scheme for combining different sources of information. We use these models to predict the functional class of Open Reading Frames (ORFs from the E. coli genome. Results The results from all three models show substantial improvement over previous methods, which were based on the C5 decision tree algorithm. The MNL model using a prior based on the hierarchy outperforms both the non-hierarchical MNL model and the nested MNL model. In contrast to previous attempts at combining the three sources of information in this dataset, our new approach to combining data sources produces a higher accuracy rate than applying our models to each data source alone. Conclusion Together, these results show that gene function can be predicted with higher accuracy than previously achieved, using Bayesian models that incorporate suitable prior information.
Bayesian Student Modeling and the Problem of Parameter Specification.
Millan, Eva; Agosta, John Mark; Perez de la Cruz, Jose Luis
2001-01-01
Discusses intelligent tutoring systems and the application of Bayesian networks to student modeling. Considers reasons for not using Bayesian networks, including the computational complexity of the algorithms and the difficulty of knowledge acquisition, and proposes an approach to simplify knowledge acquisition that applies causal independence to…
Implementing Relevance Feedback in the Bayesian Network Retrieval Model.
de Campos, Luis M.; Fernandez-Luna, Juan M.; Huete, Juan F.
2003-01-01
Discussion of relevance feedback in information retrieval focuses on a proposal for the Bayesian Network Retrieval Model. Bases the proposal on the propagation of partial evidences in the Bayesian network, representing new information obtained from the user's relevance judgments to compute the posterior relevance probabilities of the documents…
A new approach for Bayesian model averaging
Institute of Scientific and Technical Information of China (English)
TIAN XiangJun; XIE ZhengHui; WANG AiHui; YANG XiaoChun
2012-01-01
Bayesian model averaging (BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization (EM) and the Markov Chain Monte Carlo (MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the additional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA (referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algorithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is almost equivalent to that for EM.
A hierarchical model of temporal perception.
Pöppel, E
1997-05-01
Temporal perception comprises subjective phenomena such as simultaneity, successiveness, temporal order, subjective present, temporal continuity and subjective duration. These elementary temporal experiences are hierarchically related to each other. Functional system states with a duration of 30 ms are implemented by neuronal oscillations and they provide a mechanism to define successiveness. These system states are also responsible for the identification of basic events. For a sequential representation of several events time tags are allocated, resulting in an ordinal representation of such events. A mechanism of temporal integration binds successive events into perceptual units of 3 s duration. Such temporal integration, which is automatic and presemantic, is also operative in movement control and other cognitive activities. Because of the omnipresence of this integration mechanism it is used for a pragmatic definition of the subjective present. Temporal continuity is the result of a semantic connection between successive integration intervals. Subjective duration is known to depend on mental load and attentional demand, high load resulting in long time estimates. In the hierarchical model proposed, system states of 30 ms and integration intervals of 3 s, together with a memory store, provide an explanatory neuro-cognitive machinery for differential subjective duration.
Advances in Bayesian Modeling in Educational Research
Levy, Roy
2016-01-01
In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…
Royle, J. Andrew; Converse, Sarah J.
2014-01-01
Capture–recapture studies are often conducted on populations that are stratified by space, time or other factors. In this paper, we develop a Bayesian spatial capture–recapture (SCR) modelling framework for stratified populations – when sampling occurs within multiple distinct spatial and temporal strata.We describe a hierarchical model that integrates distinct models for both the spatial encounter history data from capture–recapture sampling, and also for modelling variation in density among strata. We use an implementation of data augmentation to parameterize the model in terms of a latent categorical stratum or group membership variable, which provides a convenient implementation in popular BUGS software packages.We provide an example application to an experimental study involving small-mammal sampling on multiple trapping grids over multiple years, where the main interest is in modelling a treatment effect on population density among the trapping grids.Many capture–recapture studies involve some aspect of spatial or temporal replication that requires some attention to modelling variation among groups or strata. We propose a hierarchical model that allows explicit modelling of group or strata effects. Because the model is formulated for individual encounter histories and is easily implemented in the BUGS language and other free software, it also provides a general framework for modelling individual effects, such as are present in SCR models.
Bayesian Model Selection for LISA Pathfinder
Karnesis, Nikolaos; Sopuerta, Carlos F; Gibert, Ferran; Armano, Michele; Audley, Heather; Congedo, Giuseppe; Diepholz, Ingo; Ferraioli, Luigi; Hewitson, Martin; Hueller, Mauro; Korsakova, Natalia; Plagnol, Eric; Vitale, and Stefano
2013-01-01
The main goal of the LISA Pathfinder (LPF) mission is to fully characterize the acceleration noise models and to test key technologies for future space-based gravitational-wave observatories similar to the LISA/eLISA concept. The Data Analysis (DA) team has developed complex three-dimensional models of the LISA Technology Package (LTP) experiment on-board LPF. These models are used for simulations, but more importantly, they will be used for parameter estimation purposes during flight operations. One of the tasks of the DA team is to identify the physical effects that contribute significantly to the properties of the instrument noise. A way of approaching to this problem is to recover the essential parameters of the LTP which describe the data. Thus, we want to define the simplest model that efficiently explains the observations. To do so, adopting a Bayesian framework, one has to estimate the so-called Bayes Factor between two competing models. In our analysis, we use three main different methods to estimate...
Hierarchical Data Structures, Institutional Research, and Multilevel Modeling
O'Connell, Ann A.; Reed, Sandra J.
2012-01-01
Multilevel modeling (MLM), also referred to as hierarchical linear modeling (HLM) or mixed models, provides a powerful analytical framework through which to study colleges and universities and their impact on students. Due to the natural hierarchical structure of data obtained from students or faculty in colleges and universities, MLM offers many…
Morton, Kenneth D., Jr.; Torrione, Peter A.; Collins, Leslie
2010-04-01
Time domain ground penetrating radar (GPR) has been shown to be a powerful sensing phenomenology for detecting buried objects such as landmines. Landmine detection with GPR data typically utilizes a feature-based pattern classification algorithm to discriminate buried landmines from other sub-surface objects. In high-fidelity GPR, the time-frequency characteristics of a landmine response should be indicative of the physical construction and material composition of the landmine and could therefore be useful for discrimination from other non-threatening sub-surface objects. In this research we propose modeling landmine time-domain responses with a nonparametric Bayesian time-series model and we perform clustering of these time-series models with a hierarchical nonparametric Bayesian model. Each time-series is modeled as a hidden Markov model (HMM) with autoregressive (AR) state densities. The proposed nonparametric Bayesian prior allows for automated learning of the number of states in the HMM as well as the AR order within each state density. This creates a flexible time-series model with complexity determined by the data. Furthermore, a hierarchical non-parametric Bayesian prior is used to group landmine responses with similar HMM model parameters, thus learning the number of distinct landmine response models within a data set. Model inference is accomplished using a fast variational mean field approximation that can be implemented for on-line learning.
A guide to Bayesian model selection for ecologists
Hooten, Mevin B.; Hobbs, N.T.
2015-01-01
The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.
Entrepreneurial intention modeling using hierarchical multiple regression
Directory of Open Access Journals (Sweden)
Marina Jeger
2014-12-01
Full Text Available The goal of this study is to identify the contribution of effectuation dimensions to the predictive power of the entrepreneurial intention model over and above that which can be accounted for by other predictors selected and confirmed in previous studies. As is often the case in social and behavioral studies, some variables are likely to be highly correlated with each other. Therefore, the relative amount of variance in the criterion variable explained by each of the predictors depends on several factors such as the order of variable entry and sample specifics. The results show the modest predictive power of two dimensions of effectuation prior to the introduction of the theory of planned behavior elements. The article highlights the main advantages of applying hierarchical regression in social sciences as well as in the specific context of entrepreneurial intention formation, and addresses some of the potential pitfalls that this type of analysis entails.
From least squares to multilevel modeling: A graphical introduction to Bayesian inference
Loredo, Thomas J.
2016-01-01
This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.
Directory of Open Access Journals (Sweden)
Julie Vercelloni
Full Text Available Recently, attempts to improve decision making in species management have focussed on uncertainties associated with modelling temporal fluctuations in populations. Reducing model uncertainty is challenging; while larger samples improve estimation of species trajectories and reduce statistical errors, they typically amplify variability in observed trajectories. In particular, traditional modelling approaches aimed at estimating population trajectories usually do not account well for nonlinearities and uncertainties associated with multi-scale observations characteristic of large spatio-temporal surveys. We present a Bayesian semi-parametric hierarchical model for simultaneously quantifying uncertainties associated with model structure and parameters, and scale-specific variability over time. We estimate uncertainty across a four-tiered spatial hierarchy of coral cover from the Great Barrier Reef. Coral variability is well described; however, our results show that, in the absence of additional model specifications, conclusions regarding coral trajectories become highly uncertain when considering multiple reefs, suggesting that management should focus more at the scale of individual reefs. The approach presented facilitates the description and estimation of population trajectories and associated uncertainties when variability cannot be attributed to specific causes and origins. We argue that our model can unlock value contained in large-scale datasets, provide guidance for understanding sources of uncertainty, and support better informed decision making.
Nonparametric Bayesian Modeling for Automated Database Schema Matching
Energy Technology Data Exchange (ETDEWEB)
Ferragut, Erik M [ORNL; Laska, Jason A [ORNL
2015-01-01
The problem of merging databases arises in many government and commercial applications. Schema matching, a common first step, identifies equivalent fields between databases. We introduce a schema matching framework that builds nonparametric Bayesian models for each field and compares them by computing the probability that a single model could have generated both fields. Our experiments show that our method is more accurate and faster than the existing instance-based matching algorithms in part because of the use of nonparametric Bayesian models.
A Bayesian model of category-specific emotional brain responses.
Directory of Open Access Journals (Sweden)
Tor D Wager
2015-04-01
Full Text Available Understanding emotion is critical for a science of healthy and disordered brain function, but the neurophysiological basis of emotional experience is still poorly understood. We analyzed human brain activity patterns from 148 studies of emotion categories (2159 total participants using a novel hierarchical Bayesian model. The model allowed us to classify which of five categories--fear, anger, disgust, sadness, or happiness--is engaged by a study with 66% accuracy (43-86% across categories. Analyses of the activity patterns encoded in the model revealed that each emotion category is associated with unique, prototypical patterns of activity across multiple brain systems including the cortex, thalamus, amygdala, and other structures. The results indicate that emotion categories are not contained within any one region or system, but are represented as configurations across multiple brain networks. The model provides a precise summary of the prototypical patterns for each emotion category, and demonstrates that a sufficient characterization of emotion categories relies on (a differential patterns of involvement in neocortical systems that differ between humans and other species, and (b distinctive patterns of cortical-subcortical interactions. Thus, these findings are incompatible with several contemporary theories of emotion, including those that emphasize emotion-dedicated brain systems and those that propose emotion is localized primarily in subcortical activity. They are consistent with componential and constructionist views, which propose that emotions are differentiated by a combination of perceptual, mnemonic, prospective, and motivational elements. Such brain-based models of emotion provide a foundation for new translational and clinical approaches.
Hao, Haijing
2013-01-01
Information technology adoption and diffusion is currently a significant challenge in the healthcare delivery setting. This thesis includes three papers that explore social influence on information technology adoption and sustained use in the healthcare delivery environment using conventional regression models and novel hierarchical Bayesian…
A Gaussian Mixed Model for Learning Discrete Bayesian Networks.
Balov, Nikolay
2011-02-01
In this paper we address the problem of learning discrete Bayesian networks from noisy data. Considered is a graphical model based on mixture of Gaussian distributions with categorical mixing structure coming from a discrete Bayesian network. The network learning is formulated as a Maximum Likelihood estimation problem and performed by employing an EM algorithm. The proposed approach is relevant to a variety of statistical problems for which Bayesian network models are suitable - from simple regression analysis to learning gene/protein regulatory networks from microarray data.
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2016-06-07
terms of the standard deviations (computed over 10 ensemble members) of sea surface height ( SSH ; top panel) and sea surface temperature (SST; bottom...mean SSH forecast (top panel) and SSH standard deviation of the ensemble forecast (bottom panel) on day 10 of the forecast. The concentration of...spread for SSH (top panel; cm) and SST (bottom panel; ° C). The standard deviation of the SSH and SST are computed at day 14 of the data assimilation
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2012-02-17
Climate, 21, 1891-1910. Berliner, L.M. and C.K. Wikle, 2007: Approximate importance sampling Monte Carlo for data assimilation, Physica D, 230, 37-49...representations for spatial processes, In: Handbook of Spatial Statis- tics, A.Gelfand, P. Diggle, M. Fuentes , P. Guttorp (eds), Chapman and Hall. 107-118. Wikle
Bayesian Hierarchical Modeling of Cardiac Response to Particulate Matter Exposure
Studies have linked increased levels of particulate air pollution to decreased autonomic control, as measured by heart rate variability (HRV), particularly in populations such as the elderly. In this study, we use data obtained from the 1998 USEPA epidemiology-exposure longitudin...
Bayesian approach to decompression sickness model parameter estimation.
Howle, L E; Weber, P W; Nichols, J M
2017-03-01
We examine both maximum likelihood and Bayesian approaches for estimating probabilistic decompression sickness model parameters. Maximum likelihood estimation treats parameters as fixed values and determines the best estimate through repeated trials, whereas the Bayesian approach treats parameters as random variables and determines the parameter probability distributions. We would ultimately like to know the probability that a parameter lies in a certain range rather than simply make statements about the repeatability of our estimator. Although both represent powerful methods of inference, for models with complex or multi-peaked likelihoods, maximum likelihood parameter estimates can prove more difficult to interpret than the estimates of the parameter distributions provided by the Bayesian approach. For models of decompression sickness, we show that while these two estimation methods are complementary, the credible intervals generated by the Bayesian approach are more naturally suited to quantifying uncertainty in the model parameters.
Higher-Order Item Response Models for Hierarchical Latent Traits
Huang, Hung-Yu; Wang, Wen-Chung; Chen, Po-Hsi; Su, Chi-Ming
2013-01-01
Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify…
On the renormalization group transformation for scalar hierarchical models
Energy Technology Data Exchange (ETDEWEB)
Koch, H. (Texas Univ., Austin (USA). Dept. of Mathematics); Wittwer, P. (Geneva Univ. (Switzerland). Dept. de Physique Theorique)
1991-06-01
We give a new proof for the existence of a non-Gaussian hierarchical renormalization group fixed point, using what could be called a beta-function for this problem. We also discuss the asymptotic behavior of this fixed point, and the connection between the hierarchical models of Dyson and Gallavotti. (orig.).
CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors
Directory of Open Access Journals (Sweden)
Duncan Lee
2013-11-01
Full Text Available Conditional autoregressive models are commonly used to represent spatial autocorrelation in data relating to a set of non-overlapping areal units, which arise in a wide variety of applications including agriculture, education, epidemiology and image analysis. Such models are typically specified in a hierarchical Bayesian framework, with inference based on Markov chain Monte Carlo (MCMC simulation. The most widely used software to fit such models is WinBUGS or OpenBUGS, but in this paper we introduce the R package CARBayes. The main advantage of CARBayes compared with the BUGS software is its ease of use, because: (1 the spatial adjacency information is easy to specify as a binary neighbourhood matrix; and (2 given the neighbourhood matrix the models can be implemented by a single function call in R. This paper outlines the general class of Bayesian hierarchical models that can be implemented in the CARBayes software, describes their implementation via MCMC simulation techniques, and illustrates their use with two worked examples in the fields of house price analysis and disease mapping.
Hierarchical Geometric Constraint Model for Parametric Feature Based Modeling
Institute of Scientific and Technical Information of China (English)
高曙明; 彭群生
1997-01-01
A new geometric constraint model is described,which is hierarchical and suitable for parametric feature based modeling.In this model,different levels of geometric information are repesented to support various stages of a design process.An efficient approach to parametric feature based modeling is also presented,adopting the high level geometric constraint model.The low level geometric model such as B-reps can be derived automatically from the hig level geometric constraint model,enabling designers to perform their task of detailed design.
Bayesian model discrimination for glucose-insulin homeostasis
DEFF Research Database (Denmark)
Andersen, Kim Emil; Brooks, Stephen P.; Højbjerre, Malene
the reformulation of existing deterministic models as stochastic state space models which properly accounts for both measurement and process variability. The analysis is further enhanced by Bayesian model discrimination techniques and model averaged parameter estimation which fully accounts for model as well...
Modelling of JET diagnostics using Bayesian Graphical Models
Energy Technology Data Exchange (ETDEWEB)
Svensson, J. [IPP Greifswald, Greifswald (Germany); Ford, O. [Imperial College, London (United Kingdom); McDonald, D.; Hole, M.; Nessi, G. von; Meakins, A.; Brix, M.; Thomsen, H.; Werner, A.; Sirinelli, A.
2011-07-01
The mapping between physics parameters (such as densities, currents, flows, temperatures etc) defining the plasma 'state' under a given model and the raw observations of each plasma diagnostic will 1) depend on the particular physics model used, 2) is inherently probabilistic, from uncertainties on both observations and instrumental aspects of the mapping, such as calibrations, instrument functions etc. A flexible and principled way of modelling such interconnected probabilistic systems is through so called Bayesian graphical models. Being an amalgam between graph theory and probability theory, Bayesian graphical models can simulate the complex interconnections between physics models and diagnostic observations from multiple heterogeneous diagnostic systems, making it relatively easy to optimally combine the observations from multiple diagnostics for joint inference on parameters of the underlying physics model, which in itself can be represented as part of the graph. At JET about 10 diagnostic systems have to date been modelled in this way, and has lead to a number of new results, including: the reconstruction of the flux surface topology and q-profiles without any specific equilibrium assumption, using information from a number of different diagnostic systems; profile inversions taking into account the uncertainties in the flux surface positions and a substantial increase in accuracy of JET electron density and temperature profiles, including improved pedestal resolution, through the joint analysis of three diagnostic systems. It is believed that the Bayesian graph approach could potentially be utilised for very large sets of diagnostics, providing a generic data analysis framework for nuclear fusion experiments, that would be able to optimally utilize the information from multiple diagnostics simultaneously, and where the explicit graph representation of the connections to underlying physics models could be used for sophisticated model testing. This
Detecting Hierarchical Structure in Networks
DEFF Research Database (Denmark)
Herlau, Tue; Mørup, Morten; Schmidt, Mikkel Nørgaard;
2012-01-01
a generative Bayesian model that is able to infer whether hierarchies are present or not from a hypothesis space encompassing all types of hierarchical tree structures. For efficient inference we propose a collapsed Gibbs sampling procedure that jointly infers a partition and its hierarchical structure......Many real-world networks exhibit hierarchical organization. Previous models of hierarchies within relational data has focused on binary trees; however, for many networks it is unknown whether there is hierarchical structure, and if there is, a binary tree might not account well for it. We propose....... On synthetic and real data we demonstrate that our model can detect hierarchical structure leading to better link-prediction than competing models. Our model can be used to detect if a network exhibits hierarchical structure, thereby leading to a better comprehension and statistical account the network....
Licquia, Timothy C
2014-01-01
We present improved estimates of several global properties of the Milky Way, including its current star formation rate (SFR), the stellar mass contained in its disk and bulge+bar components, as well as its total stellar mass. We do so by combining previous measurements from the literature using a hierarchical Bayesian (HB) statistical method that allows us to account for the possibility that any value may be incorrect or have underestimated errors. We show that this method is robust to a wide variety of assumptions about the nature of problems in individual measurements or error estimates. Ultimately, our analysis yields a SFR for the Galaxy of $\\dot{\\rm M}_\\star=1.65\\pm0.19$ ${\\rm M}_\\odot$ yr$^{-1}$. By combining HB methods with Monte Carlo simulations that incorporate the latest estimates of the Galactocentric radius of the Sun, $R_0$, the exponential scale-length of the disk, $L_d$, and the local surface density of stellar mass, $\\Sigma_\\star(R_0)$, we show that the mass of the Galactic bulge+bar is ${\\rm...
Technical note: Bayesian calibration of dynamic ruminant nutrition models.
Reed, K F; Arhonditsis, G B; France, J; Kebreab, E
2016-08-01
Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling.
Directory of Open Access Journals (Sweden)
Canty Angelo
2007-09-01
Full Text Available Abstract Background This study compares the Bayesian and frequentist (non-Bayesian approaches in the modelling of the association between the risk of preterm birth and maternal proximity to hazardous waste and pollution from the Sydney Tar Pond site in Nova Scotia, Canada. Methods The data includes 1604 observed cases of preterm birth out of a total population of 17559 at risk of preterm birth from 144 enumeration districts in the Cape Breton Regional Municipality. Other covariates include the distance from the Tar Pond; the rate of unemployment to population; the proportion of persons who are separated, divorced or widowed; the proportion of persons who have no high school diploma; the proportion of persons living alone; the proportion of single parent families and average income. Bayesian hierarchical Poisson regression, quasi-likelihood Poisson regression and weighted linear regression models were fitted to the data. Results The results of the analyses were compared together with their limitations. Conclusion The results of the weighted linear regression and the quasi-likelihood Poisson regression agrees with the result from the Bayesian hierarchical modelling which incorporates the spatial effects.
Hierarchical Neural Regression Models for Customer Churn Prediction
Directory of Open Access Journals (Sweden)
Golshan Mohammadi
2013-01-01
Full Text Available As customers are the main assets of each industry, customer churn prediction is becoming a major task for companies to remain in competition with competitors. In the literature, the better applicability and efficiency of hierarchical data mining techniques has been reported. This paper considers three hierarchical models by combining four different data mining techniques for churn prediction, which are backpropagation artificial neural networks (ANN, self-organizing maps (SOM, alpha-cut fuzzy c-means (α-FCM, and Cox proportional hazards regression model. The hierarchical models are ANN + ANN + Cox, SOM + ANN + Cox, and α-FCM + ANN + Cox. In particular, the first component of the models aims to cluster data in two churner and nonchurner groups and also filter out unrepresentative data or outliers. Then, the clustered data as the outputs are used to assign customers to churner and nonchurner groups by the second technique. Finally, the correctly classified data are used to create Cox proportional hazards model. To evaluate the performance of the hierarchical models, an Iranian mobile dataset is considered. The experimental results show that the hierarchical models outperform the single Cox regression baseline model in terms of prediction accuracy, Types I and II errors, RMSE, and MAD metrics. In addition, the α-FCM + ANN + Cox model significantly performs better than the two other hierarchical models.
Using consensus bayesian network to model the reactive oxygen species regulatory pathway.
Hu, Liangdong; Wang, Limin
2013-01-01
Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.
Analysis of Gumbel Model for Software Reliability Using Bayesian Paradigm
Directory of Open Access Journals (Sweden)
Raj Kumar
2012-12-01
Full Text Available In this paper, we have illustrated the suitability of Gumbel Model for software reliability data. The model parameters are estimated using likelihood based inferential procedure: classical as well as Bayesian. The quasi Newton-Raphson algorithm is applied to obtain the maximum likelihood estimates and associated probability intervals. The Bayesian estimates of the parameters of Gumbel model are obtained using Markov Chain Monte Carlo(MCMC simulation method in OpenBUGS(established software for Bayesian analysis using Markov Chain Monte Carlo methods. The R functions are developed to study the statistical properties, model validation and comparison tools of the model and the output analysis of MCMC samples generated from OpenBUGS. Details of applying MCMC to parameter estimation for the Gumbel model are elaborated and a real software reliability data set is considered to illustrate the methods of inference discussed in this paper.
Energy Technology Data Exchange (ETDEWEB)
Wang, Li; Gac, Nicolas; Mohammad-Djafari, Ali [Laboratoire des Signaux et Systèmes 3, Rue Joliot-Curie 91192 Gif sur Yvette (France)
2015-01-13
In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is estimated thanks to the prior model of the volume but also the hyper parameters of this prior. This additional complexity in the reconstruction methods when applied to large volumes (from 512{sup 3} to 8192{sup 3} voxels) results in an increasing computational cost. To reduce it, the hierarchical Bayesian methods investigated in this paper lead to an algorithm acceleration by Variational Bayesian Approximation (VBA) [1] and hardware acceleration thanks to projection and back-projection operators paralleled on many core processors like GPU [2]. In this paper, we will consider a Student-t prior on the gradient of the image implemented in a hierarchical way [3, 4, 1]. Operators H (forward or projection) and H{sup t} (adjoint or back-projection) implanted in multi-GPU [2] have been used in this study. Different methods will be evalued on synthetic volume 'Shepp and Logan' in terms of quality and time of reconstruction. We used several simple regularizations of order 1 and order 2. Other prior models also exists [5]. Sometimes for a discrete image, we can do the segmentation and reconstruction at the same time, then the reconstruction can be done with less projections.
Estimating Tree Height-Diameter Models with the Bayesian Method
Directory of Open Access Journals (Sweden)
Xiongqing Zhang
2014-01-01
Full Text Available Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS and the maximum likelihood method (ML. The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.
Study of chaos based on a hierarchical model
Energy Technology Data Exchange (ETDEWEB)
Yagi, Masatoshi; Itoh, Sanae-I. [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics
2001-12-01
Study of chaos based on a hierarchical model is briefly reviewed. Here we categorize hierarchical model equations, i.e., (1) a model with a few degrees of freedom, e.g., the Lorenz model, (2) a model with intermediate degrees of freedom like a shell model, and (3) a model with many degrees of freedom such as a Navier-Stokes equation. We discuss the nature of chaos and turbulence described by these models via Lyapunov exponents. The interpretation of results observed in fundamental plasma experiments is also shown based on a shell model. (author)
An Unsupervised Model for Exploring Hierarchical Semantics from Social Annotations
Zhou, Mianwei; Bao, Shenghua; Wu, Xian; Yu, Yong
This paper deals with the problem of exploring hierarchical semantics from social annotations. Recently, social annotation services have become more and more popular in Semantic Web. It allows users to arbitrarily annotate web resources, thus, largely lowers the barrier to cooperation. Furthermore, through providing abundant meta-data resources, social annotation might become a key to the development of Semantic Web. However, on the other hand, social annotation has its own apparent limitations, for instance, 1) ambiguity and synonym phenomena and 2) lack of hierarchical information. In this paper, we propose an unsupervised model to automatically derive hierarchical semantics from social annotations. Using a social bookmark service Del.icio.us as example, we demonstrate that the derived hierarchical semantics has the ability to compensate those shortcomings. We further apply our model on another data set from Flickr to testify our model's applicability on different environments. The experimental results demonstrate our model's efficiency.
Ensemble Bayesian model averaging using Markov Chain Monte Carlo sampling
Vrugt, J.A.; Diks, C.G.H.; Clark, M.
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 t
Bayesian Network Models for Local Dependence among Observable Outcome Variables
Almond, Russell G.; Mulder, Joris; Hemat, Lisa A.; Yan, Duanli
2009-01-01
Bayesian network models offer a large degree of flexibility for modeling dependence among observables (item outcome variables) from the same task, which may be dependent. This article explores four design patterns for modeling locally dependent observations: (a) no context--ignores dependence among observables; (b) compensatory context--introduces…
Modeling the deformation behavior of nanocrystalline alloy with hierarchical microstructures
Energy Technology Data Exchange (ETDEWEB)
Liu, Hongxi; Zhou, Jianqiu, E-mail: zhouj@njtech.edu.cn [Nanjing Tech University, Department of Mechanical Engineering (China); Zhao, Yonghao, E-mail: yhzhao@njust.edu.cn [Nanjing University of Science and Technology, Nanostructural Materials Research Center, School of Materials Science and Engineering (China)
2016-02-15
A mechanism-based plasticity model based on dislocation theory is developed to describe the mechanical behavior of the hierarchical nanocrystalline alloys. The stress–strain relationship is derived by invoking the impeding effect of the intra-granular solute clusters and the inter-granular nanostructures on the dislocation movements along the sliding path. We found that the interaction between dislocations and the hierarchical microstructures contributes to the strain hardening property and greatly influence the ductility of nanocrystalline metals. The analysis indicates that the proposed model can successfully describe the enhanced strength of the nanocrystalline hierarchical alloy. Moreover, the strain hardening rate is sensitive to the volume fraction of the hierarchical microstructures. The present model provides a new perspective to design the microstructures for optimizing the mechanical properties in nanostructural metals.
Bayesian Inference: with ecological applications
Link, William A.; Barker, Richard J.
2010-01-01
This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.
Bayesian Methods for Statistical Analysis
Puza, Borek
2015-01-01
Bayesian methods for statistical analysis is a book on statistical methods for analysing a wide variety of data. The book consists of 12 chapters, starting with basic concepts and covering numerous topics, including Bayesian estimation, decision theory, prediction, hypothesis testing, hierarchical models, Markov chain Monte Carlo methods, finite population inference, biased sampling and nonignorable nonresponse. The book contains many exercises, all with worked solutions, including complete c...
Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.
Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa
2017-01-01
TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.
Bayesian inference of chemical kinetic models from proposed reactions
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.
Moran, Emily V; Clark, James S
2011-03-01
The scale of seed and pollen movement in plants has a critical influence on population dynamics and interspecific interactions, as well as on their capacity to respond to environmental change through migration or local adaptation. However, dispersal can be challenging to quantify. Here, we present a Bayesian model that integrates genetic and ecological data to simultaneously estimate effective seed and pollen dispersal parameters and the parentage of sampled seedlings. This model is the first developed for monoecious plants that accounts for genotyping error and treats dispersal from within and beyond a plot in a fully consistent manner. The flexible Bayesian framework allows the incorporation of a variety of ecological variables, including individual variation in seed production, as well as multiple sources of uncertainty. We illustrate the method using data from a mixed population of red oak (Quercus rubra, Q. velutina, Q. falcata) in the NC piedmont. For simulated test data sets, the model successfully recovered the simulated dispersal parameters and pedigrees. Pollen dispersal in the example population was extensive, with an average father-mother distance of 178 m. Estimated seed dispersal distances at the piedmont site were substantially longer than previous estimates based on seed-trap data (average 128 m vs. 9.3 m), suggesting that, under some circumstances, oaks may be less dispersal-limited than is commonly thought, with a greater potential for range shifts in response to climate change.
A COMPOUND POISSON MODEL FOR LEARNING DISCRETE BAYESIAN NETWORKS
Institute of Scientific and Technical Information of China (English)
Abdelaziz GHRIBI; Afif MASMOUDI
2013-01-01
We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.
Bayesian Subset Modeling for High-Dimensional Generalized Linear Models
Liang, Faming
2013-06-01
This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online. © 2013 American Statistical Association.
Directory of Open Access Journals (Sweden)
Kelemen Arpad
2008-08-01
Full Text Available Abstract Background This paper addresses key biological problems and statistical issues in the analysis of large gene expression data sets that describe systemic temporal response cascades to therapeutic doses in multiple tissues such as liver, skeletal muscle, and kidney from the same animals. Affymetrix time course gene expression data U34A are obtained from three different tissues including kidney, liver and muscle. Our goal is not only to find the concordance of gene in different tissues, identify the common differentially expressed genes over time and also examine the reproducibility of the findings by integrating the results through meta analysis from multiple tissues in order to gain a significant increase in the power of detecting differentially expressed genes over time and to find the differential differences of three tissues responding to the drug. Results and conclusion Bayesian categorical model for estimating the proportion of the 'call' are used for pre-screening genes. Hierarchical Bayesian Mixture Model is further developed for the identifications of differentially expressed genes across time and dynamic clusters. Deviance information criterion is applied to determine the number of components for model comparisons and selections. Bayesian mixture model produces the gene-specific posterior probability of differential/non-differential expression and the 95% credible interval, which is the basis for our further Bayesian meta-inference. Meta-analysis is performed in order to identify commonly expressed genes from multiple tissues that may serve as ideal targets for novel treatment strategies and to integrate the results across separate studies. We have found the common expressed genes in the three tissues. However, the up/down/no regulations of these common genes are different at different time points. Moreover, the most differentially expressed genes were found in the liver, then in kidney, and then in muscle.
Bayesian Estimation of the DINA Model with Gibbs Sampling
Culpepper, Steven Andrew
2015-01-01
A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…
A Bayesian Approach for Analyzing Longitudinal Structural Equation Models
Song, Xin-Yuan; Lu, Zhao-Hua; Hser, Yih-Ing; Lee, Sik-Yum
2011-01-01
This article considers a Bayesian approach for analyzing a longitudinal 2-level nonlinear structural equation model with covariates, and mixed continuous and ordered categorical variables. The first-level model is formulated for measures taken at each time point nested within individuals for investigating their characteristics that are dynamically…
Using Consensus Bayesian Network to Model the Reactive Oxygen Species Regulatory Pathway
Liangdong Hu; Limin Wang
2013-01-01
Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks...
Shih, Ann T.; Ancel, Ersin; Jones, Sharon M.
2012-01-01
The concern for reducing aviation safety risk is rising as the National Airspace System in the United States transforms to the Next Generation Air Transportation System (NextGen). The NASA Aviation Safety Program is committed to developing an effective aviation safety technology portfolio to meet the challenges of this transformation and to mitigate relevant safety risks. The paper focuses on the reasoning of selecting Object-Oriented Bayesian Networks (OOBN) as the technique and commercial software for the accident modeling and portfolio assessment. To illustrate the benefits of OOBN in a large and complex aviation accident model, the in-flight Loss-of-Control Accident Framework (LOCAF) constructed as an influence diagram is presented. An OOBN approach not only simplifies construction and maintenance of complex causal networks for the modelers, but also offers a well-organized hierarchical network that is easier for decision makers to exploit the model examining the effectiveness of risk mitigation strategies through technology insertions.
Hierarchical modeling of bycatch rates of sea turtles in the western North Atlantic
Gardner, B.; Sullivan, P.J.; Epperly, S.; Morreale, S.J.
2008-01-01
Previous studies indicate that the locations of the endangered loggerhead Caretta caretta and critically endangered leatherback Dermochelys coriacea sea turtles are influenced by water temperatures, and that incidental catch rates in the pelagic longline fishery vary by region. We present a Bayesian hierarchical model to examine the effects of environmental variables, including water temperature, on the number of sea turtles captured in the US pelagic longline fishery in the western North Atlantic. The modeling structure is highly flexible, utilizes a Bayesian model selection technique, and is fully implemented in the software program WinBUGS. The number of sea turtles captured is modeled as a zero-inflated Poisson distribution and the model incorporates fixed effects to examine region-specific differences in the parameter estimates. Results indicate that water temperature, region, bottom depth, and target species are all significant predictors of the number of loggerhead sea turtles captured. For leatherback sea turtles, the model with only target species had the most posterior model weight, though a re-parameterization of the model indicates that temperature influences the zero-inflation parameter. The relationship between the number of sea turtles captured and the variables of interest all varied by region. This suggests that management decisions aimed at reducing sea turtle bycatch may be more effective if they are spatially explicit. ?? Inter-Research 2008.
Free-Energy Bounds for Hierarchical Spin Models
Castellana, Michele; Barra, Adriano; Guerra, Francesco
2014-04-01
In this paper we study two non-mean-field (NMF) spin models built on a hierarchical lattice: the hierarchical Edward-Anderson model (HEA) of a spin glass, and Dyson's hierarchical model (DHM) of a ferromagnet. For the HEA, we prove the existence of the thermodynamic limit of the free energy and the replica-symmetry-breaking (RSB) free-energy bounds previously derived for the Sherrington-Kirkpatrick model of a spin glass. These RSB mean-field bounds are exact only if the order-parameter fluctuations (OPF) vanish: given that such fluctuations are not negligible in NMF models, we develop a novel strategy to tackle part of OPF in hierarchical models. The method is based on absorbing part of OPF of a block of spins into an effective Hamiltonian of the underlying spin blocks. We illustrate this method for DHM and show that, compared to the mean-field bound for the free energy, it provides a tighter NMF bound, with a critical temperature closer to the exact one. To extend this method to the HEA model, a suitable generalization of Griffith's correlation inequalities for Ising ferromagnets is needed: since correlation inequalities for spin glasses are still an open topic, we leave the extension of this method to hierarchical spin glasses as a future perspective.
Spatial and spatio-temporal bayesian models with R - INLA
Blangiardo, Marta
2015-01-01
Dedication iiiPreface ix1 Introduction 11.1 Why spatial and spatio-temporal statistics? 11.2 Why do we use Bayesian methods for modelling spatial and spatio-temporal structures? 21.3 Why INLA? 31.4 Datasets 32 Introduction to 212.1 The language 212.2 objects 222.3 Data and session management 342.4 Packages 352.5 Programming in 362.6 Basic statistical analysis with 393 Introduction to Bayesian Methods 533.1 Bayesian Philosophy 533.2 Basic Probability Elements 573.3 Bayes Theorem 623.4 Prior and Posterior Distributions 643.5 Working with the Posterior Distribution 663.6 Choosing the Prior Distr
Uncertainty Modeling Based on Bayesian Network in Ontology Mapping
Institute of Scientific and Technical Information of China (English)
LI Yuhua; LIU Tao; SUN Xiaolin
2006-01-01
How to deal with uncertainty is crucial in exact concept mapping between ontologies. This paper presents a new framework on modeling uncertainty in ontologies based on bayesian networks (BN). In our approach, ontology Web language (OWL) is extended to add probabilistic markups for attaching probability information, the source and target ontologies (expressed by patulous OWL) are translated into bayesian networks (BNs), the mapping between the two ontologies can be digged out by constructing the conditional probability tables (CPTs) of the BN using a improved algorithm named I-IPFP based on iterative proportional fitting procedure (IPFP). The basic idea of this framework and algorithm are validated by positive results from computer experiments.
Bayesian probabilistic modeling for damage assessment in a bolted frame
Haynes, Colin; Todd, Michael
2012-04-01
This paper presents the development of a Bayesian framework for optimizing the design of a structural health monitoring (SHM) system. Statistical damage detection techniques are applied to a geometrically-complex, three-story structure with bolted joints. A sparse network of PZT sensor-actuators is bonded to the structure, using ultrasonic guided waves in both pulse-echo and pitch-catch modes to inspect the structure. Receiver operating characteristics are used to quantify the performance of multiple features (or detectors). The detection rate of the system is compared across different types and levels of damage. A Bayesian cost model is implemented to determine the best performing network.
Space-time Bayesian survival modeling of chronic wasting disease in deer.
Song, Hae-Ryoung; Lawson, Andrew
2009-09-01
The primary objectives of this study are to describe the spatial and temporal variation in disease prevalence of chronic wasting disease (CWD), to assess the effect of demographic factors such as age and sex on disease prevalence and to model the disease clustering effects over space and time. We propose a Bayesian hierarchical survival model where latent parameters capture temporal and spatial trends in disease incidence, incorporating several individual covariates and random effects. The model is applied to a data set which consists of 65085 harvested deer in Wisconsin from 2002 to 2006. We found significant sex effects, spatial effects, temporal effects and spatio-temporal interacted effects in CWD infection in deer in Wisconsin. The risk of infection for male deer was significantly higher than that of female deer, and CWD has been significantly different over space, time, and space and time based on the harvest samples.
Modelling hierarchical and modular complex networks: division and independence
Kim, D.-H.; Rodgers, G. J.; Kahng, B.; Kim, D.
2005-06-01
We introduce a growing network model which generates both modular and hierarchical structure in a self-organized way. To this end, we modify the Barabási-Albert model into the one evolving under the principles of division and independence as well as growth and preferential attachment (PA). A newly added vertex chooses one of the modules composed of existing vertices, and attaches edges to vertices belonging to that module following the PA rule. When the module size reaches a proper size, the module is divided into two, and a new module is created. The karate club network studied by Zachary is a simple version of the current model. We find that the model can reproduce both modular and hierarchical properties, characterized by the hierarchical clustering function of a vertex with degree k, C(k), being in good agreement with empirical measurements for real-world networks.
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...
Advanced REACH tool: A Bayesian model for occupational exposure assessment
McNally, K.; Warren, N.; Fransman, W.; Entink, R.K.; Schinkel, J.; Van Tongeren, M.; Cherrie, J.W.; Kromhout, H.; Schneider, T.; Tielemans, E.
2014-01-01
This paper describes a Bayesian model for the assessment of inhalation exposures in an occupational setting; the methodology underpins a freely available web-based application for exposure assessment, the Advanced REACH Tool (ART). The ART is a higher tier exposure tool that combines disparate sourc
A Bayesian network approach to coastal storm impact modeling
Jäger, W.S.; Den Heijer, C.; Bolle, A.; Hanea, A.M.
2015-01-01
In this paper we develop a Bayesian network (BN) that relates offshore storm conditions to their accompagnying flood characteristics and damages to residential buildings, following on the trend of integrated flood impact modeling. It is based on data from hydrodynamic storm simulations, information
Bayesian online algorithms for learning in discrete Hidden Markov Models
Alamino, Roberto C.; Caticha, Nestor
2008-01-01
We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.
Research on Bayesian Network Based User's Interest Model
Institute of Scientific and Technical Information of China (English)
ZHANG Weifeng; XU Baowen; CUI Zifeng; XU Lei
2007-01-01
It has very realistic significance for improving the quality of users' accessing information to filter and selectively retrieve the large number of information on the Internet. On the basis of analyzing the existing users' interest models and some basic questions of users' interest (representation, derivation and identification of users' interest), a Bayesian network based users' interest model is given. In this model, the users' interest reduction algorithm based on Markov Blanket model is used to reduce the interest noise, and then users' interested and not interested documents are used to train the Bayesian network. Compared to the simple model, this model has the following advantages like small space requirements, simple reasoning method and high recognition rate. The experiment result shows this model can more appropriately reflect the user's interest, and has higher performance and good usability.
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
Empirical evaluation of scoring functions for Bayesian network model selection.
Liu, Zhifa; Malone, Brandon; Yuan, Changhe
2012-01-01
In this work, we empirically evaluate the capability of various scoring functions of Bayesian networks for recovering true underlying structures. Similar investigations have been carried out before, but they typically relied on approximate learning algorithms to learn the network structures. The suboptimal structures found by the approximation methods have unknown quality and may affect the reliability of their conclusions. Our study uses an optimal algorithm to learn Bayesian network structures from datasets generated from a set of gold standard Bayesian networks. Because all optimal algorithms always learn equivalent networks, this ensures that only the choice of scoring function affects the learned networks. Another shortcoming of the previous studies stems from their use of random synthetic networks as test cases. There is no guarantee that these networks reflect real-world data. We use real-world data to generate our gold-standard structures, so our experimental design more closely approximates real-world situations. A major finding of our study suggests that, in contrast to results reported by several prior works, the Minimum Description Length (MDL) (or equivalently, Bayesian information criterion (BIC)) consistently outperforms other scoring functions such as Akaike's information criterion (AIC), Bayesian Dirichlet equivalence score (BDeu), and factorized normalized maximum likelihood (fNML) in recovering the underlying Bayesian network structures. We believe this finding is a result of using both datasets generated from real-world applications rather than from random processes used in previous studies and learning algorithms to select high-scoring structures rather than selecting random models. Other findings of our study support existing work, e.g., large sample sizes result in learning structures closer to the true underlying structure; the BDeu score is sensitive to the parameter settings; and the fNML performs pretty well on small datasets. We also
FACIAL LANDMARKING LOCALIZATION FOR EMOTION RECOGNITION USING BAYESIAN SHAPE MODELS
Directory of Open Access Journals (Sweden)
Hernan F. Garcia
2013-02-01
Full Text Available This work presents a framework for emotion recognition, based in facial expression analysis using Bayesian Shape Models (BSM for facial landmarking localization. The Facial Action Coding System (FACS compliant facial feature tracking based on Bayesian Shape Model. The BSM estimate the parameters of the model with an implementation of the EM algorithm. We describe the characterization methodology from parametric model and evaluated the accuracy for feature detection and estimation of the parameters associated with facial expressions, analyzing its robustness in pose and local variations. Then, a methodology for emotion characterization is introduced to perform the recognition. The experimental results show that the proposed model can effectively detect the different facial expressions. Outperforming conventional approaches for emotion recognition obtaining high performance results in the estimation of emotion present in a determined subject. The model used and characterization methodology showed efficient to detect the emotion type in 95.6% of the cases.
Flexible distributions for triple-goal estimates in two-stage hierarchical models
Paddock, Susan M.; Ridgeway, Greg; Lin, Rongheng; Louis, Thomas A.
2009-01-01
Performance evaluations often aim to achieve goals such as obtaining estimates of unit-specific means, ranks, and the distribution of unit-specific parameters. The Bayesian approach provides a powerful way to structure models for achieving these goals. While no single estimate can be optimal for achieving all three inferential goals, the communication and credibility of results will be enhanced by reporting a single estimate that performs well for all three. Triple goal estimates [Shen and Louis, 1998. Triple-goal estimates in two-stage hierarchical models. J. Roy. Statist. Soc. Ser. B 60, 455–471] have this performance and are appealing for performance evaluations. Because triple-goal estimates rely more heavily on the entire distribution than do posterior means, they are more sensitive to misspecification of the population distribution and we present various strategies to robustify triple-goal estimates by using nonparametric distributions. We evaluate performance based on the correctness and efficiency of the robustified estimates under several scenarios and compare empirical Bayes and fully Bayesian approaches to model the population distribution. We find that when data are quite informative, conclusions are robust to model misspecification. However, with less information in the data, conclusions can be quite sensitive to the choice of population distribution. Generally, use of a nonparametric distribution pays very little in efficiency when a parametric population distribution is valid, but successfully protects against model misspecification. PMID:19603088
A semiparametric Bayesian proportional hazards model for interval censored data with frailty effects
Directory of Open Access Journals (Sweden)
Hölzel Dieter
2009-02-01
Full Text Available Abstract Background Multivariate analysis of interval censored event data based on classical likelihood methods is notoriously cumbersome. Likelihood inference for models which additionally include random effects are not available at all. Developed algorithms bear problems for practical users like: matrix inversion, slow convergence, no assessment of statistical uncertainty. Methods MCMC procedures combined with imputation are used to implement hierarchical models for interval censored data within a Bayesian framework. Results Two examples from clinical practice demonstrate the handling of clustered interval censored event times as well as multilayer random effects for inter-institutional quality assessment. The software developed is called survBayes and is freely available at CRAN. Conclusion The proposed software supports the solution of complex analyses in many fields of clinical epidemiology as well as health services research.
A Bayesian ensemble of sensitivity measures for severe accident modeling
Energy Technology Data Exchange (ETDEWEB)
Hoseyni, Seyed Mohsen [Department of Basic Sciences, East Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of); Di Maio, Francesco, E-mail: francesco.dimaio@polimi.it [Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Vagnoli, Matteo [Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Zio, Enrico [Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Chair on System Science and Energetic Challenge, Fondation EDF – Electricite de France Ecole Centrale, Paris, and Supelec, Paris (France); Pourgol-Mohammad, Mohammad [Department of Mechanical Engineering, Sahand University of Technology, Tabriz (Iran, Islamic Republic of)
2015-12-15
Highlights: • We propose a sensitivity analysis (SA) method based on a Bayesian updating scheme. • The Bayesian updating schemes adjourns an ensemble of sensitivity measures. • Bootstrap replicates of a severe accident code output are fed to the Bayesian scheme. • The MELCOR code simulates the fission products release of LOFT LP-FP-2 experiment. • Results are compared with those of traditional SA methods. - Abstract: In this work, a sensitivity analysis framework is presented to identify the relevant input variables of a severe accident code, based on an incremental Bayesian ensemble updating method. The proposed methodology entails: (i) the propagation of the uncertainty in the input variables through the severe accident code; (ii) the collection of bootstrap replicates of the input and output of limited number of simulations for building a set of finite mixture models (FMMs) for approximating the probability density function (pdf) of the severe accident code output of the replicates; (iii) for each FMM, the calculation of an ensemble of sensitivity measures (i.e., input saliency, Hellinger distance and Kullback–Leibler divergence) and the updating when a new piece of evidence arrives, by a Bayesian scheme, based on the Bradley–Terry model for ranking the most relevant input model variables. An application is given with respect to a limited number of simulations of a MELCOR severe accident model describing the fission products release in the LP-FP-2 experiment of the loss of fluid test (LOFT) facility, which is a scaled-down facility of a pressurized water reactor (PWR).
The Revised Hierarchical Model: A critical review and assessment
Kroll, J.F.; Hell, J.G. van; Tokowicz, N.; Green, D.W.
2010-01-01
Brysbaert and Duyck (this issue) suggest that it is time to abandon the Revised Hierarchical Model (Kroll and Stewart, 1994) in favor of connectionist models such as BIA+ (Dijkstra and Van Heuven, 2002) that more accurately account for the recent evidence on non-selective access in bilingual word re
A hierarchical Markov decision process modeling feeding and marketing decisions of growing pigs
DEFF Research Database (Denmark)
Pourmoayed, Reza; Nielsen, Lars Relund; Kristensen, Anders Ringgaard
2016-01-01
Feeding is the most important cost in the production of growing pigs and has a direct impact on the marketing decisions, growth and the final quality of the meat. In this paper, we address the sequential decision problem of when to change the feed-mix within a finisher pig pen and when to pick pigs...... for marketing. We formulate a hierarchical Markov decision process with three levels representing the decision process. The model considers decisions related to feeding and marketing and finds the optimal decision given the current state of the pen. The state of the system is based on information from on......-line repeated measurements of pig weights and feeding and is updated using a Bayesian approach. Numerical examples are given to illustrate the features of the proposed optimization model....
Bayesian modeling growth curves for quail assuming skewness in errors
Directory of Open Access Journals (Sweden)
Robson Marcelo Rossi
2014-06-01
Full Text Available Bayesian modeling growth curves for quail assuming skewness in errors - To assume normal distributions in the data analysis is common in different areas of the knowledge. However we can make use of the other distributions that are capable to model the skewness parameter in the situations that is needed to model data with tails heavier than the normal. This article intend to present alternatives to the assumption of the normality in the errors, adding asymmetric distributions. A Bayesian approach is proposed to fit nonlinear models when the errors are not normal, thus, the distributions t, skew-normal and skew-t are adopted. The methodology is intended to apply to different growth curves to the quail body weights. It was found that the Gompertz model assuming skew-normal errors and skew-t errors, respectively for male and female, were the best fitted to the data.
Quasi-Bayesian software reliability model with small samples
Institute of Scientific and Technical Information of China (English)
ZHANG Jin; TU Jun-xiang; CHEN Zhuo-ning; YAN Xiao-guang
2009-01-01
In traditional Bayesian software reliability models,it was assume that all probabilities are precise.In practical applications the parameters of the probability distributions are often under uncertainty due to strong dependence on subjective information of experts' judgments on sparse statistical data.In this paper,a quasi-Bayesian software reliability model using interval-valued probabilities to clearly quantify experts' prior beliefs on possible intervals of the parameters of the probability distributions is presented.The model integrates experts' judgments with statistical data to obtain more convincible assessments of software reliability with small samples.For some actual data sets,the presented model yields better predictions than the Jelinski-Moranda (JM) model using maximum likelihood (ML).
A Bayesian Alternative for Multi-objective Ecohydrological Model Specification
Tang, Y.; Marshall, L. A.; Sharma, A.; Ajami, H.
2015-12-01
Process-based ecohydrological models combine the study of hydrological, physical, biogeochemical and ecological processes of the catchments, which are usually 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. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological framework. In our study, a formal Bayesian approach is implemented in an ecohydrological model which combines a hydrological model (HyMOD) and a dynamic vegetation model (DVM). Simulations focused on one objective likelihood (Streamflow/LAI) and multi-objective likelihoods (Streamflow and LAI) with different weights are compared. Uniform, weakly informative and strongly informative prior distributions are used in different simulations. The Kullback-leibler divergence (KLD) is used to measure the dis(similarity) between different priors and corresponding posterior distributions to examine the parameter sensitivity. Results show that different prior distributions can strongly influence posterior distributions for parameters, especially when the available data is limited or parameters are insensitive to the available data. We demonstrate differences in optimized parameters and uncertainty limits in different cases based on multi-objective likelihoods vs. single objective likelihoods. We also demonstrate the importance of appropriately defining the weights of objectives in multi-objective calibration according to different data types.
Hierarchical Policy Model for Managing Heterogeneous Security Systems
Lee, Dong-Young; Kim, Minsoo
2007-12-01
The integrated security management becomes increasingly complex as security manager must take heterogeneous security systems, different networking technologies, and distributed applications into consideration. The task of managing these security systems and applications depends on various systems and vender specific issues. In this paper, we present a hierarchical policy model which are derived from the conceptual policy, and specify means to enforce this behavior. The hierarchical policy model consist of five levels which are conceptual policy level, goal-oriented policy level, target policy level, process policy level and low-level policy.
An examination of disparities in cancer incidence in Texas using Bayesian random coefficient models
Directory of Open Access Journals (Sweden)
Corey Sparks
2015-09-01
Full Text Available Disparities in cancer risk exist between ethnic groups in the United States. These disparities often result from differential access to healthcare, differences in socioeconomic status and differential exposure to carcinogens. This study uses cancer incidence data from the population based Texas Cancer Registry to investigate the disparities in digestive and respiratory cancers from 2000 to 2008. A Bayesian hierarchical regression approach is used. All models are fit using the INLA method of Bayesian model estimation. Specifically, a spatially varying coefficient model of the disparity between Hispanic and Non-Hispanic incidence is used. Results suggest that a spatio-temporal heterogeneity model best accounts for the observed Hispanic disparity in cancer risk. Overall, there is a significant disadvantage for the Hispanic population of Texas with respect to both of these cancers, and this disparity varies significantly over space. The greatest disparities between Hispanics and Non-Hispanics in digestive and respiratory cancers occur in eastern Texas, with patterns emerging as early as 2000 and continuing until 2008.
Quick Web Services Lookup Model Based on Hierarchical Registration
Institute of Scientific and Technical Information of China (English)
谢山; 朱国进; 陈家训
2003-01-01
Quick Web Services Lookup (Q-WSL) is a new model to registration and lookup of complex services in the Internet. The model is designed to quickly find complex Web services by using hierarchical registration method. The basic concepts of Web services system are introduced and presented, and then the method of hierarchical registration of services is described. In particular, service query document description and service lookup procedure are concentrated, and it addresses how to lookup these services which are registered in the Web services system. Furthermore, an example design and an evaluation of its performance are presented.Specifically, it shows that the using of attributionbased service query document design and contentbased hierarchical registration in Q-WSL allows service requesters to discover needed services more flexibly and rapidly. It is confirmed that Q-WSL is very suitable for Web services system.
Energy Technology Data Exchange (ETDEWEB)
Lai, Canhai; Xu, Zhijie; Pan, Wenxiao; Sun, Xin; Storlie, Curtis; Marcy, Peter; Dietiker, Jean-François; Li, Tingwen; Spenik, James
2016-01-01
To quantify the predictive confidence of a solid sorbent-based carbon capture design, a hierarchical validation methodology—consisting of basic unit problems with increasing physical complexity coupled with filtered model-based geometric upscaling has been developed and implemented. This paper describes the computational fluid dynamics (CFD) multi-phase reactive flow simulations and the associated data flows among different unit problems performed within the said hierarchical validation approach. The bench-top experiments used in this calibration and validation effort were carefully designed to follow the desired simple-to-complex unit problem hierarchy, with corresponding data acquisition to support model parameters calibrations at each unit problem level. A Bayesian calibration procedure is employed and the posterior model parameter distributions obtained at one unit-problem level are used as prior distributions for the same parameters in the next-tier simulations. Overall, the results have demonstrated that the multiphase reactive flow models within MFIX can be used to capture the bed pressure, temperature, CO2 capture capacity, and kinetics with quantitative accuracy. The CFD modeling methodology and associated uncertainty quantification techniques presented herein offer a solid framework for estimating the predictive confidence in the virtual scale up of a larger carbon capture device.
Quarterly Bayesian DSGE Model of Pakistan Economy with Informality
2013-01-01
In this paper we use the Bayesian methodology to estimate the structural and shocks‟ parameters of the DSGE model in Ahmad et al. (2012). This model includes formal and informal firms both at intermediate and final goods production levels. Households derive utility from leisure, real money balances and consumption. Each household is treated as a unit of labor which is a composite of formal (skilled) and informal (unskilled) labor. The formal (skilled) labor is further divided into types “r” a...
Conceptual hierarchical modeling to describe wetland plant community organization
Little, A.M.; Guntenspergen, G.R.; Allen, T.F.H.
2010-01-01
Using multivariate analysis, we created a hierarchical modeling process that describes how differently-scaled environmental factors interact to affect wetland-scale plant community organization in a system of small, isolated wetlands on Mount Desert Island, Maine. We followed the procedure: 1) delineate wetland groups using cluster analysis, 2) identify differently scaled environmental gradients using non-metric multidimensional scaling, 3) order gradient hierarchical levels according to spatiotem-poral scale of fluctuation, and 4) assemble hierarchical model using group relationships with ordination axes and post-hoc tests of environmental differences. Using this process, we determined 1) large wetland size and poor surface water chemistry led to the development of shrub fen wetland vegetation, 2) Sphagnum and water chemistry differences affected fen vs. marsh / sedge meadows status within small wetlands, and 3) small-scale hydrologic differences explained transitions between forested vs. non-forested and marsh vs. sedge meadow vegetation. This hierarchical modeling process can help explain how upper level contextual processes constrain biotic community response to lower-level environmental changes. It creates models with more nuanced spatiotemporal complexity than classification and regression tree procedures. Using this process, wetland scientists will be able to generate more generalizable theories of plant community organization, and useful management models. ?? Society of Wetland Scientists 2009.
Update Legal Documents Using Hierarchical Ranking Models and Word Clustering
Pham, Minh Quang Nhat; Nguyen, Minh Le; Shimazu, Akira
2010-01-01
Our research addresses the task of updating legal documents when newinformation emerges. In this paper, we employ a hierarchical ranking model tothe task of updating legal documents. Word clustering features are incorporatedto the ranking models to exploit semantic relations between words. Experimentalresults on legal data built from the United States Code show that the hierarchicalranking model with word clustering outperforms baseline methods using VectorSpace Model, and word cluster-based ...
Hierarchical Non-Emitting Markov Models
Ristad, E S; Ristad, Eric Sven; Thomas, Robert G.
1998-01-01
We describe a simple variant of the interpolated Markov model with non-emitting state transitions and prove that it is strictly more powerful than any Markov model. More importantly, the non-emitting model outperforms the classic interpolated model on the natural language texts under a wide range of experimental conditions, with only a modest increase in computational requirements. The non-emitting model is also much less prone to overfitting. Keywords: Markov model, interpolated Markov model, hidden Markov model, mixture modeling, non-emitting state transitions, state-conditional interpolation, statistical language model, discrete time series, Brown corpus, Wall Street Journal.
Application of a predictive Bayesian model to environmental accounting.
Anex, R P; Englehardt, J D
2001-03-30
Environmental accounting techniques are intended to capture important environmental costs and benefits that are often overlooked in standard accounting practices. Environmental accounting methods themselves often ignore or inadequately represent large but highly uncertain environmental costs and costs conditioned by specific prior events. Use of a predictive Bayesian model is demonstrated for the assessment of such highly uncertain environmental and contingent costs. The predictive Bayesian approach presented generates probability distributions for the quantity of interest (rather than parameters thereof). A spreadsheet implementation of a previously proposed predictive Bayesian model, extended to represent contingent costs, is described and used to evaluate whether a firm should undertake an accelerated phase-out of its PCB containing transformers. Variability and uncertainty (due to lack of information) in transformer accident frequency and severity are assessed simultaneously using a combination of historical accident data, engineering model-based cost estimates, and subjective judgement. Model results are compared using several different risk measures. Use of the model for incorporation of environmental risk management into a company's overall risk management strategy is discussed.
Application of the Bayesian dynamic survival model in medicine.
He, Jianghua; McGee, Daniel L; Niu, Xufeng
2010-02-10
The Bayesian dynamic survival model (BDSM), a time-varying coefficient survival model from the Bayesian prospective, was proposed in early 1990s but has not been widely used or discussed. In this paper, we describe the model structure of the BDSM and introduce two estimation approaches for BDSMs: the Markov Chain Monte Carlo (MCMC) approach and the linear Bayesian (LB) method. The MCMC approach estimates model parameters through sampling and is computationally intensive. With the newly developed geoadditive survival models and software BayesX, the BDSM is available for general applications. The LB approach is easier in terms of computations but it requires the prespecification of some unknown smoothing parameters. In a simulation study, we use the LB approach to show the effects of smoothing parameters on the performance of the BDSM and propose an ad hoc method for identifying appropriate values for those parameters. We also demonstrate the performance of the MCMC approach compared with the LB approach and a penalized partial likelihood method available in software R packages. A gastric cancer trial is utilized to illustrate the application of the BDSM.
Modeling urban air pollution with optimized hierarchical fuzzy inference system.
Tashayo, Behnam; Alimohammadi, Abbas
2016-10-01
Environmental exposure assessments (EEA) and epidemiological studies require urban air pollution models with appropriate spatial and temporal resolutions. Uncertain available data and inflexible models can limit air pollution modeling techniques, particularly in under developing countries. This paper develops a hierarchical fuzzy inference system (HFIS) to model air pollution under different land use, transportation, and meteorological conditions. To improve performance, the system treats the issue as a large-scale and high-dimensional problem and develops the proposed model using a three-step approach. In the first step, a geospatial information system (GIS) and probabilistic methods are used to preprocess the data. In the second step, a hierarchical structure is generated based on the problem. In the third step, the accuracy and complexity of the model are simultaneously optimized with a multiple objective particle swarm optimization (MOPSO) algorithm. We examine the capabilities of the proposed model for predicting daily and annual mean PM2.5 and NO2 and compare the accuracy of the results with representative models from existing literature. The benefits provided by the model features, including probabilistic preprocessing, multi-objective optimization, and hierarchical structure, are precisely evaluated by comparing five different consecutive models in terms of accuracy and complexity criteria. Fivefold cross validation is used to assess the performance of the generated models. The respective average RMSEs and coefficients of determination (R (2)) for the test datasets using proposed model are as follows: daily PM2.5 = (8.13, 0.78), annual mean PM2.5 = (4.96, 0.80), daily NO2 = (5.63, 0.79), and annual mean NO2 = (2.89, 0.83). The obtained results demonstrate that the developed hierarchical fuzzy inference system can be utilized for modeling air pollution in EEA and epidemiological studies.
ECoS, a framework for modelling hierarchical spatial systems.
Harris, John R W; Gorley, Ray N
2003-10-01
A general framework for modelling hierarchical spatial systems has been developed and implemented as the ECoS3 software package. The structure of this framework is described, and illustrated with representative examples. It allows the set-up and integration of sets of advection-diffusion equations representing multiple constituents interacting in a spatial context. Multiple spaces can be defined, with zero, one or two-dimensions and can be nested, and linked through constituent transfers. Model structure is generally object-oriented and hierarchical, reflecting the natural relations within its real-world analogue. Velocities, dispersions and inter-constituent transfers, together with additional functions, are defined as properties of constituents to which they apply. The resulting modular structure of ECoS models facilitates cut and paste model development, and template model components have been developed for the assembly of a range of estuarine water quality models. Published examples of applications to the geochemical dynamics of estuaries are listed.
On the construction of hierarchic models
Out, D.-J.; Rikxoort, van R.P.; Bakker, R.R.
1994-01-01
One of the main problems in the field of model-based diagnosis of technical systems today is finding the most useful model or models of the system being diagnosed. Often, a model showing the physical components and the connections between them is all that is available. As systems grow larger and lar
Inference in HIV dynamics models via hierarchical likelihood
2010-01-01
HIV dynamical models are often based on non-linear systems of ordinary differential equations (ODE), which do not have analytical solution. Introducing random effects in such models leads to very challenging non-linear mixed-effects models. To avoid the numerical computation of multiple integrals involved in the likelihood, we propose a hierarchical likelihood (h-likelihood) approach, treated in the spirit of a penalized likelihood. We give the asymptotic distribution of the maximum h-likelih...
Bayesian estimation of the network autocorrelation model
Dittrich, D.; Leenders, R.T.A.J.; Mulder, J.
2017-01-01
The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of
Bayesian prediction of placebo analgesia in an instrumental learning model
Jung, Won-Mo; Lee, Ye-Seul; Wallraven, Christian; Chae, Younbyoung
2017-01-01
Placebo analgesia can be primarily explained by the Pavlovian conditioning paradigm in which a passively applied cue becomes associated with less pain. In contrast, instrumental conditioning employs an active paradigm that might be more similar to clinical settings. In the present study, an instrumental conditioning paradigm involving a modified trust game in a simulated clinical situation was used to induce placebo analgesia. Additionally, Bayesian modeling was applied to predict the placebo responses of individuals based on their choices. Twenty-four participants engaged in a medical trust game in which decisions to receive treatment from either a doctor (more effective with high cost) or a pharmacy (less effective with low cost) were made after receiving a reference pain stimulus. In the conditioning session, the participants received lower levels of pain following both choices, while high pain stimuli were administered in the test session even after making the decision. The choice-dependent pain in the conditioning session was modulated in terms of both intensity and uncertainty. Participants reported significantly less pain when they chose the doctor or the pharmacy for treatment compared to the control trials. The predicted pain ratings based on Bayesian modeling showed significant correlations with the actual reports from participants for both of the choice categories. The instrumental conditioning paradigm allowed for the active choice of optional cues and was able to induce the placebo analgesia effect. Additionally, Bayesian modeling successfully predicted pain ratings in a simulated clinical situation that fits well with placebo analgesia induced by instrumental conditioning. PMID:28225816
Characterizing economic trends by Bayesian stochastic model specification search
DEFF Research Database (Denmark)
Grassi, Stefano; Proietti, Tommaso
We extend a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. In particular, we focus on autoregressive models with possibly time-varying intercept and slope and decide...... on whether their parameters are fixed or evolutive. Stochastic model specification is carried out to discriminate two alternative hypotheses concerning the generation of trends: the trend-stationary hypothesis, on the one hand, for which the trend is a deterministic function of time and the short run......, estimated by a suitable Gibbs sampling scheme, provides useful insight on quasi-integrated nature of the specifications selected....
Use of hierarchical models to analyze European trends in congenital anomaly prevalence
DEFF Research Database (Denmark)
Cavadino, Alana; Prieto-Merino, David; Addor, Marie-Claude
2016-01-01
for the following groups of anomalies: neural tube defects, congenital heart defects, digestive system, and chromosomal anomalies. Hierarchical Poisson regression models that combined related subgroups together according to EUROCAT's hierarchy of subgroup coding were applied. Results from hierarchical models were...
AIC, BIC, Bayesian evidence against the interacting dark energy model
Energy Technology Data Exchange (ETDEWEB)
Szydlowski, Marek [Jagiellonian University, Astronomical Observatory, Krakow (Poland); Jagiellonian University, Mark Kac Complex Systems Research Centre, Krakow (Poland); Krawiec, Adam [Jagiellonian University, Institute of Economics, Finance and Management, Krakow (Poland); Jagiellonian University, Mark Kac Complex Systems Research Centre, Krakow (Poland); Kurek, Aleksandra [Jagiellonian University, Astronomical Observatory, Krakow (Poland); Kamionka, Michal [University of Wroclaw, Astronomical Institute, Wroclaw (Poland)
2015-01-01
Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative - the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam's principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock- Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam's razor we are inclined to reject this model. (orig.)
AIC, BIC, Bayesian evidence against the interacting dark energy model
Energy Technology Data Exchange (ETDEWEB)
Szydłowski, Marek, E-mail: marek.szydlowski@uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244, Kraków (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059, Kraków (Poland); Krawiec, Adam, E-mail: adam.krawiec@uj.edu.pl [Institute of Economics, Finance and Management, Jagiellonian University, Łojasiewicza 4, 30-348, Kraków (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Reymonta 4, 30-059, Kraków (Poland); Kurek, Aleksandra, E-mail: alex@oa.uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244, Kraków (Poland); Kamionka, Michał, E-mail: kamionka@astro.uni.wroc.pl [Astronomical Institute, University of Wrocław, ul. Kopernika 11, 51-622, Wrocław (Poland)
2015-01-14
Recent astronomical observations have indicated that the Universe is in a phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting ΛCDM model where an interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative—the ΛCDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam’s principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: type Ia supernova (Union2.1), h(z), baryon acoustic oscillation, the Alcock–Paczynski test, and the cosmic microwave background data, we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting ΛCDM model when compared to the ΛCDM model, while those based on the BIC indicated that there is strong evidence against it in favor of the ΛCDM model. Given the weak or almost non-existing support for the interacting ΛCDM model and bearing in mind Occam’s razor we are inclined to reject this model.
Comparing Bayesian stable isotope mixing models: Which tools are best for sediments?
Morris, David; Macko, Stephen
2016-04-01
Bayesian stable isotope mixing models have received much attention as a means of coping with multiple sources and uncertainty in isotope ecology (e.g. Phillips et al., 2014), enabling the probabilistic determination of the contributions made by each food source to the total diet of the organism in question. We have applied these techniques to marine sediments for the first time. The sediments of the Chukchi Sea and Beaufort Sea offer an opportunity to utilize these models for organic geochemistry, as there are three likely sources of organic carbon; pelagic phytoplankton, sea ice algae and terrestrial material from rivers and coastal erosion, as well as considerable variation in the marine δ13C values. Bayesian mixing models using bulk δ13C and δ15N data from Shelf Basin Interaction samples allow for the probabilistic determination of the contributions made by each of the sources to the organic carbon budget, and can be compared with existing source contribution estimates based upon biomarker models (e.g. Belicka & Harvey, 2009, Faux, Belicka, & Rodger Harvey, 2011). The δ13C of this preserved material varied from -22.1 to -16.7‰ (mean -19.4±1.3‰), while δ15N varied from 4.1 to 7.6‰ (mean 5.7±1.1‰). Using the SIAR model, we found that water column productivity was the source of between 50 and 70% of the organic carbon buried in this portion of the western Arctic with the remainder mainly supplied by sea ice algal productivity (25-35%) and terrestrial inputs (15%). With many mixing models now available, this study will compare SIAR with MixSIAR and the new FRUITS model. Monte Carlo modeling of the mixing polygon will be used to validate the models, and hierarchical models will be utilised to glean more information from the data set.
Concept Association and Hierarchical Hamming Clustering Model in Text Classification
Institute of Scientific and Technical Information of China (English)
Su Gui-yang; Li Jian-hua; Ma Ying-hua; Li Sheng-hong; Yin Zhong-hang
2004-01-01
We propose two models in this paper. The concept of association model is put forward to obtain the co-occurrence relationships among keywords in the documents and the hierarchical Hamming clustering model is used to reduce the dimensionality of the category feature vector space which can solve the problem of the extremely high dimensionality of the documents' feature space. The results of experiment indicate that it can obtain the co-occurrence relations among keywords in the documents which promote the recall of classification system effectively. The hierarchical Hamming clustering model can reduce the dimensionality of the category feature vector efficiently, the size of the vector space is only about 10% of the primary dimensionality.
Babcock, Chad; Finley, Andrew O.; Bradford, John B.; Kolka, Randall K.; Birdsey, Richard A.; Ryan, Michael G.
2015-01-01
Many studies and production inventory systems have shown the utility of coupling covariates derived from Light Detection and Ranging (LiDAR) data with forest variables measured on georeferenced inventory plots through regression models. The objective of this study was to propose and assess the use of a Bayesian hierarchical modeling framework that accommodates both residual spatial dependence and non-stationarity of model covariates through the introduction of spatial random effects. We explored this objective using four forest inventory datasets that are part of the North American Carbon Program, each comprising point-referenced measures of above-ground forest biomass and discrete LiDAR. For each dataset, we considered at least five regression model specifications of varying complexity. Models were assessed based on goodness of fit criteria and predictive performance using a 10-fold cross-validation procedure. Results showed that the addition of spatial random effects to the regression model intercept improved fit and predictive performance in the presence of substantial residual spatial dependence. Additionally, in some cases, allowing either some or all regression slope parameters to vary spatially, via the addition of spatial random effects, further improved model fit and predictive performance. In other instances, models showed improved fit but decreased predictive performance—indicating over-fitting and underscoring the need for cross-validation to assess predictive ability. The proposed Bayesian modeling framework provided access to pixel-level posterior predictive distributions that were useful for uncertainty mapping, diagnosing spatial extrapolation issues, revealing missing model covariates, and discovering locally significant parameters.
A Bayesian Nonparametric Meta-Analysis Model
Karabatsos, George; Talbott, Elizabeth; Walker, Stephen G.
2015-01-01
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall…
Bayesian geostatistical modeling of leishmaniasis incidence in Brazil.
Directory of Open Access Journals (Sweden)
Dimitrios-Alexios Karagiannis-Voules
Full Text Available BACKGROUND: Leishmaniasis is endemic in 98 countries with an estimated 350 million people at risk and approximately 2 million cases annually. Brazil is one of the most severely affected countries. METHODOLOGY: We applied Bayesian geostatistical negative binomial models to analyze reported incidence data of cutaneous and visceral leishmaniasis in Brazil covering a 10-year period (2001-2010. Particular emphasis was placed on spatial and temporal patterns. The models were fitted using integrated nested Laplace approximations to perform fast approximate Bayesian inference. Bayesian variable selection was employed to determine the most important climatic, environmental, and socioeconomic predictors of cutaneous and visceral leishmaniasis. PRINCIPAL FINDINGS: For both types of leishmaniasis, precipitation and socioeconomic proxies were identified as important risk factors. The predicted number of cases in 2010 were 30,189 (standard deviation [SD]: 7,676 for cutaneous leishmaniasis and 4,889 (SD: 288 for visceral leishmaniasis. Our risk maps predicted the highest numbers of infected people in the states of Minas Gerais and Pará for visceral and cutaneous leishmaniasis, respectively. CONCLUSIONS/SIGNIFICANCE: Our spatially explicit, high-resolution incidence maps identified priority areas where leishmaniasis control efforts should be targeted with the ultimate goal to reduce disease incidence.
Hierarchical Bulk Synchronous Parallel Model and Performance Optimization
Institute of Scientific and Technical Information of China (English)
HUANG Linpeng; SUNYongqiang; YUAN Wei
1999-01-01
Based on the framework of BSP, aHierarchical Bulk Synchronous Parallel (HBSP) performance model isintroduced in this paper to capture the performance optimizationproblem for various stages in parallel program development and toaccurately predict the performance of a parallel program byconsidering factors causing variance at local computation and globalcommunication. The related methodology has been applied to several realapplications and the results show that HBSP is a suitable model foroptimizing parallel programs.
Fractal Derivative Model for Air Permeability in Hierarchic Porous Media
Directory of Open Access Journals (Sweden)
Jie Fan
2012-01-01
Full Text Available Air permeability in hierarchic porous media does not obey Fick's equation or its modification because fractal objects have well-defined geometric properties, which are discrete and discontinuous. We propose a theoretical model dealing with, for the first time, a seemingly complex air permeability process using fractal derivative method. The fractal derivative model has been successfully applied to explain the novel air permeability phenomenon of cocoon. The theoretical analysis was in agreement with experimental results.
Hierarchical Item Response Models for Cognitive Diagnosis
Hansen, Mark Patrick
2013-01-01
Cognitive diagnosis models (see, e.g., Rupp, Templin, & Henson, 2010) have received increasing attention within educational and psychological measurement. The popularity of these models may be largely due to their perceived ability to provide useful information concerning both examinees (classifying them according to their attribute profiles)…
Hierarchical spatial models for predicting pygmy rabbit distribution and relative abundance
Wilson, T.L.; Odei, J.B.; Hooten, M.B.; Edwards, T.C.
2010-01-01
Conservationists routinely use species distribution models to plan conservation, restoration and development actions, while ecologists use them to infer process from pattern. These models tend to work well for common or easily observable species, but are of limited utility for rare and cryptic species. This may be because honest accounting of known observation bias and spatial autocorrelation are rarely included, thereby limiting statistical inference of resulting distribution maps. We specified and implemented a spatially explicit Bayesian hierarchical model for a cryptic mammal species (pygmy rabbit Brachylagus idahoensis). Our approach used two levels of indirect sign that are naturally hierarchical (burrows and faecal pellets) to build a model that allows for inference on regression coefficients as well as spatially explicit model parameters. We also produced maps of rabbit distribution (occupied burrows) and relative abundance (number of burrows expected to be occupied by pygmy rabbits). The model demonstrated statistically rigorous spatial prediction by including spatial autocorrelation and measurement uncertainty. We demonstrated flexibility of our modelling framework by depicting probabilistic distribution predictions using different assumptions of pygmy rabbit habitat requirements. Spatial representations of the variance of posterior predictive distributions were obtained to evaluate heterogeneity in model fit across the spatial domain. Leave-one-out cross-validation was conducted to evaluate the overall model fit. Synthesis and applications. Our method draws on the strengths of previous work, thereby bridging and extending two active areas of ecological research: species distribution models and multi-state occupancy modelling. Our framework can be extended to encompass both larger extents and other species for which direct estimation of abundance is difficult. ?? 2010 The Authors. Journal compilation ?? 2010 British Ecological Society.
Bayesian comparisons of codon substitution models.
Rodrigue, Nicolas; Lartillot, Nicolas; Philippe, Hervé
2008-11-01
In 1994, Muse and Gaut (MG) and Goldman and Yang (GY) proposed evolutionary models that recognize the coding structure of the nucleotide sequences under study, by defining a Markovian substitution process with a state space consisting of the 61 sense codons (assuming the universal genetic code). Several variations and extensions to their models have since been proposed, but no general and flexible framework for contrasting the relative performance of alternative approaches has yet been applied. Here, we compute Bayes factors to evaluate the relative merit of several MG and GY styles of codon substitution models, including recent extensions acknowledging heterogeneous nonsynonymous rates across sites, as well as selective effects inducing uneven amino acid or codon preferences. Our results on three real data sets support a logical model construction following the MG formulation, allowing for a flexible account of global amino acid or codon preferences, while maintaining distinct parameters governing overall nucleotide propensities. Through posterior predictive checks, we highlight the importance of such a parameterization. Altogether, the framework presented here suggests a broad modeling project in the MG style, stressing the importance of combining and contrasting available model formulations and grounding developments in a sound probabilistic paradigm.
Probe Error Modeling Research Based on Bayesian Network
Institute of Scientific and Technical Information of China (English)
Wu Huaiqiang; Xing Zilong; Zhang Jian; Yan Yan
2015-01-01
Probe calibration is carried out under specific conditions; most of the error caused by the change of speed parameter has not been corrected. In order to reduce the measuring error influence on measurement accuracy, this article analyzes the relationship between speed parameter and probe error, and use Bayesian network to establish the model of probe error. Model takes account of prior knowledge and sample data, with the updating of data, which can reflect the change of the errors of the probe and constantly revised modeling results.
A Bayesian Network View on Nested Effects Models
Directory of Open Access Journals (Sweden)
Fröhlich Holger
2009-01-01
Full Text Available Nested effects models (NEMs are a class of probabilistic models that were designed to reconstruct a hidden signalling structure from a large set of observable effects caused by active interventions into the signalling pathway. We give a more flexible formulation of NEMs in the language of Bayesian networks. Our framework constitutes a natural generalization of the original NEM model, since it explicitly states the assumptions that are tacitly underlying the original version. Our approach gives rise to new learning methods for NEMs, which have been implemented in the /Bioconductor package nem. We validate these methods in a simulation study and apply them to a synthetic lethality dataset in yeast.
Bayesian inference and model comparison for metallic fatigue data
Babuška, Ivo
2016-02-23
In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. To assess the robustness of the estimation of the quantile functions, we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions. We implement and apply Bayesian model comparison methods, such as Bayes factor ranking and predictive information criteria based on cross-validation techniques under various a priori scenarios.
Bayesian Thurstonian models for ranking data using JAGS.
Johnson, Timothy R; Kuhn, Kristine M
2013-09-01
A Thurstonian model for ranking data assumes that observed rankings are consistent with those of a set of underlying continuous variables. This model is appealing since it renders ranking data amenable to familiar models for continuous response variables-namely, linear regression models. To date, however, the use of Thurstonian models for ranking data has been very rare in practice. One reason for this may be that inferences based on these models require specialized technical methods. These methods have been developed to address computational challenges involved in these models but are not easy to implement without considerable technical expertise and are not widely available in software packages. To address this limitation, we show that Bayesian Thurstonian models for ranking data can be very easily implemented with the JAGS software package. We provide JAGS model files for Thurstonian ranking models for general use, discuss their implementation, and illustrate their use in analyses.
Hierarchical, model-based risk management of critical infrastructures
Energy Technology Data Exchange (ETDEWEB)
Baiardi, F. [Polo G.Marconi La Spezia, Universita di Pisa, Pisa (Italy); Dipartimento di Informatica, Universita di Pisa, L.go B.Pontecorvo 3 56127, Pisa (Italy)], E-mail: f.baiardi@unipi.it; Telmon, C.; Sgandurra, D. [Dipartimento di Informatica, Universita di Pisa, L.go B.Pontecorvo 3 56127, Pisa (Italy)
2009-09-15
Risk management is a process that includes several steps, from vulnerability analysis to the formulation of a risk mitigation plan that selects countermeasures to be adopted. With reference to an information infrastructure, we present a risk management strategy that considers a sequence of hierarchical models, each describing dependencies among infrastructure components. A dependency exists anytime a security-related attribute of a component depends upon the attributes of other components. We discuss how this notion supports the formal definition of risk mitigation plan and the evaluation of the infrastructure robustness. A hierarchical relation exists among models that are analyzed because each model increases the level of details of some components in a previous one. Since components and dependencies are modeled through a hypergraph, to increase the model detail level, some hypergraph nodes are replaced by more and more detailed hypergraphs. We show how critical information for the assessment can be automatically deduced from the hypergraph and define conditions that determine cases where a hierarchical decomposition simplifies the assessment. In these cases, the assessment has to analyze the hypergraph that replaces the component rather than applying again all the analyses to a more detailed, and hence larger, hypergraph. We also show how the proposed framework supports the definition of a risk mitigation plan and discuss some indicators of the overall infrastructure robustness. Lastly, the development of tools to support the assessment is discussed.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Guannan [ORNL; Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL
2012-09-01
Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional
Predicting coastal cliff erosion using a Bayesian probabilistic model
Hapke, C.; Plant, N.
2010-01-01
Regional coastal cliff retreat is difficult to model due to the episodic nature of failures and the along-shore variability of retreat events. There is a growing demand, however, for predictive models that can be used to forecast areas vulnerable to coastal erosion hazards. Increasingly, probabilistic models are being employed that require data sets of high temporal density to define the joint probability density function that relates forcing variables (e.g. wave conditions) and initial conditions (e.g. cliff geometry) to erosion events. In this study we use a multi-parameter Bayesian network to investigate correlations between key variables that control and influence variations in cliff retreat processes. The network uses Bayesian statistical methods to estimate event probabilities using existing observations. Within this framework, we forecast the spatial distribution of cliff retreat along two stretches of cliffed coast in Southern California. The input parameters are the height and slope of the cliff, a descriptor of material strength based on the dominant cliff-forming lithology, and the long-term cliff erosion rate that represents prior behavior. The model is forced using predicted wave impact hours. Results demonstrate that the Bayesian approach is well-suited to the forward modeling of coastal cliff retreat, with the correct outcomes forecast in 70-90% of the modeled transects. The model also performs well in identifying specific locations of high cliff erosion, thus providing a foundation for hazard mapping. This approach can be employed to predict cliff erosion at time-scales ranging from storm events to the impacts of sea-level rise at the century-scale. ?? 2010.
Classification using Hierarchical Naive Bayes models
DEFF Research Database (Denmark)
Langseth, Helge; Dyhre Nielsen, Thomas
2006-01-01
Classification problems have a long history in the machine learning literature. One of the simplest, and yet most consistently well-performing set of classifiers is the Naïve Bayes models. However, an inherent problem with these classifiers is the assumption that all attributes used to describe...... an instance are conditionally independent given the class of that instance. When this assumption is violated (which is often the case in practice) it can reduce classification accuracy due to “information double-counting” and interaction omission. In this paper we focus on a relatively new set of models...... in the context of classification. Experimental results show that the learned models can significantly improve classification accuracy as compared to other frameworks....
DPpackage: Bayesian Semi- and Nonparametric Modeling in R
Directory of Open Access Journals (Sweden)
Alejandro Jara
2011-04-01
Full Text Available Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on a function space, such as the space of all probability distributions or the space of all regression functions. Unfortunately, posterior distributions ranging over function spaces are highly complex and hence sampling methods play a key role. This paper provides an introduction to a simple, yet comprehensive, set of programs for the implementation of some Bayesian nonparametric and semiparametric models in R, DPpackage. Currently, DPpackage includes models for marginal and conditional density estimation, receiver operating characteristic curve analysis, interval-censored data, binary regression data, item response data, longitudinal and clustered data using generalized linear mixed models, and regression data using generalized additive models. The package also contains functions to compute pseudo-Bayes factors for model comparison and for eliciting the precision parameter of the Dirichlet process prior, and a general purpose Metropolis sampling algorithm. To maximize computational efficiency, the actual sampling for each model is carried out using compiled C, C++ or Fortran code.
Skilloscopy: Bayesian modeling of decision makers' skill
Di Fatta, Giuseppe; Haworth, Guy
2013-01-01
This paper proposes and demonstrates an approach, Skilloscopy, to the assessment of decision makers. In an increasingly sophisticated, connected and information-rich world, decision making is becoming both more important and more difficult. At the same time, modelling decision-making on computers is becoming more feasible and of interest, partly because the information-input to those decisions is increasingly on record. The aims of Skilloscopy are to rate and rank decision makers in a d...
Dettmer, Jan; Molnar, Sheri; Steininger, Gavin; Dosso, Stan E.; Cassidy, John F.
2012-02-01
This paper applies a general trans-dimensional Bayesian inference methodology and hierarchical autoregressive data-error models to the inversion of microtremor array dispersion data for shear wave velocity (vs) structure. This approach accounts for the limited knowledge of the optimal earth model parametrization (e.g. the number of layers in the vs profile) and of the data-error statistics in the resulting vs parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A trans-dimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the indexing parameter) are considered in the results. The earth model is parametrized in terms of a partition model with interfaces given over a depth-range of interest. In this work, the number of interfaces (layers) in the partition model represents the trans-dimensional model indexing. In addition, serial data-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate data-error statistics, and have no requirement for computing the inverse or determinant of a data-error covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the
Continuum damage modeling and simulation of hierarchical dental enamel
Ma, Songyun; Scheider, Ingo; Bargmann, Swantje
2016-05-01
Dental enamel exhibits high fracture toughness and stiffness due to a complex hierarchical and graded microstructure, optimally organized from nano- to macro-scale. In this study, a 3D representative volume element (RVE) model is adopted to study the deformation and damage behavior of the fibrous microstructure. A continuum damage mechanics model coupled to hyperelasticity is developed for modeling the initiation and evolution of damage in the mineral fibers as well as protein matrix. Moreover, debonding of the interface between mineral fiber and protein is captured by employing a cohesive zone model. The dependence of the failure mechanism on the aspect ratio of the mineral fibers is investigated. In addition, the effect of the interface strength on the damage behavior is studied with respect to geometric features of enamel. Further, the effect of an initial flaw on the overall mechanical properties is analyzed to understand the superior damage tolerance of dental enamel. The simulation results are validated by comparison to experimental data from micro-cantilever beam testing at two hierarchical levels. The transition of the failure mechanism at different hierarchical levels is also well reproduced in the simulations.
A Hierarchical Probability Model of Colon Cancer
Kelly, Michael
2010-01-01
We consider a model of fixed size $N = 2^l$ in which there are $l$ generations of daughter cells and a stem cell. In each generation $i$ there are $2^{i-1}$ daughter cells. At each integral time unit the cells split so that the stem cell splits into a stem cell and generation 1 daughter cell and the generation $i$ daughter cells become two cells of generation $i+1$. The last generation is removed from the population. The stem cell gets first and second mutations at rates $u_1$ and $u_2$ and the daughter cells get first and second mutations at rates $v_1$ and $v_2$. We find the distribution for the time it takes to get two mutations as $N$ goes to infinity and the mutation rates go to 0. We also find the distribution for the location of the mutations. Several outcomes are possible depending on how fast the rates go to 0. The model considered has been proposed by Komarova (2007) as a model for colon cancer.
Blundell, Charles; Heller, Katherine A
2012-01-01
Hierarchical structure is ubiquitous in data across many domains. There are many hier- archical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these meth- ods limit discoverable hierarchies to those with binary branching structure. This lim- itation, while computationally convenient, is often undesirable. In this paper we ex- plore a Bayesian hierarchical clustering algo- rithm that can produce trees with arbitrary branching structure at each node, known as rose trees. We interpret these trees as mixtures over partitions of a data set, and use a computationally efficient, greedy ag- glomerative algorithm to find the rose trees which have high marginal likelihood given the data. Lastly, we perform experiments which demonstrate that rose trees are better models of data than the typical binary trees returned by other hierarchical clustering algorithms.
A Bayesian Model Committee Approach to Forecasting Global Solar Radiation
Lauret, Philippe; Muselli, Marc; David, Mathieu; Diagne, Hadja; Voyant, Cyril
2012-01-01
This paper proposes to use a rather new modelling approach in the realm of solar radiation forecasting. In this work, two forecasting models: Autoregressive Moving Average (ARMA) and Neural Network (NN) models are combined to form a model committee. The Bayesian inference is used to affect a probability to each model in the committee. Hence, each model's predictions are weighted by their respective probability. The models are fitted to one year of hourly Global Horizontal Irradiance (GHI) measurements. Another year (the test set) is used for making genuine one hour ahead (h+1) out-of-sample forecast comparisons. The proposed approach is benchmarked against the persistence model. The very first results show an improvement brought by this approach.
Hierarchical Model Predictive Control for Resource Distribution
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, K; Stoustrup, Jakob
2010-01-01
This paper deals with hierarchichal model predictive control (MPC) of distributed systems. A three level hierachical approach is proposed, consisting of a high level MPC controller, a second level of so-called aggregators, controlled by an online MPC-like algorithm, and a lower level of autonomous...... facilitates plug-and-play addition of subsystems without redesign of any controllers. The method is supported by a number of simulations featuring a three-level smart-grid power control system for a small isolated power grid....
Bayesian parameter estimation for nonlinear modelling of biological pathways
Directory of Open Access Journals (Sweden)
Ghasemi Omid
2011-12-01
Full Text Available Abstract Background The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. Results We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC method. We applied this approach to the biological pathways involved in the left ventricle (LV response to myocardial infarction (MI and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly
Study of TEC fluctuation via stochastic models and Bayesian inversion
Bires, A.; Roininen, L.; Damtie, B.; Nigussie, M.; Vanhamäki, H.
2016-11-01
We propose stochastic processes to be used to model the total electron content (TEC) observation. Based on this, we model the rate of change of TEC (ROT) variation during ionospheric quiet conditions with stationary processes. During ionospheric disturbed conditions, for example, when irregularity in ionospheric electron density distribution occurs, stationarity assumption over long time periods is no longer valid. In these cases, we make the parameter estimation for short time scales, during which we can assume stationarity. We show the relationship between the new method and commonly used TEC characterization parameters ROT and the ROT Index (ROTI). We construct our parametric model within the framework of Bayesian statistical inverse problems and hence give the solution as an a posteriori probability distribution. Bayesian framework allows us to model measurement errors systematically. Similarly, we mitigate variation of TEC due to factors which are not of ionospheric origin, like due to the motion of satellites relative to the receiver, by incorporating a priori knowledge in the Bayesian model. In practical computations, we draw the so-called maximum a posteriori estimates, which are our ROT and ROTI estimates, from the posterior distribution. Because the algorithm allows to estimate ROTI at each observation time, the estimator does not depend on the period of time for ROTI computation. We verify the method by analyzing TEC data recorded by GPS receiver located in Ethiopia (11.6°N, 37.4°E). The results indicate that the TEC fluctuations caused by the ionospheric irregularity can be effectively detected and quantified from the estimated ROT and ROTI values.
A study of finite mixture model: Bayesian approach on financial time series data
Phoong, Seuk-Yen; Ismail, Mohd Tahir
2014-07-01
Recently, statistician have emphasized on the fitting finite mixture model by using Bayesian method. Finite mixture model is a mixture of distributions in modeling a statistical distribution meanwhile Bayesian method is a statistical method that use to fit the mixture model. Bayesian method is being used widely because it has asymptotic properties which provide remarkable result. In addition, Bayesian method also shows consistency characteristic which means the parameter estimates are close to the predictive distributions. In the present paper, the number of components for mixture model is studied by using Bayesian Information Criterion. Identify the number of component is important because it may lead to an invalid result. Later, the Bayesian method is utilized to fit the k-component mixture model in order to explore the relationship between rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia. Lastly, the results showed that there is a negative effect among rubber price and stock market price for all selected countries.
A Bayesian subgroup analysis using collections of ANOVA models.
Liu, Jinzhong; Sivaganesan, Siva; Laud, Purushottam W; Müller, Peter
2017-03-20
We develop a Bayesian approach to subgroup analysis using ANOVA models with multiple covariates, extending an earlier work. We assume a two-arm clinical trial with normally distributed response variable. We also assume that the covariates for subgroup finding are categorical and are a priori specified, and parsimonious easy-to-interpret subgroups are preferable. We represent the subgroups of interest by a collection of models and use a model selection approach to finding subgroups with heterogeneous effects. We develop suitable priors for the model space and use an objective Bayesian approach that yields multiplicity adjusted posterior probabilities for the models. We use a structured algorithm based on the posterior probabilities of the models to determine which subgroup effects to report. Frequentist operating characteristics of the approach are evaluated using simulation. While our approach is applicable in more general cases, we mainly focus on the 2 × 2 case of two covariates each at two levels for ease of presentation. The approach is illustrated using a real data example.
Hierarchical models and the analysis of bird survey information
Sauer, J.R.; Link, W.A.
2003-01-01
Management of birds often requires analysis of collections of estimates. We describe a hierarchical modeling approach to the analysis of these data, in which parameters associated with the individual species estimates are treated as random variables, and probability statements are made about the species parameters conditioned on the data. A Markov-Chain Monte Carlo (MCMC) procedure is used to fit the hierarchical model. This approach is computer intensive, and is based upon simulation. MCMC allows for estimation both of parameters and of derived statistics. To illustrate the application of this method, we use the case in which we are interested in attributes of a collection of estimates of population change. Using data for 28 species of grassland-breeding birds from the North American Breeding Bird Survey, we estimate the number of species with increasing populations, provide precision-adjusted rankings of species trends, and describe a measure of population stability as the probability that the trend for a species is within a certain interval. Hierarchical models can be applied to a variety of bird survey applications, and we are investigating their use in estimation of population change from survey data.
Two Bayesian tests of the GLOMOsys Model.
Field, Sarahanne M; Wagenmakers, Eric-Jan; Newell, Ben R; Zeelenberg, René; van Ravenzwaaij, Don
2016-12-01
Priming is arguably one of the key phenomena in contemporary social psychology. Recent retractions and failed replication attempts have led to a division in the field between proponents and skeptics and have reinforced the importance of confirming certain priming effects through replication. In this study, we describe the results of 2 preregistered replication attempts of 1 experiment by Förster and Denzler (2012). In both experiments, participants first processed letters either globally or locally, then were tested using a typicality rating task. Bayes factor hypothesis tests were conducted for both experiments: Experiment 1 (N = 100) yielded an indecisive Bayes factor of 1.38, indicating that the in-lab data are 1.38 times more likely to have occurred under the null hypothesis than under the alternative. Experiment 2 (N = 908) yielded a Bayes factor of 10.84, indicating strong support for the null hypothesis that global priming does not affect participants' mean typicality ratings. The failure to replicate this priming effect challenges existing support for the GLOMO(sys) model. (PsycINFO Database Record
Objective Bayesian Comparison of Constrained Analysis of Variance Models.
Consonni, Guido; Paroli, Roberta
2016-10-04
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means [Formula: see text] through an analysis of variance (ANOVA), a model may specify that [Formula: see text], while another one may state that [Formula: see text], and finally a third model may instead suggest that all means are unrestricted. This is a challenging problem, because it involves a combination of nonnested models, as well as nested models having the same dimension. We adopt an objective Bayesian approach, requiring no prior specification from the user, and derive the posterior probability of each model under consideration. Our method is based on the intrinsic prior methodology, suitably modified to accommodate equality and inequality constraints. Focussing on normal ANOVA models, a comparative assessment is carried out through simulation studies. We also present an application to real data collected in a psychological experiment.
Forecasting natural gas consumption in China by Bayesian Model Averaging
Directory of Open Access Journals (Sweden)
Wei Zhang
2015-11-01
Full Text Available With rapid growth of natural gas consumption in China, it is in urgent need of more accurate and reliable models to make a reasonable forecast. Considering the limitations of the single model and the model uncertainty, this paper presents a combinative method to forecast natural gas consumption by Bayesian Model Averaging (BMA. It can effectively handle the uncertainty associated with model structure and parameters, and thus improves the forecasting accuracy. This paper chooses six variables for forecasting the natural gas consumption, including GDP, urban population, energy consumption structure, industrial structure, energy efficiency and exports of goods and services. The results show that comparing to Gray prediction model, Linear regression model and Artificial neural networks, the BMA method provides a flexible tool to forecast natural gas consumption that will have a rapid growth in the future. This study can provide insightful information on natural gas consumption in the future.
Coordinated Resource Management Models in Hierarchical Systems
Directory of Open Access Journals (Sweden)
Gabsi Mounir
2013-03-01
Full Text Available In response to the trend of efficient global economy, constructing a global logistic model has garnered much attention from the industry .Location selection is an important issue for those international companies that are interested in building a global logistics management system. Infrastructure in Developing Countries are based on the use of both classical and modern control technology, for which the most important components are professional levels of structure knowledge, dynamics and management processes, threats and interference and external and internal attacks. The problem of control flows of energy and materials resources in local and regional structures in normal and marginal, emergency operation provoked information attacks or threats on failure flows are further relevant especially when considering the low level of professional ,psychological and cognitive training of operational personnel manager. Logistics Strategies include the business goals requirements, allowable decisions tactics, and vision for designing and operating a logistics system .In this paper described the selection module coordinating flow management strategies based on the use of resources and logistics systems concepts.
Predictive RANS simulations via Bayesian Model-Scenario Averaging
Energy Technology Data Exchange (ETDEWEB)
Edeling, W.N., E-mail: W.N.Edeling@tudelft.nl [Arts et Métiers ParisTech, DynFluid laboratory, 151 Boulevard de l' Hospital, 75013 Paris (France); Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, Delft (Netherlands); Cinnella, P., E-mail: P.Cinnella@ensam.eu [Arts et Métiers ParisTech, DynFluid laboratory, 151 Boulevard de l' Hospital, 75013 Paris (France); Dwight, R.P., E-mail: R.P.Dwight@tudelft.nl [Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, Delft (Netherlands)
2014-10-15
The turbulence closure model is the dominant source of error in most Reynolds-Averaged Navier–Stokes simulations, yet no reliable estimators for this error component currently exist. Here we develop a stochastic, a posteriori error estimate, calibrated to specific classes of flow. It is based on variability in model closure coefficients across multiple flow scenarios, for multiple closure models. The variability is estimated using Bayesian calibration against experimental data for each scenario, and Bayesian Model-Scenario Averaging (BMSA) is used to collate the resulting posteriors, to obtain a stochastic estimate of a Quantity of Interest (QoI) in an unmeasured (prediction) scenario. The scenario probabilities in BMSA are chosen using a sensor which automatically weights those scenarios in the calibration set which are similar to the prediction scenario. The methodology is applied to the class of turbulent boundary-layers subject to various pressure gradients. For all considered prediction scenarios the standard-deviation of the stochastic estimate is consistent with the measurement ground truth. Furthermore, the mean of the estimate is more consistently accurate than the individual model predictions.
Bayesian item fit analysis for unidimensional item response theory models.
Sinharay, Sandip
2006-11-01
Assessing item fit for unidimensional item response theory models for dichotomous items has always been an issue of enormous interest, but there exists no unanimously agreed item fit diagnostic for these models, and hence there is room for further investigation of the area. This paper employs the posterior predictive model-checking method, a popular Bayesian model-checking tool, to examine item fit for the above-mentioned models. An item fit plot, comparing the observed and predicted proportion-correct scores of examinees with different raw scores, is suggested. This paper also suggests how to obtain posterior predictive p-values (which are natural Bayesian p-values) for the item fit statistics of Orlando and Thissen that summarize numerically the information in the above-mentioned item fit plots. A number of simulation studies and a real data application demonstrate the effectiveness of the suggested item fit diagnostics. The suggested techniques seem to have adequate power and reasonable Type I error rate, and psychometricians will find them promising.
Quantum-Like Bayesian Networks for Modeling Decision Making.
Moreira, Catarina; Wichert, Andreas
2016-01-01
In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.
Predictive RANS simulations via Bayesian Model-Scenario Averaging
Edeling, W. N.; Cinnella, P.; Dwight, R. P.
2014-10-01
The turbulence closure model is the dominant source of error in most Reynolds-Averaged Navier-Stokes simulations, yet no reliable estimators for this error component currently exist. Here we develop a stochastic, a posteriori error estimate, calibrated to specific classes of flow. It is based on variability in model closure coefficients across multiple flow scenarios, for multiple closure models. The variability is estimated using Bayesian calibration against experimental data for each scenario, and Bayesian Model-Scenario Averaging (BMSA) is used to collate the resulting posteriors, to obtain a stochastic estimate of a Quantity of Interest (QoI) in an unmeasured (prediction) scenario. The scenario probabilities in BMSA are chosen using a sensor which automatically weights those scenarios in the calibration set which are similar to the prediction scenario. The methodology is applied to the class of turbulent boundary-layers subject to various pressure gradients. For all considered prediction scenarios the standard-deviation of the stochastic estimate is consistent with the measurement ground truth. Furthermore, the mean of the estimate is more consistently accurate than the individual model predictions.
Quantum-Like Bayesian Networks for Modeling Decision Making
Directory of Open Access Journals (Sweden)
Catarina eMoreira
2016-01-01
Full Text Available In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.
Generalized linear models with coarsened covariates: a practical Bayesian approach.
Johnson, Timothy R; Wiest, Michelle M
2014-06-01
Coarsened covariates are a common and sometimes unavoidable phenomenon encountered in statistical modeling. Covariates are coarsened when their values or categories have been grouped. This may be done to protect privacy or to simplify data collection or analysis when researchers are not aware of their drawbacks. Analyses with coarsened covariates based on ad hoc methods can compromise the validity of inferences. One valid method for accounting for a coarsened covariate is to use a marginal likelihood derived by summing or integrating over the unknown realizations of the covariate. However, algorithms for estimation based on this approach can be tedious to program and can be computationally expensive. These are significant obstacles to their use in practice. To overcome these limitations, we show that when expressed as a Bayesian probability model, a generalized linear model with a coarsened covariate can be posed as a tractable missing data problem where the missing data are due to censoring. We also show that this model is amenable to widely available general-purpose software for simulation-based inference for Bayesian probability models, providing researchers a very practical approach for dealing with coarsened covariates.
BAYESIAN ESTIMATION IN SHARED COMPOUND POISSON FRAILTY MODELS
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David D. Hanagal
2015-06-01
Full Text Available In this paper, we study the compound Poisson distribution as the shared frailty distribution and two different baseline distributions namely Pareto and linear failure rate distributions for modeling survival data. We are using the Markov Chain Monte Carlo (MCMC technique to estimate parameters of the proposed models by introducing the Bayesian estimation procedure. In the present study, a simulation is done to compare the true values of parameters with the estimated values. We try to fit the proposed models to a real life bivariate survival data set of McGrilchrist and Aisbett (1991 related to kidney infection. Also, we present a comparison study for the same data by using model selection criterion, and suggest a better frailty model out of two proposed frailty models.
Experimental validation of a Bayesian model of visual acuity.
LENUS (Irish Health Repository)
Dalimier, Eugénie
2009-01-01
Based on standard procedures used in optometry clinics, we compare measurements of visual acuity for 10 subjects (11 eyes tested) in the presence of natural ocular aberrations and different degrees of induced defocus, with the predictions given by a Bayesian model customized with aberrometric data of the eye. The absolute predictions of the model, without any adjustment, show good agreement with the experimental data, in terms of correlation and absolute error. The efficiency of the model is discussed in comparison with image quality metrics and other customized visual process models. An analysis of the importance and customization of each stage of the model is also given; it stresses the potential high predictive power from precise modeling of ocular and neural transfer functions.
Hierarchical Heteroclinics in Dynamical Model of Cognitive Processes: Chunking
Afraimovich, Valentin S.; Young, Todd R.; Rabinovich, Mikhail I.
Combining the results of brain imaging and nonlinear dynamics provides a new hierarchical vision of brain network functionality that is helpful in understanding the relationship of the network to different mental tasks. Using these ideas it is possible to build adequate models for the description and prediction of different cognitive activities in which the number of variables is usually small enough for analysis. The dynamical images of different mental processes depend on their temporal organization and, as a rule, cannot be just simple attractors since cognition is characterized by transient dynamics. The mathematical image for a robust transient is a stable heteroclinic channel consisting of a chain of saddles connected by unstable separatrices. We focus here on hierarchical chunking dynamics that can represent several cognitive activities. Chunking is the dynamical phenomenon that means dividing a long information chain into shorter items. Chunking is known to be important in many processes of perception, learning, memory and cognition. We prove that in the phase space of the model that describes chunking there exists a new mathematical object — heteroclinic sequence of heteroclinic cycles — using the technique of slow-fast approximations. This new object serves as a skeleton of motions reflecting sequential features of hierarchical chunking dynamics and is an adequate image of the chunking processing.
Wu, Haiyan
2013-01-01
General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…
Theory-based Bayesian models of inductive learning and reasoning.
Tenenbaum, Joshua B; Griffiths, Thomas L; Kemp, Charles
2006-07-01
Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.
Bayesian Gaussian Copula Factor Models for Mixed Data.
Murray, Jared S; Dunson, David B; Carin, Lawrence; Lucas, Joseph E
2013-06-01
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.
Bayesian statistic methods and theri application in probabilistic simulation models
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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.
Hierarchical modeling of cluster size in wildlife surveys
Royle, J. Andrew
2008-01-01
Clusters or groups of individuals are the fundamental unit of observation in many wildlife sampling problems, including aerial surveys of waterfowl, marine mammals, and ungulates. Explicit accounting of cluster size in models for estimating abundance is necessary because detection of individuals within clusters is not independent and detectability of clusters is likely to increase with cluster size. This induces a cluster size bias in which the average cluster size in the sample is larger than in the population at large. Thus, failure to account for the relationship between delectability and cluster size will tend to yield a positive bias in estimates of abundance or density. I describe a hierarchical modeling framework for accounting for cluster-size bias in animal sampling. The hierarchical model consists of models for the observation process conditional on the cluster size distribution and the cluster size distribution conditional on the total number of clusters. Optionally, a spatial model can be specified that describes variation in the total number of clusters per sample unit. Parameter estimation, model selection, and criticism may be carried out using conventional likelihood-based methods. An extension of the model is described for the situation where measurable covariates at the level of the sample unit are available. Several candidate models within the proposed class are evaluated for aerial survey data on mallard ducks (Anas platyrhynchos).
Preferential sampling and Bayesian geostatistics: Statistical modeling and examples.
Cecconi, Lorenzo; Grisotto, Laura; Catelan, Dolores; Lagazio, Corrado; Berrocal, Veronica; Biggeri, Annibale
2016-08-01
Preferential sampling refers to any situation in which the spatial process and the sampling locations are not stochastically independent. In this paper, we present two examples of geostatistical analysis in which the usual assumption of stochastic independence between the point process and the measurement process is violated. To account for preferential sampling, we specify a flexible and general Bayesian geostatistical model that includes a shared spatial random component. We apply the proposed model to two different case studies that allow us to highlight three different modeling and inferential aspects of geostatistical modeling under preferential sampling: (1) continuous or finite spatial sampling frame; (2) underlying causal model and relevant covariates; and (3) inferential goals related to mean prediction surface or prediction uncertainty.
Uncovering Transcriptional Regulatory Networks by Sparse Bayesian Factor Model
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Qi Yuan(Alan
2010-01-01
Full Text Available Abstract The problem of uncovering transcriptional regulation by transcription factors (TFs based on microarray data is considered. A novel Bayesian sparse correlated rectified factor model (BSCRFM is proposed that models the unknown TF protein level activity, the correlated regulations between TFs, and the sparse nature of TF-regulated genes. The model admits prior knowledge from existing database regarding TF-regulated target genes based on a sparse prior and through a developed Gibbs sampling algorithm, a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can be obtained. The proposed model and the Gibbs sampling algorithm were evaluated on the simulated systems, and results demonstrated the validity and effectiveness of the proposed approach. The proposed model was then applied to the breast cancer microarray data of patients with Estrogen Receptor positive ( status and Estrogen Receptor negative ( status, respectively.
Efficient multilevel brain tumor segmentation with integrated bayesian model classification.
Corso, J J; Sharon, E; Dube, S; El-Saden, S; Sinha, U; Yuille, A
2008-05-01
We present a new method for automatic segmentation of heterogeneous image data that takes a step toward bridging the gap between bottom-up affinity-based segmentation methods and top-down generative model based approaches. The main contribution of the paper is a Bayesian formulation for incorporating soft model assignments into the calculation of affinities, which are conventionally model free. We integrate the resulting model-aware affinities into the multilevel segmentation by weighted aggregation algorithm, and apply the technique to the task of detecting and segmenting brain tumor and edema in multichannel magnetic resonance (MR) volumes. The computationally efficient method runs orders of magnitude faster than current state-of-the-art techniques giving comparable or improved results. Our quantitative results indicate the benefit of incorporating model-aware affinities into the segmentation process for the difficult case of glioblastoma multiforme brain tumor.
Uncovering Transcriptional Regulatory Networks by Sparse Bayesian Factor Model
Meng, Jia; Zhang, Jianqiu(Michelle); Qi, Yuan(Alan); Chen, Yidong; Huang, Yufei
2010-12-01
The problem of uncovering transcriptional regulation by transcription factors (TFs) based on microarray data is considered. A novel Bayesian sparse correlated rectified factor model (BSCRFM) is proposed that models the unknown TF protein level activity, the correlated regulations between TFs, and the sparse nature of TF-regulated genes. The model admits prior knowledge from existing database regarding TF-regulated target genes based on a sparse prior and through a developed Gibbs sampling algorithm, a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can be obtained. The proposed model and the Gibbs sampling algorithm were evaluated on the simulated systems, and results demonstrated the validity and effectiveness of the proposed approach. The proposed model was then applied to the breast cancer microarray data of patients with Estrogen Receptor positive ([InlineEquation not available: see fulltext.]) status and Estrogen Receptor negative ([InlineEquation not available: see fulltext.]) status, respectively.
A hierarchical model for estimating density in camera-trap studies
Royle, J. Andrew; Nichols, James D.; Karanth, K.Ullas; Gopalaswamy, Arjun M.
2009-01-01
Estimating animal density using capture–recapture data from arrays of detection devices such as camera traps has been problematic due to the movement of individuals and heterogeneity in capture probability among them induced by differential exposure to trapping.We develop a spatial capture–recapture model for estimating density from camera-trapping data which contains explicit models for the spatial point process governing the distribution of individuals and their exposure to and detection by traps.We adopt a Bayesian approach to analysis of the hierarchical model using the technique of data augmentation.The model is applied to photographic capture–recapture data on tigers Panthera tigris in Nagarahole reserve, India. Using this model, we estimate the density of tigers to be 14·3 animals per 100 km2 during 2004.Synthesis and applications. Our modelling framework largely overcomes several weaknesses in conventional approaches to the estimation of animal density from trap arrays. It effectively deals with key problems such as individual heterogeneity in capture probabilities, movement of traps, presence of potential ‘holes’ in the array and ad hoc estimation of sample area. The formulation, thus, greatly enhances flexibility in the conduct of field surveys as well as in the analysis of data, from studies that may involve physical, photographic or DNA-based ‘captures’ of individual animals.
Iglesias, Juan Eugenio; Sabuncu, Mert Rory; Van Leemput, Koen
2012-01-01
Many successful segmentation algorithms are based on Bayesian models in which prior anatomical knowledge is combined with the available image information. However, these methods typically have many free parameters that are estimated to obtain point estimates only, whereas a faithful Bayesian analysis would also consider all possible alternate values these parameters may take. In this paper, we propose to incorporate the uncertainty of the free parameters in Bayesian segmentation models more a...
Bayesian inference for generalized linear models for spiking neurons
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Sebastian Gerwinn
2010-05-01
Full Text Available Generalized Linear Models (GLMs are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate.
MODELING INFORMATION SYSTEM AVAILABILITY BY USING BAYESIAN BELIEF NETWORK APPROACH
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Semir Ibrahimović
2016-03-01
Full Text Available Modern information systems are expected to be always-on by providing services to end-users, regardless of time and location. This is particularly important for organizations and industries where information systems support real-time operations and mission-critical applications that need to be available on 24 7 365 basis. Examples of such entities include process industries, telecommunications, healthcare, energy, banking, electronic commerce and a variety of cloud services. This article presents a modified Bayesian Belief Network model for predicting information system availability, introduced initially by Franke, U. and Johnson, P. (in article “Availability of enterprise IT systems – an expert based Bayesian model”. Software Quality Journal 20(2, 369-394, 2012 based on a thorough review of several dimensions of the information system availability, we proposed a modified set of determinants. The model is parameterized by using probability elicitation process with the participation of experts from the financial sector of Bosnia and Herzegovina. The model validation was performed using Monte Carlo simulation.
Bayesian network as a modelling tool for risk management in agriculture
DEFF Research Database (Denmark)
Rasmussen, Svend; Madsen, Anders Læsø; Lund, Mogens
. In this paper we use Bayesian networks as an integrated modelling approach for representing uncertainty and analysing risk management in agriculture. It is shown how historical farm account data may be efficiently used to estimate conditional probabilities, which are the core elements in Bayesian network models....... We further show how the Bayesian network model RiBay is used for stochastic simulation of farm income, and we demonstrate how RiBay can be used to simulate risk management at the farm level. It is concluded that the key strength of a Bayesian network is the transparency of assumptions...
Impacts of forest fragmentation on species richness: a hierarchical approach to community modelling
Zipkin, Elise F.; DeWan, Amielle; Royle, J. Andrew
2009-01-01
1. Species richness is often used as a tool for prioritizing conservation action. One method for predicting richness and other summaries of community structure is to develop species-specific models of occurrence probability based on habitat or landscape characteristics. However, this approach can be challenging for rare or elusive species for which survey data are often sparse. 2. Recent developments have allowed for improved inference about community structure based on species-specific models of occurrence probability, integrated within a hierarchical modelling framework. This framework offers advantages to inference about species richness over typical approaches by accounting for both species-level effects and the aggregated effects of landscape composition on a community as a whole, thus leading to increased precision in estimates of species richness by improving occupancy estimates for all species, including those that were observed infrequently. 3. We developed a hierarchical model to assess the community response of breeding birds in the Hudson River Valley, New York, to habitat fragmentation and analysed the model using a Bayesian approach. 4. The model was designed to estimate species-specific occurrence and the effects of fragment area and edge (as measured through the perimeter and the perimeter/area ratio, P/A), while accounting for imperfect detection of species. 5. We used the fitted model to make predictions of species richness within forest fragments of variable morphology. The model revealed that species richness of the observed bird community was maximized in small forest fragments with a high P/A. However, the number of forest interior species, a subset of the community with high conservation value, was maximized in large fragments with low P/A. 6. Synthesis and applications. Our results demonstrate the importance of understanding the responses of both individual, and groups of species, to environmental heterogeneity while illustrating the utility
An Extended Hierarchical Trusted Model for Wireless Sensor Networks
Institute of Scientific and Technical Information of China (English)
DU Ruiying; XU Mingdi; ZHANG Huanguo
2006-01-01
Cryptography and authentication are traditional approach for providing network security. However, they are not sufficient for solving the problems which malicious nodes compromise whole wireless sensor network leading to invalid data transmission and wasting resource by using vicious behaviors. This paper puts forward an extended hierarchical trusted architecture for wireless sensor network, and establishes trusted congregations by three-tier framework. The method combines statistics, economics with encrypt mechanism for developing two trusted models which evaluate cluster head nodes and common sensor nodes respectively. The models form logical trusted-link from command node to common sensor nodes and guarantees the network can run in secure and reliable circumstance.
Enhancing debris flow modeling parameters integrating Bayesian networks
Graf, C.; Stoffel, M.; Grêt-Regamey, A.
2009-04-01
Applied debris-flow modeling requires suitably constraint input parameter sets. Depending on the used model, there is a series of parameters to define before running the model. Normally, the data base describing the event, the initiation conditions, the flow behavior, the deposition process and mainly the potential range of possible debris flow events in a certain torrent is limited. There are only some scarce places in the world, where we fortunately can find valuable data sets describing event history of debris flow channels delivering information on spatial and temporal distribution of former flow paths and deposition zones. Tree-ring records in combination with detailed geomorphic mapping for instance provide such data sets over a long time span. Considering the significant loss potential associated with debris-flow disasters, it is crucial that decisions made in regard to hazard mitigation are based on a consistent assessment of the risks. This in turn necessitates a proper assessment of the uncertainties involved in the modeling of the debris-flow frequencies and intensities, the possible run out extent, as well as the estimations of the damage potential. In this study, we link a Bayesian network to a Geographic Information System in order to assess debris-flow risk. We identify the major sources of uncertainty and show the potential of Bayesian inference techniques to improve the debris-flow model. We model the flow paths and deposition zones of a highly active debris-flow channel in the Swiss Alps using the numerical 2-D model RAMMS. Because uncertainties in run-out areas cause large changes in risk estimations, we use the data of flow path and deposition zone information of reconstructed debris-flow events derived from dendrogeomorphological analysis covering more than 400 years to update the input parameters of the RAMMS model. The probabilistic model, which consistently incorporates this available information, can serve as a basis for spatial risk
Bayesian experimental design for models with intractable likelihoods.
Drovandi, Christopher C; Pettitt, Anthony N
2013-12-01
In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the precision of the ABC posterior distribution, which we form efficiently via the ABC rejection algorithm based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology for Markov process models of epidemics and macroparasite population evolution. The macroparasite example involves a multivariate process and we assess the loss of information from not observing all variables.
Recursive Bayesian recurrent neural networks for time-series modeling.
Mirikitani, Derrick T; Nikolaev, Nikolay
2010-02-01
This paper develops a probabilistic approach to recursive second-order training of recurrent neural networks (RNNs) for improved time-series modeling. A general recursive Bayesian Levenberg-Marquardt algorithm is derived to sequentially update the weights and the covariance (Hessian) matrix. The main strengths of the approach are a principled handling of the regularization hyperparameters that leads to better generalization, and stable numerical performance. The framework involves the adaptation of a noise hyperparameter and local weight prior hyperparameters, which represent the noise in the data and the uncertainties in the model parameters. Experimental investigations using artificial and real-world data sets show that RNNs equipped with the proposed approach outperform standard real-time recurrent learning and extended Kalman training algorithms for recurrent networks, as well as other contemporary nonlinear neural models, on time-series modeling.
Markov chain Monte Carlo simulation for Bayesian Hidden Markov Models
Chan, Lay Guat; Ibrahim, Adriana Irawati Nur Binti
2016-10-01
A hidden Markov model (HMM) is a mixture model which has a Markov chain with finite states as its mixing distribution. HMMs have been applied to a variety of fields, such as speech and face recognitions. The main purpose of this study is to investigate the Bayesian approach to HMMs. Using this approach, we can simulate from the parameters' posterior distribution using some Markov chain Monte Carlo (MCMC) sampling methods. HMMs seem to be useful, but there are some limitations. Therefore, by using the Mixture of Dirichlet processes Hidden Markov Model (MDPHMM) based on Yau et. al (2011), we hope to overcome these limitations. We shall conduct a simulation study using MCMC methods to investigate the performance of this model.
Bayesian Model Selection with Network Based Diffusion Analysis.
Whalen, Andrew; Hoppitt, William J E
2016-01-01
A number of recent studies have used Network Based Diffusion Analysis (NBDA) to detect the role of social transmission in the spread of a novel behavior through a population. In this paper we present a unified framework for performing NBDA in a Bayesian setting, and demonstrate how the Watanabe Akaike Information Criteria (WAIC) can be used for model selection. We present a specific example of applying this method to Time to Acquisition Diffusion Analysis (TADA). To examine the robustness of this technique, we performed a large scale simulation study and found that NBDA using WAIC could recover the correct model of social transmission under a wide range of cases, including under the presence of random effects, individual level variables, and alternative models of social transmission. This work suggests that NBDA is an effective and widely applicable tool for uncovering whether social transmission underpins the spread of a novel behavior, and may still provide accurate results even when key model assumptions are relaxed.
A Bayesian threshold-normal mixture model for analysis of a continuous mastitis-related trait.
Ødegård, J; Madsen, P; Gianola, D; Klemetsdal, G; Jensen, J; Heringstad, B; Korsgaard, I R
2005-07-01
Mastitis is associated with elevated somatic cell count in milk, inducing a positive correlation between milk somatic cell score (SCS) and the absence or presence of the disease. In most countries, selection against mastitis has focused on selecting parents with genetic evaluations that have low SCS. Univariate or multivariate mixed linear models have been used for statistical description of SCS. However, an observation of SCS can be regarded as drawn from a 2- (or more) component mixture defined by the (usually) unknown health status of a cow at the test-day on which SCS is recorded. A hierarchical 2-component mixture model was developed, assuming that the health status affecting the recorded test-day SCS is completely specified by an underlying liability variable. Based on the observed SCS, inferences can be drawn about disease status and parameters of both SCS and liability to mastitis. The prior probability of putative mastitis was allowed to vary between subgroups (e.g., herds, families), by specifying fixed and random effects affecting both SCS and liability. Using simulation, it was found that a Bayesian model fitted to the data yielded parameter estimates close to their true values. The model provides selection criteria that are more appealing than selection for lower SCS. The proposed model can be extended to handle a wide range of problems related to genetic analyses of mixture traits.
Long-Lead Prediction of Pacific SSTs via Bayesian Dynamic Modeling.
Berliner, L. Mark; Wikle, Christopher K.; Cressie, Noel
2000-11-01
Tropical Pacific sea surface temperatures (SSTs) and the accompanying El Niño-Southern Oscillation phenomenon are recognized as significant components of climate behavior. The atmospheric and oceanic processes involved display highly complicated variability over both space and time. Researchers have applied both physically derived modeling and statistical approaches to develop long-lead predictions of tropical Pacific SSTs. The comparative successes of these two approaches are a subject of substantial inquiry and some controversy. Presented in this article is a new procedure for long-lead forecasting of tropical Pacific SST fields that expresses qualitative aspects of scientific paradigms for SST dynamics in a statistical manner. Through this combining of substantial physical understanding and statistical modeling and learning, this procedure acquires considerable predictive skill. Specifically, a Markov model, applied to a low-order (empirical orthogonal function-based) dynamical system of tropical Pacific SST, with stochastic regime transition, is considered. The approach accounts explicitly for uncertainty in the formulation of the model, which leads to realistic error bounds on forecasts. The methodology that makes this possible is hierarchical Bayesian dynamical modeling.
Mendes, B. S.; Draper, D.
2008-12-01
The issue of model uncertainty and model choice is central in any groundwater modeling effort [Neuman and Wierenga, 2003]; among the several approaches to the problem we favour using Bayesian statistics because it is a method that integrates in a natural way uncertainties (arising from any source) and experimental data. In this work, we experiment with several Bayesian approaches to model choice, focusing primarily on demonstrating the usefulness of the Reversible Jump Markov Chain Monte Carlo (RJMCMC) simulation method [Green, 1995]; this is an extension of the now- common MCMC methods. Standard MCMC techniques approximate posterior distributions for quantities of interest, often by creating a random walk in parameter space; RJMCMC allows the random walk to take place between parameter spaces with different dimensionalities. This fact allows us to explore state spaces that are associated with different deterministic models for experimental data. Our work is exploratory in nature; we restrict our study to comparing two simple transport models applied to a data set gathered to estimate the breakthrough curve for a tracer compound in groundwater. One model has a mean surface based on a simple advection dispersion differential equation; the second model's mean surface is also governed by a differential equation but in two dimensions. We focus on artificial data sets (in which truth is known) to see if model identification is done correctly, but we also address the issues of over and under-paramerization, and we compare RJMCMC's performance with other traditional methods for model selection and propagation of model uncertainty, including Bayesian model averaging, BIC and DIC.References Neuman and Wierenga (2003). A Comprehensive Strategy of Hydrogeologic Modeling and Uncertainty Analysis for Nuclear Facilities and Sites. NUREG/CR-6805, Division of Systems Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research, U. S. Nuclear Regulatory Commission
C-HiLasso: A Collaborative Hierarchical Sparse Modeling Framework
Sprechmann, Pablo; Sapiro, Guillermo; Eldar, Yonina
2010-01-01
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso model at the individual feature level, with the block-sparsity property of the Group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the Hierarchical Lasso (HiLasso), which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level, but not necessarily at the lower (inside the group) level, obtaining the collaborative HiLasso model (C-HiLasso). Such signals then share the same active groups, or classes, but not necessarily the same active set. This model is very well suited for ap...
A Bisimulation-based Hierarchical Framework for Software Development Models
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Ping Liang
2013-08-01
Full Text Available Software development models have been ripen since the emergence of software engineering, like waterfall model, V-model, spiral model, etc. To ensure the successful implementation of those models, various metrics for software products and development process have been developed along, like CMMI, software metrics, and process re-engineering, etc. The quality of software products and processes can be ensured in consistence as much as possible and the abstract integrity of a software product can be achieved. However, in reality, the maintenance of software products is still high and even higher along with software evolution due to the inconsistence occurred by changes and inherent errors of software products. It is better to build up a robust software product that can sustain changes as many as possible. Therefore, this paper proposes a process algebra based hierarchical framework to extract an abstract equivalent of deliverable at the end of phases of a software product from its software development models. The process algebra equivalent of the deliverable is developed hierarchically with the development of the software product, applying bi-simulation to test run the deliverable of phases to guarantee the consistence and integrity of the software development and product in a trivially mathematical way. And an algorithm is also given to carry out the assessment of the phase deliverable in process algebra.
Facial animation on an anatomy-based hierarchical face model
Zhang, Yu; Prakash, Edmond C.; Sung, Eric
2003-04-01
In this paper we propose a new hierarchical 3D facial model based on anatomical knowledge that provides high fidelity for realistic facial expression animation. Like real human face, the facial model has a hierarchical biomechanical structure, incorporating a physically-based approximation to facial skin tissue, a set of anatomically-motivated facial muscle actuators and underlying skull structure. The deformable skin model has multi-layer structure to approximate different types of soft tissue. It takes into account the nonlinear stress-strain relationship of the skin and the fact that soft tissue is almost incompressible. Different types of muscle models have been developed to simulate distribution of the muscle force on the skin due to muscle contraction. By the presence of the skull model, our facial model takes advantage of both more accurate facial deformation and the consideration of facial anatomy during the interactive definition of facial muscles. Under the muscular force, the deformation of the facial skin is evaluated using numerical integration of the governing dynamic equations. The dynamic facial animation algorithm runs at interactive rate with flexible and realistic facial expressions to be generated.
Bayesian Dose-Response Modeling in Sparse Data
Kim, Steven B.
This book discusses Bayesian dose-response modeling in small samples applied to two different settings. The first setting is early phase clinical trials, and the second setting is toxicology studies in cancer risk assessment. In early phase clinical trials, experimental units are humans who are actual patients. Prior to a clinical trial, opinions from multiple subject area experts are generally more informative than the opinion of a single expert, but we may face a dilemma when they have disagreeing prior opinions. In this regard, we consider compromising the disagreement and compare two different approaches for making a decision. In addition to combining multiple opinions, we also address balancing two levels of ethics in early phase clinical trials. The first level is individual-level ethics which reflects the perspective of trial participants. The second level is population-level ethics which reflects the perspective of future patients. We extensively compare two existing statistical methods which focus on each perspective and propose a new method which balances the two conflicting perspectives. In toxicology studies, experimental units are living animals. Here we focus on a potential non-monotonic dose-response relationship which is known as hormesis. Briefly, hormesis is a phenomenon which can be characterized by a beneficial effect at low doses and a harmful effect at high doses. In cancer risk assessments, the estimation of a parameter, which is known as a benchmark dose, can be highly sensitive to a class of assumptions, monotonicity or hormesis. In this regard, we propose a robust approach which considers both monotonicity and hormesis as a possibility. In addition, We discuss statistical hypothesis testing for hormesis and consider various experimental designs for detecting hormesis based on Bayesian decision theory. Past experiments have not been optimally designed for testing for hormesis, and some Bayesian optimal designs may not be optimal under a
A hierarchical neuronal model for generation and online recognition of birdsongs.
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Izzet B Yildiz
2011-12-01
Full Text Available The neuronal system underlying learning, generation and recognition of song in birds is one of the best-studied systems in the neurosciences. Here, we use these experimental findings to derive a neurobiologically plausible, dynamic, hierarchical model of birdsong generation and transform it into a functional model of birdsong recognition. The generation model consists of neuronal rate models and includes critical anatomical components like the premotor song-control nucleus HVC (proper name, the premotor nucleus RA (robust nucleus of the arcopallium, and a model of the syringeal and respiratory organs. We use Bayesian inference of this dynamical system to derive a possible mechanism for how birds can efficiently and robustly recognize the songs of their conspecifics in an online fashion. Our results indicate that the specific way birdsong is generated enables a listening bird to robustly and rapidly perceive embedded information at multiple time scales of a song. The resulting mechanism can be useful for investigating the functional roles of auditory recognition areas and providing predictions for future birdsong experiments.
Perceptual decision making: Drift-diffusion model is equivalent to a Bayesian model
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Sebastian eBitzer
2014-02-01
Full Text Available Behavioural data obtained with perceptual decision making experiments are typically analysed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence towards a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses.
MATHEMATICAL RISK ANALYSIS: VIA NICHOLAS RISK MODEL AND BAYESIAN ANALYSIS
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Anass BAYAGA
2010-07-01
Full Text Available The objective of this second part of a two-phased study was to explorethe predictive power of quantitative risk analysis (QRA method andprocess within Higher Education Institution (HEI. The method and process investigated the use impact analysis via Nicholas risk model and Bayesian analysis, with a sample of hundred (100 risk analysts in a historically black South African University in the greater Eastern Cape Province.The first findings supported and confirmed previous literature (KingIII report, 2009: Nicholas and Steyn, 2008: Stoney, 2007: COSA, 2004 that there was a direct relationship between risk factor, its likelihood and impact, certiris paribus. The second finding in relation to either controlling the likelihood or the impact of occurrence of risk (Nicholas risk model was that to have a brighter risk reward, it was important to control the likelihood ofoccurrence of risks as compared with its impact so to have a direct effect on entire University. On the Bayesian analysis, thus third finding, the impact of risk should be predicted along three aspects. These aspects included the human impact (decisions made, the property impact (students and infrastructural based and the business impact. Lastly, the study revealed that although in most business cases, where as business cycles considerably vary dependingon the industry and or the institution, this study revealed that, most impacts in HEI (University was within the period of one academic.The recommendation was that application of quantitative risk analysisshould be related to current legislative framework that affects HEI.
Aggregated Residential Load Modeling Using Dynamic Bayesian Networks
Energy Technology Data Exchange (ETDEWEB)
Vlachopoulou, Maria; Chin, George; Fuller, Jason C.; Lu, Shuai
2014-09-28
Abstract—It is already obvious that the future power grid will have to address higher demand for power and energy, and to incorporate renewable resources of different energy generation patterns. Demand response (DR) schemes could successfully be used to manage and balance power supply and demand under operating conditions of the future power grid. To achieve that, more advanced tools for DR management of operations and planning are necessary that can estimate the available capacity from DR resources. In this research, a Dynamic Bayesian Network (DBN) is derived, trained, and tested that can model aggregated load of Heating, Ventilation, and Air Conditioning (HVAC) systems. DBNs can provide flexible and powerful tools for both operations and planing, due to their unique analytical capabilities. The DBN model accuracy and flexibility of use is demonstrated by testing the model under different operational scenarios.
Extended Bayesian Information Criteria for Gaussian Graphical Models
Foygel, Rina
2010-01-01
Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow. Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs. We demonstrate the performance of this criterion on simulated data when used in conjunction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordi...
Development of a Bayesian Belief Network Runway Incursion Model
Green, Lawrence L.
2014-01-01
In a previous paper, a statistical analysis of runway incursion (RI) events was conducted to ascertain their relevance to the top ten Technical Challenges (TC) of the National Aeronautics and Space Administration (NASA) Aviation Safety Program (AvSP). The study revealed connections to perhaps several of the AvSP top ten TC. That data also identified several primary causes and contributing factors for RI events that served as the basis for developing a system-level Bayesian Belief Network (BBN) model for RI events. The system-level BBN model will allow NASA to generically model the causes of RI events and to assess the effectiveness of technology products being developed under NASA funding. These products are intended to reduce the frequency of RI events in particular, and to improve runway safety in general. The development, structure and assessment of that BBN for RI events by a Subject Matter Expert panel are documented in this paper.
Bayesian reduced-order models for multiscale dynamical systems
Koutsourelakis, P S
2010-01-01
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical interest is computationally infeasible or impractical. In complex systems, with limited physical insight on the coherent behavior of their constituents, the only available information is data obtained from simulations of the trajectories of huge numbers of degrees of freedom over microscopic time scales. This paper discusses a Bayesian approach to deriving probabilistic coarse-grained models that simultaneously address the problems of identifying appropriate reduced coordinates and the effective dynamics in this lower-dimensional representation. At the core of the models proposed lie simple, low-dimensional dynamical systems which serve as the building blocks of the global model. These approximate the latent, generating sources and parameterize the reduced-order dynamics. We d...
Performance and Prediction: Bayesian Modelling of Fallible Choice in Chess
Haworth, Guy; Regan, Ken; di Fatta, Giuseppe
Evaluating agents in decision-making applications requires assessing their skill and predicting their behaviour. Both are well developed in Poker-like situations, but less so in more complex game and model domains. This paper addresses both tasks by using Bayesian inference in a benchmark space of reference agents. The concepts are explained and demonstrated using the game of chess but the model applies generically to any domain with quantifiable options and fallible choice. Demonstration applications address questions frequently asked by the chess community regarding the stability of the rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The last include alleged under-performance, fabrication of tournament results, and clandestine use of computer advice during competition. Beyond the model world of games, the aim is to improve fallible human performance in complex, high-value tasks.
Advances in Bayesian Model Based Clustering Using Particle Learning
Energy Technology Data Exchange (ETDEWEB)
Merl, D M
2009-11-19
Recent work by Carvalho, Johannes, Lopes and Polson and Carvalho, Lopes, Polson and Taddy introduced a sequential Monte Carlo (SMC) alternative to traditional iterative Monte Carlo strategies (e.g. MCMC and EM) for Bayesian inference for a large class of dynamic models. The basis of SMC techniques involves representing the underlying inference problem as one of state space estimation, thus giving way to inference via particle filtering. The key insight of Carvalho et al was to construct the sequence of filtering distributions so as to make use of the posterior predictive distribution of the observable, a distribution usually only accessible in certain Bayesian settings. Access to this distribution allows a reversal of the usual propagate and resample steps characteristic of many SMC methods, thereby alleviating to a large extent many problems associated with particle degeneration. Furthermore, Carvalho et al point out that for many conjugate models the posterior distribution of the static variables can be parametrized in terms of [recursively defined] sufficient statistics of the previously observed data. For models where such sufficient statistics exist, particle learning as it is being called, is especially well suited for the analysis of streaming data do to the relative invariance of its algorithmic complexity with the number of data observations. Through a particle learning approach, a statistical model can be fit to data as the data is arriving, allowing at any instant during the observation process direct quantification of uncertainty surrounding underlying model parameters. Here we describe the use of a particle learning approach for fitting a standard Bayesian semiparametric mixture model as described in Carvalho, Lopes, Polson and Taddy. In Section 2 we briefly review the previously presented particle learning algorithm for the case of a Dirichlet process mixture of multivariate normals. In Section 3 we describe several novel extensions to the original
About wave field modeling in hierarchic medium with fractal inclusions
Hachay, Olga; Khachay, Andrey
2014-05-01
The processes of oil gaseous deposits outworking are linked with moving of polyphase multicomponent media, which are characterized by no equilibrium and nonlinear rheological features. The real behavior of layered systems is defined as complicated rheology moving liquids and structural morphology of porous media. It is eargently needed to account those factors for substantial description of the filtration processes. Additionally we must account also the synergetic effects. That allows suggesting new methods of control and managing of complicated natural systems, which can research these effects. Thus our research is directed to the layered system, from which we have to outwork oil and which is a complicated hierarchic dynamical system with fractal inclusions. In that paper we suggest the algorithm of modeling of 2-d seismic field distribution in the heterogeneous medium with hierarchic inclusions. Also we can compare the integral 2-D for seismic field in a frame of local hierarchic heterogeneity with a porous inclusion and pure elastic inclusion for the case when the parameter Lame is equal to zero for the inclusions and the layered structure. For that case we can regard the problem for the latitude and longitudinal waves independently. Here we shall analyze the first case. The received results can be used for choosing criterions of joined seismic methods for high complicated media research.If the boundaries of the inclusion of the k rank are fractals, the surface and contour integrals in the integral equations must be changed to repeated fractional integrals of Riman-Liuvill type .Using the developed earlier 3-d method of induction electromagnetic frequency geometric monitoring we showed the opportunity of defining of physical and structural features of hierarchic oil layer structure and estimating of water saturating by crack inclusions. For visualization we had elaborated some algorithms and programs for constructing cross sections for two hierarchic structural
Doing bayesian data analysis a tutorial with R and BUGS
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
Mapping malaria risk in Bangladesh using Bayesian geostatistical models.
Reid, Heidi; Haque, Ubydul; Clements, Archie C A; Tatem, Andrew J; Vallely, Andrew; Ahmed, Syed Masud; Islam, Akramul; Haque, Rashidul
2010-10-01
Background malaria-control programs are increasingly dependent on accurate risk maps to effectively guide the allocation of interventions and resources. Advances in model-based geostatistics and geographical information systems (GIS) have enabled researchers to better understand factors affecting malaria transmission and thus, more accurately determine the limits of malaria transmission globally and nationally. Here, we construct Plasmodium falciparum risk maps for Bangladesh for 2007 at a scale enabling the malaria-control bodies to more accurately define the needs of the program. A comprehensive malaria-prevalence survey (N = 9,750 individuals; N = 354 communities) was carried out in 2007 across the regions of Bangladesh known to be endemic for malaria. Data were corrected to a standard age range of 2 to less than 10 years. Bayesian geostatistical logistic regression models with environmental covariates were used to predict P. falciparum prevalence for 2- to 10-year-old children (PfPR(2-10)) across the endemic areas of Bangladesh. The predictions were combined with gridded population data to estimate the number of individuals living in different endemicity classes. Across the endemic areas, the average PfPR(2-10) was 3.8%. Environmental variables selected for prediction were vegetation cover, minimum temperature, and elevation. Model validation statistics revealed that the final Bayesian geostatistical model had good predictive ability. Risk maps generated from the model showed a heterogeneous distribution of PfPR(2-10) ranging from 0.5% to 50%; 3.1 million people were estimated to be living in areas with a PfPR(2-10) greater than 1%. Contemporary GIS and model-based geostatistics can be used to interpolate malaria risk in Bangladesh. Importantly, malaria risk was found to be highly varied across the endemic regions, necessitating the targeting of resources to reduce the burden in these areas.
Bayesian network approach for modeling local failure in lung cancer
Oh, Jung Hun; Craft, Jeffrey; Al-Lozi, Rawan; Vaidya, Manushka; Meng, Yifan; Deasy, Joseph O; Bradley, Jeffrey D; Naqa, Issam El
2011-01-01
Locally advanced non-small cell lung cancer (NSCLC) patients suffer from a high local failure rate following radiotherapy. Despite many efforts to develop new dose-volume models for early detection of tumor local failure, there was no reported significant improvement in their application prospectively. Based on recent studies of biomarker proteins’ role in hypoxia and inflammation in predicting tumor response to radiotherapy, we hypothesize that combining physical and biological factors with a suitable framework could improve the overall prediction. To test this hypothesis, we propose a graphical Bayesian network framework for predicting local failure in lung cancer. The proposed approach was tested using two different datasets of locally advanced NSCLC patients treated with radiotherapy. The first dataset was collected retrospectively, which is comprised of clinical and dosimetric variables only. The second dataset was collected prospectively in which in addition to clinical and dosimetric information, blood was drawn from the patients at various time points to extract candidate biomarkers as well. Our preliminary results show that the proposed method can be used as an efficient method to develop predictive models of local failure in these patients and to interpret relationships among the different variables in the models. We also demonstrate the potential use of heterogenous physical and biological variables to improve the model prediction. With the first dataset, we achieved better performance compared with competing Bayesian-based classifiers. With the second dataset, the combined model had a slightly higher performance compared to individual physical and biological models, with the biological variables making the largest contribution. Our preliminary results highlight the potential of the proposed integrated approach for predicting post-radiotherapy local failure in NSCLC patients. PMID:21335651
Linguistic steganography on Twitter: hierarchical language modeling with manual interaction
Wilson, Alex; Blunsom, Phil; Ker, Andrew D.
2014-02-01
This work proposes a natural language stegosystem for Twitter, modifying tweets as they are written to hide 4 bits of payload per tweet, which is a greater payload than previous systems have achieved. The system, CoverTweet, includes novel components, as well as some already developed in the literature. We believe that the task of transforming covers during embedding is equivalent to unilingual machine translation (paraphrasing), and we use this equivalence to de ne a distortion measure based on statistical machine translation methods. The system incorporates this measure of distortion to rank possible tweet paraphrases, using a hierarchical language model; we use human interaction as a second distortion measure to pick the best. The hierarchical language model is designed to model the speci c language of the covers, which in this setting is the language of the Twitter user who is embedding. This is a change from previous work, where general-purpose language models have been used. We evaluate our system by testing the output against human judges, and show that humans are unable to distinguish stego tweets from cover tweets any better than random guessing.
Dynamical Properties of Potassium Ion Channels with a Hierarchical Model
Institute of Scientific and Technical Information of China (English)
ZHAN Yong; AN Hai-Long; YU Hui; ZHANG Su-Hua; HAN Ying-Rong
2006-01-01
@@ It is well known that potassium ion channels have higher permeability than K ions, and the permeable rate of a single K ion channel is about 108 ions per second. We develop a hierarchical model of potassium ion channel permeation involving ab initio quantum calculations and Brownian dynamics simulations, which can consistently explain a range of channel dynamics. The results show that the average velocity of K ions, the mean permeable time of K ions and the permeable rate of single channel are about 0.92nm/ns, 4.35ns and 2.30×108 ions/s,respectively.
A Hierarchical Model for Continuous Gesture Recognition Using Kinect
DEFF Research Database (Denmark)
Jensen, Søren Kejser; Moesgaard, Christoffer; Nielsen, Christoffer Samuel
2013-01-01
Human gesture recognition is an area, which has been studied thoroughly in recent years,and close to100% recognition rates in restricted environments have been achieved, often either with single separated gestures in the input stream, or with computationally intensive systems. The results...... are unfortunately not as striking, when it comes to a continuous stream of gestures. In this paper we introduce a hierarchical system for gesture recognition for use in a gaming setting, with a continuous stream of data. Layer 1 is based on Nearest Neighbor Search and layer 2 uses Hidden Markov Models. The system...
Hierarchical Stochastic Simulation Algorithm for SBML Models of Genetic Circuits
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Leandro eWatanabe
2014-11-01
Full Text Available This paper describes a hierarchical stochastic simulation algorithm which has been implemented within iBioSim, a tool used to model, analyze, and visualize genetic circuits. Many biological analysis tools flatten out hierarchy before simulation, but there are many disadvantages associated with this approach. First, the memory required to represent the model can quickly expand in the process. Second, the flattening process is computationally expensive. Finally, when modeling a dynamic cellular population within iBioSim, inlining the hierarchy of the model is inefficient since models must grow dynamically over time. This paper discusses a new approach to handle hierarchy on the fly to make the tool faster and more memory-efficient. This approach yields significant performance improvements as compared to the former flat analysis method.
A Hierarchical Model Architecture for Enterprise Integration in Chemical Industries
Institute of Scientific and Technical Information of China (English)
华贲; 周章玉; 成思危
2001-01-01
Towards integration of supply chain, manufacturing/production and investment decision making, this paper presents a hierarchical model architecture which contains six sub-models covering the areas of manufacturing control, production operation, design and revamp, production management, supply chain and investment decision making. Six types of flow, material, energy, information, humanware, partsware and capital are ciasified. These flows connect enterprise components/subsystems to formulate system topology and logical structure. Enterprise components/subsystems are abstracted to generic elementary and composite classes. Finally, the model architecture is applied to a management system of an integrated suply chain, and suggestion are made on the usage of the model architecture and further development of the model as well as imvlementation issues.
Hierarchical Model for the Evolution of Cloud Complexes
Sánchez, N; Sanchez, Nestor; Parravano, Antonio
1999-01-01
The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment. Based on this picture, a hierarchical model for the evolution of Cloud Complexes, including star formation, is constructed, that follows the mass evolution of each sub-structure by computing its mass exchange (evaporation or condensation) with its parent and children, which depends on the radiation density at the interphase. For the set of parameters used as a reference model, the system produces IMFs with a maximum at too high mass (~2 M_sun) and the characteristic times for evolution seem too long. We show that these properties can be improved by adjusting model parameters. However, the emphasis here is to illustrate some general properties of this nonlinear model for the star formation process. Notwithstanding the simplifications involved, the model reveals an essential fe...
Modelling of population dynamics of red king crab using Bayesian approach
Directory of Open Access Journals (Sweden)
Bakanev Sergey ...
2012-10-01
Modeling population dynamics based on the Bayesian approach enables to successfully resolve the above issues. The integration of the data from various studies into a unified model based on Bayesian parameter estimation method provides a much more detailed description of the processes occurring in the population.
Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data
Lee, Sik-Yum
2006-01-01
A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…
Dynamic Bayesian Network Modeling of Game Based Diagnostic Assessments. CRESST Report 837
Levy, Roy
2014-01-01
Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…
Bayesian Framework for Water Quality Model Uncertainty Estimation and Risk Management
A formal Bayesian methodology is presented for integrated model calibration and risk-based water quality management using Bayesian Monte Carlo simulation and maximum likelihood estimation (BMCML). The primary focus is on lucid integration of model calibration with risk-based wat...
Bayesian geostatistical modeling of Malaria Indicator Survey data in Angola.
Directory of Open Access Journals (Sweden)
Laura Gosoniu
Full Text Available The 2006-2007 Angola Malaria Indicator Survey (AMIS is the first nationally representative household survey in the country assessing coverage of the key malaria control interventions and measuring malaria-related burden among children under 5 years of age. In this paper, the Angolan MIS data were analyzed to produce the first smooth map of parasitaemia prevalence based on contemporary nationwide empirical data in the country. Bayesian geostatistical models were fitted to assess the effect of interventions after adjusting for environmental, climatic and socio-economic factors. Non-linear relationships between parasitaemia risk and environmental predictors were modeled by categorizing the covariates and by employing two non-parametric approaches, the B-splines and the P-splines. The results of the model validation showed that the categorical model was able to better capture the relationship between parasitaemia prevalence and the environmental factors. Model fit and prediction were handled within a Bayesian framework using Markov chain Monte Carlo (MCMC simulations. Combining estimates of parasitaemia prevalence with the number of children under we obtained estimates of the number of infected children in the country. The population-adjusted prevalence ranges from in Namibe province to in Malanje province. The odds of parasitaemia in children living in a household with at least ITNs per person was by 41% lower (CI: 14%, 60% than in those with fewer ITNs. The estimates of the number of parasitaemic children produced in this paper are important for planning and implementing malaria control interventions and for monitoring the impact of prevention and control activities.
Modeling Land-Use Decision Behavior with Bayesian Belief Networks
Directory of Open Access Journals (Sweden)
Inge Aalders
2008-06-01
Full Text Available The ability to incorporate and manage the different drivers of land-use change in a modeling process is one of the key challenges because they are complex and are both quantitative and qualitative in nature. This paper uses Bayesian belief networks (BBN to incorporate characteristics of land managers in the modeling process and to enhance our understanding of land-use change based on the limited and disparate sources of information. One of the two models based on spatial data represented land managers in the form of a quantitative variable, the area of individual holdings, whereas the other model included qualitative data from a survey of land managers. Random samples from the spatial data provided evidence of the relationship between the different variables, which I used to develop the BBN structure. The model was tested for four different posterior probability distributions, and results showed that the trained and learned models are better at predicting land use than the uniform and random models. The inference from the model demonstrated the constraints that biophysical characteristics impose on land managers; for older land managers without heirs, there is a higher probability of the land use being arable agriculture. The results show the benefits of incorporating a more complex notion of land managers in land-use models, and of using different empirical data sources in the modeling process. Future research should focus on incorporating more complex social processes into the modeling structure, as well as incorporating spatio-temporal dynamics in a BBN.
Japanese Dairy Cattle Productivity Analysis using Bayesian Network Model (BNM
Directory of Open Access Journals (Sweden)
Iqbal Ahmed
2016-11-01
Full Text Available Japanese Dairy Cattle Productivity Analysis is carried out based on Bayesian Network Model (BNM. Through the experiment with 280 Japanese anestrus Holstein dairy cow, it is found that the estimation for finding out the presence of estrous cycle using BNM represents almost 55% accuracy while considering all samples. On the contrary, almost 73% accurate estimation could be achieved while using suspended likelihood in sample datasets. Moreover, while the proposed BNM model have more confidence then the estimation accuracy is lies in between 93 to 100%. In addition, this research also reveals the optimum factors to find out the presence of estrous cycle among the 270 individual dairy cows. The objective estimation methods using BNM definitely lead a unique idea to overcome the error of subjective estimation of having estrous cycle among these Japanese dairy cattle.
Kang, Hakmook; Ombao, Hernando; Fonnesbeck, Christopher; Ding, Zhaohua; Morgan, Victoria L
2017-03-19
Current approaches separately analyze concurrently acquired diffusion tensor imaging (DTI) and functional magnetic resonance imaging (fMRI) data. The primary limitation of these approaches is that they do not take advantage of the information from DTI that could potentially enhance estimation of resting state functional connectivity (FC) between brain regions. To overcome this limitation, we develop a Bayesian hierarchical spatio-temporal model that incorporates structural connectivity into estimating FC. In our proposed approach, structural connectivity (SC) based on DTI data is used to construct an informative prior for functional connectivity based on resting state fMRI data via the Cholesky decomposition. Simulation studies showed that incorporating the two data produced significantly reduced mean squared errors compared to the standard approach of separately analyzing the two data from different modalities. We applied our model to analyze the resting state DTI and fMRI data collected to estimate FC between the brain regions that were hypothetically important in the origination and spread of temporal lobe epilepsy seizures. Our analysis concludes that the proposed model achieves smaller false positive rates and is much robust to data decimation compared to the conventional approach.
Predicting bison migration out of Yellowstone National Park using bayesian models.
Directory of Open Access Journals (Sweden)
Chris Geremia
Full Text Available Long distance migrations by ungulate species often surpass the boundaries of preservation areas where conflicts with various publics lead to management actions that can threaten populations. We chose the partially migratory bison (Bison bison population in Yellowstone National Park as an example of integrating science into management policies to better conserve migratory ungulates. Approximately 60% of these bison have been exposed to bovine brucellosis and thousands of migrants exiting the park boundary have been culled during the past two decades to reduce the risk of disease transmission to cattle. Data were assimilated using models representing competing hypotheses of bison migration during 1990-2009 in a hierarchal bayesian framework. Migration differed at the scale of herds, but a single unifying logistic model was useful for predicting migrations by both herds. Migration beyond the northern park boundary was affected by herd size, accumulated snow water equivalent, and aboveground dried biomass. Migration beyond the western park boundary was less influenced by these predictors and process model performance suggested an important control on recent migrations was excluded. Simulations of migrations over the next decade suggest that allowing increased numbers of bison beyond park boundaries during severe climate conditions may be the only means of avoiding episodic, large-scale reductions to the Yellowstone bison population in the foreseeable future. This research is an example of how long distance migration dynamics can be incorporated into improved management policies.
A Bayesian spatio-temporal geostatistical model with an auxiliary lattice for large datasets
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.
Bayesian selection of nucleotide substitution models and their site assignments.
Wu, Chieh-Hsi; Suchard, Marc A; Drummond, Alexei J
2013-03-01
Probabilistic inference of a phylogenetic tree from molecular sequence data is predicated on a substitution model describing the relative rates of change between character states along the tree for each site in the multiple sequence alignment. Commonly, one assumes that the substitution model is homogeneous across sites within large partitions of the alignment, assigns these partitions a priori, and then fixes their underlying substitution model to the best-fitting model from a hierarchy of named models. Here, we introduce an automatic model selection and model averaging approach within a Bayesian framework that simultaneously estimates the number of partitions, the assignment of sites to partitions, the substitution model for each partition, and the uncertainty in these selections. This new approach is implemented as an add-on to the BEAST 2 software platform. We find that this approach dramatically improves the fit of the nucleotide substitution model compared with existing approaches, and we show, using a number of example data sets, that as many as nine partitions are required to explain the heterogeneity in nucleotide substitution process across sites in a single gene analysis. In some instances, this improved modeling of the substitution process can have a measurable effect on downstream inference, including the estimated phylogeny, relative divergence times, and effective population size histories.
Reconstruction of late Holocene climate based on tree growth and mechanistic hierarchical models
Tipton, John; Hooten, Mevin B.; Pederson, Neil; Tingley, Martin; Bishop, Daniel
2016-01-01
Reconstruction of pre-instrumental, late Holocene climate is important for understanding how climate has changed in the past and how climate might change in the future. Statistical prediction of paleoclimate from tree ring widths is challenging because tree ring widths are a one-dimensional summary of annual growth that represents a multi-dimensional set of climatic and biotic influences. We develop a Bayesian hierarchical framework using a nonlinear, biologically motivated tree ring growth model to jointly reconstruct temperature and precipitation in the Hudson Valley, New York. Using a common growth function to describe the response of a tree to climate, we allow for species-specific parameterizations of the growth response. To enable predictive backcasts, we model the climate variables with a vector autoregressive process on an annual timescale coupled with a multivariate conditional autoregressive process that accounts for temporal correlation and cross-correlation between temperature and precipitation on a monthly scale. Our multi-scale temporal model allows for flexibility in the climate response through time at different temporal scales and predicts reasonable climate scenarios given tree ring width data.
Inference in HIV dynamics models via hierarchical likelihood
Commenges, D; Putter, H; Thiebaut, R
2010-01-01
HIV dynamical models are often based on non-linear systems of ordinary differential equations (ODE), which do not have analytical solution. Introducing random effects in such models leads to very challenging non-linear mixed-effects models. To avoid the numerical computation of multiple integrals involved in the likelihood, we propose a hierarchical likelihood (h-likelihood) approach, treated in the spirit of a penalized likelihood. We give the asymptotic distribution of the maximum h-likelihood estimators (MHLE) for fixed effects, a result that may be relevant in a more general setting. The MHLE are slightly biased but the bias can be made negligible by using a parametric bootstrap procedure. We propose an efficient algorithm for maximizing the h-likelihood. A simulation study, based on a classical HIV dynamical model, confirms the good properties of the MHLE. We apply it to the analysis of a clinical trial.
Item Response Theory Using Hierarchical Generalized Linear Models
Directory of Open Access Journals (Sweden)
Hamdollah Ravand
2015-03-01
Full Text Available Multilevel models (MLMs are flexible in that they can be employed to obtain item and person parameters, test for differential item functioning (DIF and capture both local item and person dependence. Papers on the MLM analysis of item response data have focused mostly on theoretical issues where applications have been add-ons to simulation studies with a methodological focus. Although the methodological direction was necessary as a first step to show how MLMs can be utilized and extended to model item response data, the emphasis needs to be shifted towards providing evidence on how applications of MLMs in educational testing can provide the benefits that have been promised. The present study uses foreign language reading comprehension data to illustrate application of hierarchical generalized models to estimate person and item parameters, differential item functioning (DIF, and local person dependence in a three-level model.
Diagnosing Hybrid Systems: a Bayesian Model Selection Approach
McIlraith, Sheila A.
2005-01-01
In this paper we examine the problem of monitoring and diagnosing noisy complex dynamical systems that are modeled as hybrid systems-models of continuous behavior, interleaved by discrete transitions. In particular, we examine continuous systems with embedded supervisory controllers that experience abrupt, partial or full failure of component devices. Building on our previous work in this area (MBCG99;MBCG00), our specific focus in this paper ins on the mathematical formulation of the hybrid monitoring and diagnosis task as a Bayesian model tracking algorithm. The nonlinear dynamics of many hybrid systems present challenges to probabilistic tracking. Further, probabilistic tracking of a system for the purposes of diagnosis is problematic because the models of the system corresponding to failure modes are numerous and generally very unlikely. To focus tracking on these unlikely models and to reduce the number of potential models under consideration, we exploit logic-based techniques for qualitative model-based diagnosis to conjecture a limited initial set of consistent candidate models. In this paper we discuss alternative tracking techniques that are relevant to different classes of hybrid systems, focusing specifically on a method for tracking multiple models of nonlinear behavior simultaneously using factored sampling and conditional density propagation. To illustrate and motivate the approach described in this paper we examine the problem of monitoring and diganosing NASA's Sprint AERCam, a small spherical robotic camera unit with 12 thrusters that enable both linear and rotational motion.
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.
Bayesian network models for error detection in radiotherapy plans.
Kalet, Alan M; Gennari, John H; Ford, Eric C; Phillips, Mark H
2015-04-07
The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network's conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.
Study of hierarchical federation architecture using multi-resolution modeling
Institute of Scientific and Technical Information of China (English)
HAO Yan-ling; SHEN Dong-hui; QIAN Hua-ming; DENG Ming-hui
2004-01-01
This paper aims at finding a solution to the problem aroused in complex system simulation, where a specific functional federation is coupled with other simulation systems. In other words, the communication information within the system may be received by other federates that participated in this united simulation. For the purpose of ensuring simulation system unitary character, a hierarchical federation architecture (HFA) is taken. Also considering the real situation, where federates in a complicated simulation system can be made simpler to an extent, a multi-resolution modeling (MRM) method is imported to implement the design of hierarchical federation. By utilizing the multiple resolution entity (MRE) modeling approach, MRE for federates are designed out. When different level training simulation is required, the appropriate MRE at corresponding layers can be called. The design method realizes the reuse feature of the simulation system and reduces simulation complexity and improves the validity of system Simulation Cost (SC). Taking submarine voyage training simulator (SVTS) for instance, a HFA for submarine is constructed inthis paper, which approves the feasibility of studied approach.
A stochastic model for detecting overlapping and hierarchical community structure.
Directory of Open Access Journals (Sweden)
Xiaochun Cao
Full Text Available Community detection is a fundamental problem in the analysis of complex networks. Recently, many researchers have concentrated on the detection of overlapping communities, where a vertex may belong to more than one community. However, most current methods require the number (or the size of the communities as a priori information, which is usually unavailable in real-world networks. Thus, a practical algorithm should not only find the overlapping community structure, but also automatically determine the number of communities. Furthermore, it is preferable if this method is able to reveal the hierarchical structure of networks as well. In this work, we firstly propose a generative model that employs a nonnegative matrix factorization (NMF formulization with a l(2,1 norm regularization term, balanced by a resolution parameter. The NMF has the nature that provides overlapping community structure by assigning soft membership variables to each vertex; the l(2,1 regularization term is a technique of group sparsity which can automatically determine the number of communities by penalizing too many nonempty communities; and hence the resolution parameter enables us to explore the hierarchical structure of networks. Thereafter, we derive the multiplicative update rule to learn the model parameters, and offer the proof of its correctness. Finally, we test our approach on a variety of synthetic and real-world networks, and compare it with some state-of-the-art algorithms. The results validate the superior performance of our new method.
Evidence on Features of a DSGE Business Cycle Model from Bayesian Model Averaging
R.W. Strachan (Rodney); H.K. van Dijk (Herman)
2012-01-01
textabstractThe empirical support for features of a Dynamic Stochastic General Equilibrium model with two technology shocks is valuated using Bayesian model averaging over vector autoregressions. The model features include equilibria, restrictions on long-run responses, a structural break of unknown
Hierarchical Modelling of Flood Risk for Engineering Decision Analysis
DEFF Research Database (Denmark)
Custer, Rocco
. The methodology is applied to the disaggregation of portfolios of buildings in two communes in Switzerland. The relevance of disaggregation uncertainty to natural hazard risk assessment is illustrated with a simple flood risk assessment example. A second challenge - fragility and vulnerability modelling of all...... in the present thesis. First, design and optimisation of a hierarchical flood protection system generally entails decisions about structures at different spatial scales, which, in turn, may require risk assessment at different spatial resolutions and levels of detail. Consistent risk modelling at different...... spatial scales may therefore require up- and downscaling of data and models under due consideration of uncertainties and dependencies. In this thesis, a methodology is proposed for spatially disaggregating an aggregated building portfolio considering disaggregation uncertainty and spatial correlation...
Learning Hierarchical User Interest Models from Web Pages
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
We propose an algorithm for learning hierarchical user interest models according to the Web pages users have browsed. In this algorithm, the interests of a user are represented into a tree which is called a user interest tree, the content and the structure of which can change simultaneously to adapt to the changes in a user's interests. This expression represents a user's specific and general interests as a continuum. In some sense, specific interests correspond to short-term interests, while general interests correspond to long-term interests. So this representation more really reflects the users' interests. The algorithm can automatically model a user's multiple interest domains, dynamically generate the interest models and prune a user interest tree when the number of the nodes in it exceeds given value. Finally, we show the experiment results in a Chinese Web Site.
Multi-mode clustering model for hierarchical wireless sensor networks
Hu, Xiangdong; Li, Yongfu; Xu, Huifen
2017-03-01
The topology management, i.e., clusters maintenance, of wireless sensor networks (WSNs) is still a challenge due to its numerous nodes, diverse application scenarios and limited resources as well as complex dynamics. To address this issue, a multi-mode clustering model (M2 CM) is proposed to maintain the clusters for hierarchical WSNs in this study. In particular, unlike the traditional time-trigger model based on the whole-network and periodic style, the M2 CM is proposed based on the local and event-trigger operations. In addition, an adaptive local maintenance algorithm is designed for the broken clusters in the WSNs using the spatial-temporal demand changes accordingly. Numerical experiments are performed using the NS2 network simulation platform. Results validate the effectiveness of the proposed model with respect to the network maintenance costs, node energy consumption and transmitted data as well as the network lifetime.
Bayesian modeling of consumer behavior in the presence of anonymous visits
Novak, Julie Esther
Tailoring content to consumers has become a hallmark of marketing and digital media, particularly as it has become easier to identify customers across usage or purchase occasions. However, across a wide variety of contexts, companies find that customers do not consistently identify themselves, leaving a substantial fraction of anonymous visits. We develop a Bayesian hierarchical model that allows us to probabilistically assign anonymous sessions to users. These probabilistic assignments take into account a customer's demographic information, frequency of visitation, activities taken when visiting, and times of arrival. We present two studies, one with synthetic and one with real data, where we demonstrate improved performance over two popular practices (nearest-neighbor matching and deleting the anonymous visits) due to increased efficiency and reduced bias driven by the non-ignorability of which types of events are more likely to be anonymous. Using our proposed model, we avoid potential bias in understanding the effect of a firm's marketing on its customers, improve inference about the total number of customers in the dataset, and provide more precise targeted marketing to both previously observed and unobserved customers.
Bayesian Modeling of MPSS Data: Gene Expression Analysis of Bovine Salmonella Infection
Dhavala, Soma S.
2010-09-01
Massively Parallel Signature Sequencing (MPSS) is a high-throughput, counting-based technology available for gene expression profiling. It produces output that is similar to Serial Analysis of Gene Expression and is ideal for building complex relational databases for gene expression. Our goal is to compare the in vivo global gene expression profiles of tissues infected with different strains of Salmonella obtained using the MPSS technology. In this article, we develop an exact ANOVA type model for this count data using a zero-inflatedPoisson distribution, different from existing methods that assume continuous densities. We adopt two Bayesian hierarchical models-one parametric and the other semiparametric with a Dirichlet process prior that has the ability to "borrow strength" across related signatures, where a signature is a specific arrangement of the nucleotides, usually 16-21 base pairs long. We utilize the discreteness of Dirichlet process prior to cluster signatures that exhibit similar differential expression profiles. Tests for differential expression are carried out using nonparametric approaches, while controlling the false discovery rate. We identify several differentially expressed genes that have important biological significance and conclude with a summary of the biological discoveries. This article has supplementary materials online. © 2010 American Statistical Association.
Bridging groundwater models and decision support with a Bayesian network
Fienen, Michael N.; Masterson, John P.; Plant, Nathaniel G.; Gutierrez, Benjamin T.; Thieler, E. Robert
2013-01-01
Resource managers need to make decisions to plan for future environmental conditions, particularly sea level rise, in the face of substantial uncertainty. Many interacting processes factor in to the decisions they face. Advances in process models and the quantification of uncertainty have made models a valuable tool for this purpose. Long-simulation runtimes and, often, numerical instability make linking process models impractical in many cases. A method for emulating the important connections between model input and forecasts, while propagating uncertainty, has the potential to provide a bridge between complicated numerical process models and the efficiency and stability needed for decision making. We explore this using a Bayesian network (BN) to emulate a groundwater flow model. We expand on previous approaches to validating a BN by calculating forecasting skill using cross validation of a groundwater model of Assateague Island in Virginia and Maryland, USA. This BN emulation was shown to capture the important groundwater-flow characteristics and uncertainty of the groundwater system because of its connection to island morphology and sea level. Forecast power metrics associated with the validation of multiple alternative BN designs guided the selection of an optimal level of BN complexity. Assateague island is an ideal test case for exploring a forecasting tool based on current conditions because the unique hydrogeomorphological variability of the island includes a range of settings indicative of past, current, and future conditions. The resulting BN is a valuable tool for exploring the response of groundwater conditions to sea level rise in decision support.
Evaluating a fish monitoring protocol using state-space hierarchical models
Russell, Robin E.; Schmetterling, David A.; Guy, Chris S.; Shepard, Bradley B.; McFarland, Robert; Skaar, Donald
2012-01-01
Using data collected from three river reaches in Montana, we evaluated our ability to detect population trends and predict fish future fish abundance. Data were collected as part of a long-term monitoring program conducted by Montana Fish, Wildlife and Parks to primarily estimate rainbow (Oncorhynchus mykiss) and brown trout (Salmo trutta) abundance in numerous rivers across Montana. We used a hierarchical Bayesian mark-recapture model to estimate fish abundance over time in each of the three river reaches. We then fit a state-space Gompertz model to estimate current trends and future fish populations. Density dependent effects were detected in 1 of the 6 fish populations. Predictions of future fish populations displayed wide credible intervals. Our simulations indicated that given the observed variation in the abundance estimates, the probability of detecting a 30% decline in fish populations over a five-year period was less than 50%. We recommend a monitoring program that is closely tied to management objectives and reflects the precision necessary to make informed management decisions.