Directory of Open Access Journals (Sweden)
Githure John I
2009-09-01
Full Text Available Abstract Background Autoregressive regression coefficients for Anopheles arabiensis aquatic habitat models are usually assessed using global error techniques and are reported as error covariance matrices. A global statistic, however, will summarize error estimates from multiple habitat locations. This makes it difficult to identify where there are clusters of An. arabiensis aquatic habitats of acceptable prediction. It is therefore useful to conduct some form of spatial error analysis to detect clusters of An. arabiensis aquatic habitats based on uncertainty residuals from individual sampled habitats. In this research, a method of error estimation for spatial simulation models was demonstrated using autocorrelation indices and eigenfunction spatial filters to distinguish among the effects of parameter uncertainty on a stochastic simulation of ecological sampled Anopheles aquatic habitat covariates. A test for diagnostic checking error residuals in an An. arabiensis aquatic habitat model may enable intervention efforts targeting productive habitats clusters, based on larval/pupal productivity, by using the asymptotic distribution of parameter estimates from a residual autocovariance matrix. The models considered in this research extends a normal regression analysis previously considered in the literature. Methods Field and remote-sampled data were collected during July 2006 to December 2007 in Karima rice-village complex in Mwea, Kenya. SAS 9.1.4® was used to explore univariate statistics, correlations, distributions, and to generate global autocorrelation statistics from the ecological sampled datasets. A local autocorrelation index was also generated using spatial covariance parameters (i.e., Moran's Indices in a SAS/GIS® database. The Moran's statistic was decomposed into orthogonal and uncorrelated synthetic map pattern components using a Poisson model with a gamma-distributed mean (i.e. negative binomial regression. The eigenfunction
An Autoregressive Method for Simulation Output Analysis.
1982-12-01
Spectral Density Function 24 3 THE AUTOREGRESSIVE METHOD AND ITS APPLICATIONS...precision of point estimates can be approximated arbitrarily closely by the spectral density function at zero of a finite order autoregressive process...also develop some approximation theorems for continuous spectral density function . It is then demonstrated that a continuous spectral density function
Autoregressive hidden Markov models for the early detection of neonatal sepsis.
Stanculescu, Ioan; Williams, Christopher K I; Freer, Yvonne
2014-09-01
Late onset neonatal sepsis is one of the major clinical concerns when premature babies receive intensive care. Current practice relies on slow laboratory testing of blood cultures for diagnosis. A valuable research question is whether sepsis can be reliably detected before the blood sample is taken. This paper investigates the extent to which physiological events observed in the patient's monitoring traces could be used for the early detection of neonatal sepsis. We model the distribution of these events with an autoregressive hidden Markov model (AR-HMM). Both learning and inference carefully use domain knowledge to extract the baby's true physiology from the monitoring data. Our model can produce real-time predictions about the onset of the infection and also handles missing data. We evaluate the effectiveness of the AR-HMM for sepsis detection on a dataset collected from the Neonatal Intensive Care Unit at the Royal Infirmary of Edinburgh.
Bias-correction in vector autoregressive models: A simulation study
DEFF Research Database (Denmark)
Engsted, Tom; Pedersen, Thomas Quistgaard
We analyze and compare the properties of various methods for bias-correcting parameter estimates in vector autoregressions. First, we show that two analytical bias formulas from the existing literature are in fact identical. Next, based on a detailed simulation study, we show that this simple and...
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.
Parallel Markov chain Monte Carlo simulations.
Ren, Ruichao; Orkoulas, G
2007-06-07
With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.
Institute of Scientific and Technical Information of China (English)
DONG Ming
2008-01-01
As a new maintenance method, CBM (condition based maintenance) is becoming more and more important for the health management of complicated and costly equipment. A prerequisite to widespread deployment of CBM technology and prac-tice in industry is effective diagnostics and prognostics. Recently, a pattern recog-nition technique called HMM (hidden Markov model) was widely used in many fields. However, due to some unrealistic assumptions, diagnositic results from HMM were not so good, and it was difficult to use HMM directly for prognosis. By relaxing the unrealistic assumptions in HMM, this paper presents a novel approach to equip-ment health management based on auto-regressive hidden semi-Markov model (AR-HSMM). Compared with HMM, AR-HSMM has three advantages: 1)It allows explicitly modeling the time duration of the hidden states and therefore is capable of prognosis. 2) It can relax observations' independence assumption by accom-modating a link between consecutive observations. 3) It does not follow the unre-alistic Markov chain's memoryless assumption and therefore provides more pow-erful modeling and analysis capability for real problems. To facilitate the computation in the proposed AR-HSMM-based diagnostics and prognostics, new forwardbackward variables are defined and a modified forward-backward algorithm is developed. The evaluation of the proposed methodology was carried out through a real world application case study: health diagnosis and prognosis of hydraulic pumps in Caterpillar Inc. The testing results show that the proposed new approach based on AR-HSMM is effective and can provide useful support for the decision-making in equipment health management.
Bias-Correction in Vector Autoregressive Models: A Simulation Study
Directory of Open Access Journals (Sweden)
Tom Engsted
2014-03-01
Full Text Available We analyze the properties of various methods for bias-correcting parameter estimates in both stationary and non-stationary vector autoregressive models. First, we show that two analytical bias formulas from the existing literature are in fact identical. Next, based on a detailed simulation study, we show that when the model is stationary this simple bias formula compares very favorably to bootstrap bias-correction, both in terms of bias and mean squared error. In non-stationary models, the analytical bias formula performs noticeably worse than bootstrapping. Both methods yield a notable improvement over ordinary least squares. We pay special attention to the risk of pushing an otherwise stationary model into the non-stationary region of the parameter space when correcting for bias. Finally, we consider a recently proposed reduced-bias weighted least squares estimator, and we find that it compares very favorably in non-stationary models.
DEFF Research Database (Denmark)
Pinson, Pierre; Madsen, Henrik
2008-01-01
Better modelling and forecasting of very short-term power fluctuations at large offshore wind farms may significantly enhance control and management strategies of their power output. The paper introduces a new methodology for modelling and forecasting such very short-term fluctuations. The propos...... consists in 1-step ahead forecasting exercise on time-series of wind generation with a time resolution of 10 minute. The quality of the introduced forecasting methodology and its interest for better understanding power fluctuations are finally discussed.......Better modelling and forecasting of very short-term power fluctuations at large offshore wind farms may significantly enhance control and management strategies of their power output. The paper introduces a new methodology for modelling and forecasting such very short-term fluctuations. The proposed...... methodology is based on a Markov-switching autoregressive model with time-varying coefficients. An advantage of the method is that one can easily derive full predictive densities. The quality of this methodology is demonstrated from the test case of 2 large offshore wind farms in Denmark. The exercise...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time...... series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of the asymptotic covariance, which is used in the simulations and the analysis of some...
Cosmological Markov Chain Monte Carlo simulation with Cmbeasy
Müller, C M
2004-01-01
We introduce a Markov Chain Monte Carlo simulation and data analysis package for the cosmological computation package Cmbeasy. We have taken special care in implementing an adaptive step algorithm for the Markov Chain Monte Carlo in order to improve convergence. Data analysis routines are provided which allow to test models of the Universe against up-to-date measurements of the Cosmic Microwave Background, Supernovae Ia and Large Scale Structure. The observational data is provided with the software for convenient usage. The package is publicly available as part of the Cmbeasy software at www.cmbeasy.org.
Directory of Open Access Journals (Sweden)
Carlos Alejandro De Luna Ortega
2006-01-01
Full Text Available En este artículo se aborda el diseño de un reconocedor de voz, con el idioma español mexicano, del estado de Aguascalientes, de palabras aisladas, con dependencia del hablante y vocabulario pequeño, empleando Redes Neuronales Artificiales (ANN por sus siglas en inglés, Alineamiento Dinámico del Tiempo (DTW por sus siglas en inglés y Modelos Ocultos de Markov (HMM por sus siglas en inglés para la realización del algoritmo de reconocimiento.
Revisiting Weak Simulation for Substochastic Markov Chains
DEFF Research Database (Denmark)
Jansen, David N.; Song, Lei; Zhang, Lijun
2013-01-01
The spectrum of branching-time relations for probabilistic systems has been investigated thoroughly by Baier, Hermanns, Katoen and Wolf (2003, 2005), including weak simulation for systems involving substochastic distributions. Weak simulation was proven to be sound w.r.t. the liveness fragment...
Loukas, Constantinos; Georgiou, Evangelos
2013-01-01
There is currently great interest in analyzing the workflow of minimally invasive operations performed in a physical or simulation setting, with the aim of extracting important information that can be used for skills improvement, optimization of intraoperative processes, and comparison of different interventional strategies. The first step in achieving this goal is to segment the operation into its key interventional phases, which is currently approached by modeling a multivariate signal that describes the temporal usage of a predefined set of tools. Although this technique has shown promising results, it is challenged by the manual extraction of the tool usage sequence and the inability to simultaneously evaluate the surgeon's skills. In this paper we describe an alternative methodology for surgical phase segmentation and performance analysis based on Gaussian mixture multivariate autoregressive (GMMAR) models of the hand kinematics. Unlike previous work in this area, our technique employs signals from orientation sensors, attached to the endoscopic instruments of a virtual reality simulator, without considering which tools are employed at each time-step of the operation. First, based on pre-segmented hand motion signals, a training set of regression coefficients is created for each surgical phase using multivariate autoregressive (MAR) models. Then, a signal from a new operation is processed with GMMAR, wherein each phase is modeled by a Gaussian component of regression coefficients. These coefficients are compared to those of the training set. The operation is segmented according to the prior probabilities of the surgical phases estimated via GMMAR. The method also allows for the study of motor behavior and hand motion synchronization demonstrated in each phase, a quality that can be incorporated into modern laparoscopic simulators for skills assessment.
Directory of Open Access Journals (Sweden)
Vasios C.E.
2003-01-01
Full Text Available In the present work, a new method for the classification of Event Related Potentials (ERPs is proposed. The proposed method consists of two modules: the feature extraction module and the classification module. The feature extraction module comprises the implementation of the Multivariate Autoregressive model in conjunction with the Simulated Annealing technique, for the selection of optimum features from ERPs. The classification module is implemented with a single three-layer neural network, trained with the back-propagation algorithm and classifies the data into two classes: patients and control subjects. The method, in the form of a Decision Support System (DSS, has been thoroughly tested to a number of patient data (OCD, FES, depressives and drug users, resulting successful classification up to 100%.
Parallel algorithms for simulating continuous time Markov chains
Nicol, David M.; Heidelberger, Philip
1992-01-01
We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.
Noncausal Bayesian Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...
Srinath, Srikar; Poyneer, Lisa A.; Rudy, Alexander R.; Ammons, S. M.
2014-08-01
The advent of expensive, large-aperture telescopes and complex adaptive optics (AO) systems has strengthened the need for detailed simulation of such systems from the top of the atmosphere to control algorithms. The credibility of any simulation is underpinned by the quality of the atmosphere model used for introducing phase variations into the incident photons. Hitherto, simulations which incorporate wind layers have relied upon phase screen generation methods that tax the computation and memory capacities of the platforms on which they run. This places limits on parameters of a simulation, such as exposure time or resolution, thus compromising its utility. As aperture sizes and fields of view increase the problem will only get worse. We present an autoregressive method for evolving atmospheric phase that is efficient in its use of computation resources and allows for variability in the power contained in frozen flow or stochastic components of the atmosphere. Users have the flexibility of generating atmosphere datacubes in advance of runs where memory constraints allow to save on computation time or of computing the phase at each time step for long exposure times. Preliminary tests of model atmospheres generated using this method show power spectral density and rms phase in accordance with established metrics for Kolmogorov models.
Simulation-based algorithms for Markov decision processes
Chang, Hyeong Soo; Fu, Michael C; Marcus, Steven I
2013-01-01
Markov decision process (MDP) models are widely used for modeling sequential decision-making problems that arise in engineering, economics, computer science, and the social sciences. Many real-world problems modeled by MDPs have huge state and/or action spaces, giving an opening to the curse of dimensionality and so making practical solution of the resulting models intractable. In other cases, the system of interest is too complex to allow explicit specification of some of the MDP model parameters, but simulation samples are readily available (e.g., for random transitions and costs). For these settings, various sampling and population-based algorithms have been developed to overcome the difficulties of computing an optimal solution in terms of a policy and/or value function. Specific approaches include adaptive sampling, evolutionary policy iteration, evolutionary random policy search, and model reference adaptive search. This substantially enlarged new edition reflects the latest developments in novel ...
Improvement of Fuzzy Image Contrast Enhancement Using Simulated Ergodic Fuzzy Markov Chains
Directory of Open Access Journals (Sweden)
Behrouz Fathi-Vajargah
2014-01-01
Full Text Available This paper presents a novel fuzzy enhancement technique using simulated ergodic fuzzy Markov chains for low contrast brain magnetic resonance imaging (MRI. The fuzzy image contrast enhancement is proposed by weighted fuzzy expected value. The membership values are then modified to enhance the image using ergodic fuzzy Markov chains. The qualitative performance of the proposed method is compared to another method in which ergodic fuzzy Markov chains are not considered. The proposed method produces better quality image.
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
2009-01-01
In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies...... to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and past observations. As a particular example, we consider...... an exponential autoregressive Poisson model for time series. Under geometric ergodicity, the maximum likelihood estimators are shown to be asymptotically Gaussian in the linear model. In addition, we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbæk, Anders; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model...... for time series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric ergodicity...
Srinath, Sriakr; Rudy, Alexander R; Ammons, S Mark
2015-01-01
We present a sample-based, autoregressive (AR) method for the generation and time evolution of atmospheric phase screens that is computationally efficient and uses a single parameter per Fourier mode to vary the power contained in the frozen flow and stochastic components. We address limitations of Fourier-based methods such as screen periodicity and low spatial frequency power content. Comparisons of adaptive optics (AO) simulator performance when fed AR phase screens and translating phase screens reveal significantly elevated residual closed-loop temporal power for small increases in added stochastic content at each time step, thus displaying the importance of properly modeling atmospheric "boiling". We present preliminary evidence that our model fits to AO telemetry are better reflections of real conditions than the pure frozen flow assumption.
Experimental Simulations of Extreme Precipitation Based on the Multi-Status Markov Chain Model
Institute of Scientific and Technical Information of China (English)
DING Yuguo; ZHANG Jinling; JIANG Zhihong
2010-01-01
A multi-status Markov chain model is proposed to produce daily rainrall, and based on which extreme rainfall is simulated with the generalized Pareto distribution (GPD). The simulated daily rainfall shows high precision at most stations, especially in pluvial regions of East China. The analysis reveals that the multi-status Markov chain model excels the bi-status Markov chain model in simulating climatic features of extreme rainfall. Results from the selected six stations demonstrate excellent simulations in the following aspects: standard deviation of monthly precipitation, daily maximum precipitation, the monthly mean rainfall days, standard deviation of daily precipitation and mean daily precipitation, which are proved to be consistent with the observations. A comparative study involving 78 stations in East China also reveals good consistency in monthly mean rainfall days and mean daily maximum rainfall, except mean daily rainfall. Simulation results at the above 6 stations have shown satisfactory fitting capability of the extreme precipitation GPD method. Good analogy is also found between simulation and observation in threshold and return values. As the errors of the threshold decrease, so do the differences between the return and real values. All the above demonstrates the applicability of the Markov chain model to extreme rainfall simulations.
Vrugt, J.A.; Braak, ter C.J.F.; Clark, M.P.; Hyman, J.M.; Robinson, B.A.
2008-01-01
There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled di
Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation
Minasny, B.; Vrugt, J.A.; McBratney, A.B.
2011-01-01
This paper demonstrates for the first time the use of Markov Chain Monte Carlo (MCMC) simulation for parameter inference in model-based soil geostatistics. We implemented the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm to jointly summarize the posterior distributi
Improving the kinetics from molecular simulations using biased Markov state models
Rudzinski, Joseph F.; Kremer, Kurt; Bereau, Tristan
Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between simulated and experimentally-measured observables. This work presents a robust and systematic framework for reweighting the ensemble of dynamical paths sampled in a molecular simulation in order to ensure consistency with a set of given kinetic observables. The method employs the well-developed Markov state modeling framework in order to efficiently treat simulated dynamical paths. We demonstrate that, for two distinct coarse-grained peptide models, biasing the Markov state model to reproduce a small number of reference kinetic constraints significantly improves the dynamical properties of the model, while simultaneously refining the static equilibrium properties.
A new method for the fast simulation of models of highly dependable Markov system
Institute of Scientific and Technical Information of China (English)
XIAO Gang; LI Zhizhong
2005-01-01
To fast evaluate the small probability that starts from the all-components-up state, the system hits the failed sets before returning to the all-components-up state, Important Sampling or Important Splitting is used commonly. In this paper, a new approach distinguished from Important Sampling and Important Splitting is presented to estimate this small probability of highly dependable Markov system. This new approach achieves variance reduction through improving the estimator itself. The new estimator is derived from the integral equation describing the state transitions of Markov system. That the variance of this estimator is less than that of naive simulation at all time is proved theoretically. Two example involved reliability models with deferred repair are used to compare the methods of RB, IGBS, SB-RBS, naive simulation, and the method presented in this paper. Results show our method has the least RE.
A fast exact simulation method for a class of Markov jump processes
Energy Technology Data Exchange (ETDEWEB)
Li, Yao, E-mail: yaoli@math.umass.edu [Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 10003 (United States); Hu, Lili, E-mail: lilyhu86@gmail.com [School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
2015-11-14
A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.
A fast exact simulation method for a class of Markov jump processes
Li, Yao; Hu, Lili
2015-11-01
A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.
Physical time scale in kinetic Monte Carlo simulations of continuous-time Markov chains.
Serebrinsky, Santiago A
2011-03-01
We rigorously establish a physical time scale for a general class of kinetic Monte Carlo algorithms for the simulation of continuous-time Markov chains. This class of algorithms encompasses rejection-free (or BKL) and rejection (or "standard") algorithms. For rejection algorithms, it was formerly considered that the availability of a physical time scale (instead of Monte Carlo steps) was empirical, at best. Use of Monte Carlo steps as a time unit now becomes completely unnecessary.
Ababaei, Behnam; Sohrabi, Teymour; Mirzaei, Farhad
2014-10-01
Most stochastic weather generators have their focus on precipitation because it is the most important variable affecting environmental processes. One of the methods to reproduce the precipitation occurrence time series is to use a Markov process. But, in addition to the simulation of short-term autocorrelations in one station, it is sometimes important to preserve the spatial linear correlations (SLC) between neighboring stations as well. In this research, an extension of one-site Markov models was proposed to preserve the SLC between neighboring stations. Qazvin station was utilized as the reference station and Takestan (TK), Magsal, Nirougah, and Taleghan stations were used as the target stations. The performances of different models were assessed in relation to the simulation of dry and wet spells and short-term dependencies in precipitation time series. The results revealed that in TK station, a Markov model with a first-order spatial model could be selected as the best model, while in the other stations, a model with the order of two or three could be selected. The selected (i.e., best) models were assessed in relation to preserving the SLC between neighboring stations. The results depicted that these models were very capable in preserving the SLC between the reference station and any of the target stations. But, their performances were weaker when the SLC between the other stations were compared. In order to resolve this issue, spatially correlated random numbers were utilized instead of independent random numbers while generating synthetic time series using the Markov models. Although this method slightly reduced the model performances in relation to dry and wet spells and short-term dependencies, the improvements related to the simulation of the SLC between the other stations were substantial.
Rudzinski, Joseph F; Bereau, Tristan
2016-01-01
Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between simulated and reference (e.g., from experiments or higher-level simulations) observables. To bound the microscopic information generated by computer simulations within reference measurements, we propose a method that reweights the microscopic transitions of the system to improve consistency with a set of coarse kinetic observables. The method employs the well-developed Markov state modeling framework to efficiently link microscopic dynamics with long-time scale constraints, thereby consistently addressing a wide range of time scales. To emphasize the robustness of the method, we consider two distinct coarse-grained models with significant kinetic inconsistencies. When applied to the simulated conformational dynamics of small peptides, the reweighting procedure systematically ...
Testing Homogeneity of Mixture of Skew-normal Distributions Via Markov Chain Monte Carlo Simulation
Directory of Open Access Journals (Sweden)
Rahman Farnoosh Morteza Ebrahimi
2015-05-01
Full Text Available The main purpose of this study is to intoduce an optimal penalty function for testing homogeneity of finite mixture of skew-normal distribution based on Markov Chain Monte Carlo (MCMC simulation. In the present study the penalty function is considered as a parametric function in term of parameter of mixture models and a Baysian approach is employed to estimating the parameters of model. In order to examine the efficiency of the present study in comparison with the previous approaches, some simulation studies are presented.
Institute of Scientific and Technical Information of China (English)
Zhao Zhi-Jin; Zheng Shi-Lian; Xu Chun-Yun; Kong Xian-Zheng
2007-01-01
Hidden Markov models (HMMs) have been used to model burst error sources of wireless channels. This paper proposes a hybrid method of using genetic algorithm (GA) and simulated annealing (SA) to train HMM for discrete channel modelling. The proposed method is compared with pure GA, and experimental results show that the HMMs trained by the hybrid method can better describe the error sequences due to SA's ability of facilitating hill-climbing at the later stage of the search. The burst error statistics of the HMMs trained by the proposed method and the corresponding error sequences are also presented to validate the proposed method.
Maginnis, P. A.; West, M.; Dullerud, G. E.
2016-10-01
We propose an algorithm to accelerate Monte Carlo simulation for a broad class of stochastic processes. Specifically, the class of countable-state, discrete-time Markov chains driven by additive Poisson noise, or lattice discrete-time Markov chains. In particular, this class includes simulation of reaction networks via the tau-leaping algorithm. To produce the speedup, we simulate pairs of fair-draw trajectories that are negatively correlated. Thus, when averaged, these paths produce an unbiased Monte Carlo estimator that has reduced variance and, therefore, reduced error. Numerical results for three example systems included in this work demonstrate two to four orders of magnitude reduction of mean-square error. The numerical examples were chosen to illustrate different application areas and levels of system complexity. The areas are: gene expression (affine state-dependent rates), aerosol particle coagulation with emission and human immunodeficiency virus infection (both with nonlinear state-dependent rates). Our algorithm views the system dynamics as a "black-box", i.e., we only require control of pseudorandom number generator inputs. As a result, typical codes can be retrofitted with our algorithm using only minor changes. We prove several analytical results. Among these, we characterize the relationship of covariances between paths in the general nonlinear state-dependent intensity rates case, and we prove variance reduction of mean estimators in the special case of affine intensity rates.
Numazawa, Satoshi; Smith, Roger
2011-10-01
Classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The scheme is then used to determine transitions that can be applied in a lattice-based kinetic Monte Carlo (KMC) atomistic simulation model. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multidimensional Boolean valued functions in three-dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology-dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion. Excellent agreement with observed experimental results is obtained.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on fast Markov chain simulation for generating the samples distributed in failure region and saddlepoint approximation(SA) technique,an efficient reliability analysis method is presented to evaluate the small failure probability of non-linear limit state function(LSF) with non-normal variables.In the presented method,the failure probability of the non-linear LSF is transformed into a product of the failure probability of the introduced linear LSF and a feature ratio factor.The introduced linear LSF which approximately has the same maximum likelihood points as the non-linear LSF is constructed and its failure probability can be calculated by SA technique.The feature ratio factor,which can be evaluated on the basis of multiplicative rule of probability,exhibits the relation between the failure probability of the non-linear LSF and that of the linear LSF,and it can be fast computed by utilizing the Markov chain algorithm to directly simulate the samples distributed in the failure regions of the non-linear LSF and those of the linear LSF.Moreover,the expectation and variance of the failure probability estimate are derived.The results of several examples demonstrate that the presented method has wide applicability,can be easily implemented,and possesses high precision and high efficiency.
Rudzinski, Joseph F.; Kremer, Kurt; Bereau, Tristan
2016-02-01
Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between simulated and reference (e.g., from experiments or higher-level simulations) observables. To bound the microscopic information generated by computer simulations within reference measurements, we propose a method that reweights the microscopic transitions of the system to improve consistency with a set of coarse kinetic observables. The method employs the well-developed Markov state modeling framework to efficiently link microscopic dynamics with long-time scale constraints, thereby consistently addressing a wide range of time scales. To emphasize the robustness of the method, we consider two distinct coarse-grained models with significant kinetic inconsistencies. When applied to the simulated conformational dynamics of small peptides, the reweighting procedure systematically improves the time scale separation of the slowest processes. Additionally, constraining the forward and backward rates between metastable states leads to slight improvement of their relative stabilities and, thus, refined equilibrium properties of the resulting model. Finally, we find that difficulties in simultaneously describing both the simulated data and the provided constraints can help identify specific limitations of the underlying simulation approach.
Simulating Replica Exchange: Markov State Models, Proposal Schemes, and the Infinite Swapping Limit.
Zhang, Bin W; Dai, Wei; Gallicchio, Emilio; He, Peng; Xia, Junchao; Tan, Zhiqiang; Levy, Ronald M
2016-08-25
Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host-guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations.
Energy Technology Data Exchange (ETDEWEB)
Kim, Joo Yeon; Jang, Han Ki; Jang, Sol Ah; Park, Tae Jin [Korean Association for Radiation Application, Seoul (Korea, Republic of)
2014-04-15
There is a question that the simulation actually leads to draws from its target distribution and the most basic one is whether such Markov chains can always be constructed and all chain values sampled from them. The problem to be solved is the determination of how large this iteration should be to achieve the target distribution. This problem can be answered as convergence monitoring. In this paper, two widely used methods, such as autocorrelation and potential scale reduction factor (PSRF) in MCMC are characterized. There is no general agreement on the subject of the convergence. Although it is generally agreed that running n parallel chains in practice is computationally inefficient and unnecessary, running multiple parallel chains is generally applied for the convergence monitoring due to easy implementation. The main debate is the number of parallel chains needed. If the convergence properties of the chain are well understood then clearly a single chain suffices. Therefore, autocorrelation using single chain and multiple parallel ones are tried and their results then compared with each other in this study. And, the following question is answered from the two convergence results: Have the Markov chain realizations for achieved the target distribution?.
Markov Chain Monte Carlo simulation for projection of end stage renal disease patients in Greece.
Rodina-Theocharaki, A; Bliznakova, K; Pallikarakis, N
2012-07-01
End stage renal disease (ESRD) treatment methods are considered to be among the most expensive procedures for chronic conditions worldwide which also have severe impact on patients' quality of life. During the last decade, Greece has been among the countries with the highest incidence and prevalence, while at the same time with the lowest kidney transplantation rates. Predicting future patients' number on Renal Replacement Therapy (RRT) is essential for health care providers in order to achieve more effective resource management. In this study a Markov Chain Monte Carlo (MCMC) simulation is presented for predicting the future number of ESRD patients for the period 2009-2020 in Greece. The MCMC model comprises Monte Carlo sampling techniques applied on probability distributions of the constructed Markov Chain. The model predicts that there will be 15,147 prevalent patients on RRT in Greece by 2020. Additionally, a cost-effectiveness analysis was performed on a scenario of gradually reducing the hemodialysis patients in favor of increasing the transplantation number by 2020. The proposed scenario showed net savings of 86.54 million Euros for the period 2009-2020 compared to the base-case prediction.
Smith, Jason F; Chen, Kewei; Pillai, Ajay S; Horwitz, Barry
2013-01-01
The number and variety of connectivity estimation methods is likely to continue to grow over the coming decade. Comparisons between methods are necessary to prune this growth to only the most accurate and robust methods. However, the nature of connectivity is elusive with different methods potentially attempting to identify different aspects of connectivity. Commonalities of connectivity definitions across methods upon which base direct comparisons can be difficult to derive. Here, we explicitly define "effective connectivity" using a common set of observation and state equations that are appropriate for three connectivity methods: dynamic causal modeling (DCM), multivariate autoregressive modeling (MAR), and switching linear dynamic systems for fMRI (sLDSf). In addition while deriving this set, we show how many other popular functional and effective connectivity methods are actually simplifications of these equations. We discuss implications of these connections for the practice of using one method to simulate data for another method. After mathematically connecting the three effective connectivity methods, simulated fMRI data with varying numbers of regions and task conditions is generated from the common equation. This simulated data explicitly contains the type of the connectivity that the three models were intended to identify. Each method is applied to the simulated data sets and the accuracy of parameter identification is analyzed. All methods perform above chance levels at identifying correct connectivity parameters. The sLDSf method was superior in parameter estimation accuracy to both DCM and MAR for all types of comparisons.
Directory of Open Access Journals (Sweden)
Jason Fitzgerald Smith
2013-05-01
Full Text Available The number and variety of connectivity estimation methods is likely to continue to grow over the coming decade. Comparisons between methods are necessary to prune this growth to only the most accurate and robust methods. However, the nature of connectivity is elusive with different methods potentially attempting to identify different aspects of connectivity. Commonalities of connectivity definitions across methods upon which base direct comparisons can be difficult to derive. Here we explicitly define effective connectivity using a common set of observation and state equations that are appropriate for three connectivity methods: Dynamic Causal Modeling (DCM, Multivariate Autoregressive Modeling (MAR, and Switching Linear Dynamic Systems for fMRI (sLDSf. In addition while deriving this set, we show how many other popular functional and effective connectivity methods are actually simplifications of these equations. We discuss implications of these connections for the practice of using one method to simulate data for another method. After mathematically connecting the three effective connectivity methods, simulated fMRI data with varying numbers of regions and task conditions is generated from the common equation. This simulated data explicitly contains the type of the connectivity that the three models were intended to identify. Each method is applied to the simulated data sets and the accuracy of parameter identification is analyzed. All methods perform above chance levels at identifying correct connectivity parameters. The sLDSf method was superior in parameter estimation accuracy to both DCM and MAR for all types of comparisons.
Smith, Jason F.; Chen, Kewei; Pillai, Ajay S.; Horwitz, Barry
2013-01-01
The number and variety of connectivity estimation methods is likely to continue to grow over the coming decade. Comparisons between methods are necessary to prune this growth to only the most accurate and robust methods. However, the nature of connectivity is elusive with different methods potentially attempting to identify different aspects of connectivity. Commonalities of connectivity definitions across methods upon which base direct comparisons can be difficult to derive. Here, we explicitly define “effective connectivity” using a common set of observation and state equations that are appropriate for three connectivity methods: dynamic causal modeling (DCM), multivariate autoregressive modeling (MAR), and switching linear dynamic systems for fMRI (sLDSf). In addition while deriving this set, we show how many other popular functional and effective connectivity methods are actually simplifications of these equations. We discuss implications of these connections for the practice of using one method to simulate data for another method. After mathematically connecting the three effective connectivity methods, simulated fMRI data with varying numbers of regions and task conditions is generated from the common equation. This simulated data explicitly contains the type of the connectivity that the three models were intended to identify. Each method is applied to the simulated data sets and the accuracy of parameter identification is analyzed. All methods perform above chance levels at identifying correct connectivity parameters. The sLDSf method was superior in parameter estimation accuracy to both DCM and MAR for all types of comparisons. PMID:23717258
Schmandt, Nicolaus T; Galán, Roberto F
2012-09-14
Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be replaced with their mean if state B is not directly connected to A, which shortens computing time considerably. We show the accuracy and efficacy of our approximation theoretically and in simulations of stochastic ion-channel gating in neurons.
Improved Subset Autoregression: With R Package
Directory of Open Access Journals (Sweden)
A. I. McLeod
2008-07-01
Full Text Available The FitAR R (R Development Core Team 2008 package that is available on the Comprehensive R Archive Network is described. This package provides a comprehensive approach to fitting autoregressive and subset autoregressive time series. For long time series with complicated autocorrelation behavior, such as the monthly sunspot numbers, subset autoregression may prove more feasible and/or parsimonious than using AR or ARMA models. The two principal functions in this package are SelectModel and FitAR for automatic model selection and model fitting respectively. In addition to the regular autoregressive model and the usual subset autoregressive models (Tong 1977, these functions implement a new family of models. This new family of subset autoregressive models is obtained by using the partial autocorrelations as parameters and then selecting a subset of these parameters. Further properties and results for these models are discussed in McLeod and Zhang (2006. The advantages of this approach are that not only is an efficient algorithm for exact maximum likelihood implemented but that efficient methods are derived for selecting high-order subset models that may occur in massive datasets containing long time series. A new improved extended {BIC} criterion, {UBIC}, developed by Chen and Chen (2008 is implemented for subset model selection. A complete suite of model building functions for each of the three types of autoregressive models described above are included in the package. The package includes functions for time series plots, diagnostic testing and plotting, bootstrapping, simulation, forecasting, Box-Cox analysis, spectral density estimation and other useful time series procedures. As well as methods for standard generic functions including print, plot, predict and others, some new generic functions and methods are supplied that make it easier to work with the output from FitAR for bootstrapping, simulation, spectral density estimation and Box
RESTART simulation of non-Markov consecutive-k-out-of-n: F repairable systems
Energy Technology Data Exchange (ETDEWEB)
Villen-Altamirano, Jose, E-mail: jvillen@eui.upm.e [Departamento de Matematica Aplicada (E.U. Informatica), Universidad Politecnica de Madrid, Calle Arboleda s/n, 28031 Madrid (Spain)
2010-03-15
The reliability of consecutive-k-out-of-n: F repairable systems and (k-1)-step Markov dependence is studied. The model analyzed in this paper is more general than those of previous studies given that repair time and component lifetimes are random variables that follow a general distribution. The system has one repair service which adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly dependable systems, the RESTART method was used for the estimation of steady-state unavailability, MTBF and unreliability. Probabilities up to the order of 10{sup -16} have been accurately estimated with little computational effort. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty for the application of this method is to find a suitable function, called the importance function, to define the regions. Given the simplicity involved in changing some model assumptions with RESTART, the importance function used in this paper could be useful for dependability estimation of many systems.
PHAISTOS: a framework for Markov chain Monte Carlo simulation and inference of protein structure.
Boomsma, Wouter; Frellsen, Jes; Harder, Tim; Bottaro, Sandro; Johansson, Kristoffer E; Tian, Pengfei; Stovgaard, Kasper; Andreetta, Christian; Olsson, Simon; Valentin, Jan B; Antonov, Lubomir D; Christensen, Anders S; Borg, Mikael; Jensen, Jan H; Lindorff-Larsen, Kresten; Ferkinghoff-Borg, Jesper; Hamelryck, Thomas
2013-07-15
We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force-fields are available within the framework: PROFASI and OPLS-AA/L, the latter including the generalized Born surface area solvent model. A flexible command-line and configuration-file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.
Karnon, Jonathan
2003-10-01
Markov models have traditionally been used to evaluate the cost-effectiveness of competing health care technologies that require the description of patient pathways over extended time horizons. Discrete event simulation (DES) is a more flexible, but more complicated decision modelling technique, that can also be used to model extended time horizons. Through the application of a Markov process and a DES model to an economic evaluation comparing alternative adjuvant therapies for early breast cancer, this paper compares the respective processes and outputs of these alternative modelling techniques. DES displays increased flexibility in two broad areas, though the outputs from the two modelling techniques were similar. These results indicate that the use of DES may be beneficial only when the available data demonstrates particular characteristics.
Vrugt, J.A.; Braak, ter C.J.F.; Diks, C.G.H.; Robinson, B.A.; Hyman, J.M.; Higdon, D.
2009-01-01
Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well-constructed MCMC schemes to the appropriate
Vrugt, J.A.; Braak, C.J.F.; Diks, C.G.H.; Robinson, B.A.; Hyman, J.M.; Higdon, D.
2009-01-01
Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well constructed MCMC schemes to the appropriate
Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations
Vousden, Will; Mandel, Ilya
2015-01-01
Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multi-modal probability distributions. Most popular methods, such as Markov chain Monte Carlo sampling, perform poorly on strongly multi-modal probability distributions, rarely jumping between modes or settling on just one mode without finding others. Parallel tempering addresses this problem by sampling simultaneously with separate Markov chains from tempered versions of the target distribution with reduced contrast levels. Gaps between modes can be traversed at higher temperatures, while individual modes can be efficiently explored at lower temperatures. In this paper, we investigate how one might choose the ladder of temperatures to achieve lower autocorrelation time for the sampler (and therefore more efficient sampling). In particular, we present a simple, easily-implemented algorithm for dynamically adapting the temperature configuration of a sampler while sampling in order to ...
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-28
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
Markov Chains and Markov Processes
2016-01-01
Markov chain, which was named after Andrew Markov is a mathematical system that transfers a state to another state. Many real world systems contain uncertainty. This study helps us to understand the basic idea of a Markov chain and how is been useful in our daily lives. For some times there had been suspense on distinct predictions and future existences. Also in different games there had been different expectations or results involved. That is the reason why we need Markov chains to predict o...
Panels and Time Series Analysis: Markov Chains and Autoregressive Processes
1976-07-01
techniques and objectives were described by Lazarsfeld , Berelson, and Gauciet in The People’s Choice (19h4). That study uas based on re- peated interviews of...unmx onn 2~lC Paul F. Lazarsfela, ed. , ’The Fr- Pr-.s ;itzncoc itl p.i7-66. AndesonV.W. (191:1) , Ar Intrcouuetior t u ’, An alyjsis , John Wiley arnd
Institute of Scientific and Technical Information of China (English)
CHEN Xu; YU Shi-Xiao; ZHANG Ya-Ping
2013-01-01
Using the fuzzy rule-based classification method,normalized difference vegetation index (NDVI) images acquired from 1982 to 1998 were classified into seventeen phases.Based on these classification images,a probabilistic cellular automata-Markov Chain model was developed and used to simulate a land cover scenario of China for the year 2014.Spatiotemporal dynamics of land use/cover in China from 1982 to 2014 were then analyzed and evaluated.The results showed that the change trends of land cover type from 1998 to 2014 would be contrary to those from 1982 to 1998.In particular,forestland and grassland areas decreased by 1.56％ and 1.46％,respectively,from 1982 to 1998,and should increase by 1.5％ and 2.3％ from 1998 to 2014,respectively.
Implementing Bayesian Vector Autoregressions Implementing Bayesian Vector Autoregressions
Directory of Open Access Journals (Sweden)
Richard M. Todd
1988-03-01
Full Text Available Implementing Bayesian Vector Autoregressions This paper discusses how the Bayesian approach can be used to construct a type of multivariate forecasting model known as a Bayesian vector autoregression (BVAR. In doing so, we mainly explain Doan, Littermann, and Sims (1984 propositions on how to estimate a BVAR based on a certain family of prior probability distributions. indexed by a fairly small set of hyperparameters. There is also a discussion on how to specify a BVAR and set up a BVAR database. A 4-variable model is used to iliustrate the BVAR approach.
The impact of missing data in a generalized integer-valued autoregression model for count data.
Alosh, Mohamed
2009-11-01
The impact of the missing data mechanism on estimates of model parameters for continuous data has been extensively investigated in the literature. In comparison, minimal research has been carried out for the impact of missing count data. The focus of this article is to investigate the impact of missing data on a transition model, termed the generalized autoregressive model of order 1 for longitudinal count data. The model has several features, including modeling dependence and accounting for overdispersion in the data, that make it appealing for the clinical trial setting. Furthermore, the model can be viewed as a natural extension of the commonly used log-linear model. Following introduction of the model and discussion of its estimation we investigate the impact of different missing data mechanisms on estimates of the model parameters through a simulation experiment. The findings of the simulation experiment show that, as in the case of normally distributed data, estimates under the missing completely at random (MCAR) and missing at random (MAR) mechanisms are close to their analogue for the full dataset and that the missing not at random (MNAR) mechanism has the greatest bias. Furthermore, estimates based on imputing the last observed value carried forward (LOCF) for missing data under the MAR assumption are similar to those of the MAR. This latter finding might be attributed to the Markov property underlying the model and to the high level of dependence among successive observations used in the simulation experiment. Finally, we consider an application of the generalized autoregressive model to a longitudinal epilepsy dataset analyzed in the literature.
Saloranta, Tuomo M; Armitage, James M; Haario, Heikki; Naes, Kristoffer; Cousins, Ian T; Barton, David N
2008-01-01
Multimedia environmental fate models are useful tools to investigate the long-term impacts of remediation measures designed to alleviate potential ecological and human health concerns in contaminated areas. Estimating and communicating the uncertainties associated with the model simulations is a critical task for demonstrating the transparency and reliability of the results. The Extended Fourier Amplitude Sensitivity Test(Extended FAST) method for sensitivity analysis and Bayesian Markov chain Monte Carlo (MCMC) method for uncertainty analysis and model calibration have several advantages over methods typically applied for multimedia environmental fate models. Most importantly, the simulation results and their uncertainties can be anchored to the available observations and their uncertainties. We apply these techniques for simulating the historical fate of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) in the Grenland fjords, Norway, and for predicting the effects of different contaminated sediment remediation (capping) scenarios on the future levels of PCDD/Fs in cod and crab therein. The remediation scenario simulations show that a significant remediation effect can first be seen when significant portions of the contaminated sediment areas are cleaned up, and that increase in capping area leads to both earlier achievement of good fjord status and narrower uncertainty in the predicted timing for this.
Blind identification of threshold auto-regressive model for machine fault diagnosis
Institute of Scientific and Technical Information of China (English)
LI Zhinong; HE Yongyong; CHU Fulei; WU Zhaotong
2007-01-01
A blind identification method was developed for the threshold auto-regressive (TAR) model. The method had good identification accuracy and rapid convergence, especially for higher order systems. The proposed method was then combined with the hidden Markov model (HMM) to determine the auto-regressive (AR) coefficients for each interval used for feature extraction, with the HMM as a classifier. The fault diagnoses during the speed-up and speed- down processes for rotating machinery have been success- fully completed. The result of the experiment shows that the proposed method is practical and effective.
Dynamic temperature selection for parallel tempering in Markov chain Monte Carlo simulations
Vousden, W. D.; Farr, W. M.; Mandel, I.
2016-01-01
Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multimodal probability distributions. Most popular methods, such as MCMC sampling, perform poorly on strongly multimodal probability distributions, rarely jumping between modes or settling on just one mode without finding others. Parallel tempering addresses this problem by sampling simultaneously with separate Markov chains from tempered versions of the target distribution with reduced contrast levels. Gaps between modes can be traversed at higher temperatures, while individual modes can be efficiently explored at lower temperatures. In this paper, we investigate how one might choose the ladder of temperatures to achieve more efficient sampling, as measured by the autocorrelation time of the sampler. In particular, we present a simple, easily implemented algorithm for dynamically adapting the temperature configuration of a sampler while sampling. This algorithm dynamically adjusts the temperature spacing to achieve a uniform rate of exchanges between chains at neighbouring temperatures. We compare the algorithm to conventional geometric temperature configurations on a number of test distributions and on an astrophysical inference problem, reporting efficiency gains by a factor of 1.2-2.5 over a well-chosen geometric temperature configuration and by a factor of 1.5-5 over a poorly chosen configuration. On all of these problems, a sampler using the dynamical adaptations to achieve uniform acceptance ratios between neighbouring chains outperforms one that does not.
An autoregressive growth model for longitudinal item analysis.
Jeon, Minjeong; Rabe-Hesketh, Sophia
2016-09-01
A first-order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits. Specifically, the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time, or the lagged response. An initial conditions problem arises because there is no lagged response at the initial time period. We handle this problem by adapting solutions proposed for dynamic models in panel data econometrics. Asymptotic and finite sample power for the autoregressive parameters are investigated. The consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first-order autoregressive growth model. The proposed methods are applied to longitudinal data on Korean students' self-esteem.
DEFF Research Database (Denmark)
Li, Chunjian; Andersen, Søren Vang
2007-01-01
We propose two blind system identification methods that exploit the underlying dynamics of non-Gaussian signals. The two signal models to be identified are: an Auto-Regressive (AR) model driven by a discrete-state Hidden Markov process, and the same model whose output is perturbed by white Gaussian...
Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.
2010-10-01
Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.
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.
A stochastic Markov chain approach for tennis: Monte Carlo simulation and modeling
Aslam, Kamran
This dissertation describes the computational formulation of probability density functions (pdfs) that facilitate head-to-head match simulations in tennis along with ranking systems developed from their use. A background on the statistical method used to develop the pdfs , the Monte Carlo method, and the resulting rankings are included along with a discussion on ranking methods currently being used both in professional sports and in other applications. Using an analytical theory developed by Newton and Keller in [34] that defines a tennis player's probability of winning a game, set, match and single elimination tournament, a computational simulation has been developed in Matlab that allows further modeling not previously possible with the analytical theory alone. Such experimentation consists of the exploration of non-iid effects, considers the concept the varying importance of points in a match and allows an unlimited number of matches to be simulated between unlikely opponents. The results of these studies have provided pdfs that accurately model an individual tennis player's ability along with a realistic, fair and mathematically sound platform for ranking them.
A Note on Parameter Estimations of Panel Vector Autoregressive Models with Intercorrelation
Institute of Scientific and Technical Information of China (English)
Jian-hong Wu; Li-xing Zhu; Zai-xing Li
2009-01-01
This note considers parameter estimation for panel vector autoregressive models with intercorrela-tion. Conditional least squares estimators are derived and the asymptotic normality is established. A simulation is carried out for illustration.
Directory of Open Access Journals (Sweden)
Chow John L
2006-03-01
Full Text Available Abstract Background Management of acute respiratory distress syndrome (ARDS in the intensive care unit (ICU is clinically challenging and costly. Neuromuscular blocking agents may facilitate mechanical ventilation and improve oxygenation, but may result in prolonged recovery of neuromuscular function and acute quadriplegic myopathy syndrome (AQMS. The goal of this study was to address a hypothetical question via computer modeling: Would a reduction in intubation time of 6 hours and/or a reduction in the incidence of AQMS from 25% to 21%, provide enough benefit to justify a drug with an additional expenditure of $267 (the difference in acquisition cost between a generic and brand name neuromuscular blocker? Methods The base case was a 55 year-old man in the ICU with ARDS who receives neuromuscular blockade for 3.5 days. A Markov model was designed with hypothetical patients in 1 of 6 mutually exclusive health states: ICU-intubated, ICU-extubated, hospital ward, long-term care, home, or death, over a period of 6 months. The net monetary benefit was computed. Results Our computer simulation modeling predicted the mean cost for ARDS patients receiving standard care for 6 months to be $62,238 (5% – 95% percentiles $42,259 – $83,766, with an overall 6-month mortality of 39%. Assuming a ceiling ratio of $35,000, even if a drug (that cost $267 more hypothetically reduced AQMS from 25% to 21% and decreased intubation time by 6 hours, the net monetary benefit would only equal $137. Conclusion ARDS patients receiving a neuromuscular blocker have a high mortality, and unpredictable outcome, which results in large variability in costs per case. If a patient dies, there is no benefit to any drug that reduces ventilation time or AQMS incidence. A prospective, randomized pharmacoeconomic study of neuromuscular blockers in the ICU to asses AQMS or intubation times is impractical because of the highly variable clinical course of patients with ARDS.
Jadoon, K. Z.; Altaf, M. U.; McCabe, M. F.; Hoteit, I.; Moghadas, D.
2014-12-01
In arid and semi-arid regions, soil salinity has a major impact on agro-ecosystems, agricultural productivity, environment and sustainability. High levels of soil salinity adversely affect plant growth and productivity, soil and water quality, and may eventually result in soil erosion and land degradation. Being essentially a hazard, it's important to monitor and map soil salinity at an early stage to effectively use soil resources and maintain soil salinity level below the salt tolerance of crops. In this respect, low frequency electromagnetic induction (EMI) systems can be used as a noninvasive method to map the distribution of soil salinity at the field scale and at a high spatial resolution. In this contribution, an EMI system (the CMD Mini-Explorer) is used to estimate soil salinity using a Bayesian approach implemented via a Markov chain Monte Carlo (MCMC) sampling for inversion of multi-configuration EMI measurements. In-situ and EMI measurements were conducted across a farm where Acacia trees are irrigated with brackish water using a drip irrigation system. The electromagnetic forward model is based on the full solution of Maxwell's equation, and the subsurface is considered as a three-layer problem. In total, five parameters (electrical conductivity of three layers and thickness of top two layers) were inverted and modeled electrical conductivities were converted into the universal standard of soil salinity measurement (i.e. using the method of electrical conductivity of a saturated soil paste extract). Simulation results demonstrate that the proposed scheme successfully recovers soil salinity and reduces the uncertainties in the prior estimate. Analysis of the resulting posterior distribution of parameters indicates that electrical conductivity of the top two layers and the thickness of the first layer are well constrained by the EMI measurements. The proposed approach allows for quantitative mapping and monitoring of the spatial electrical conductivity
Li, Jun
2013-09-01
We present a single-particle Lennard-Jones (L-J) model for CO2 and N2. Simplified L-J models for other small polyatomic molecules can be obtained following the methodology described herein. The phase-coexistence diagrams of single-component systems computed using the proposed single-particle models for CO2 and N2 agree well with experimental data over a wide range of temperatures. These diagrams are computed using the Markov Chain Monte Carlo method based on the Gibbs-NVT ensemble. This good agreement validates the proposed simplified models. That is, with properly selected parameters, the single-particle models have similar accuracy in predicting gas-phase properties as more complex, state-of-the-art molecular models. To further test these single-particle models, three binary mixtures of CH4, CO2 and N2 are studied using a Gibbs-NPT ensemble. These results are compared against experimental data over a wide range of pressures. The single-particle model has similar accuracy in the gas phase as traditional models although its deviation in the liquid phase is greater. Since the single-particle model reduces the particle number and avoids the time-consuming Ewald summation used to evaluate Coulomb interactions, the proposed model improves the computational efficiency significantly, particularly in the case of high liquid density where the acceptance rate of the particle-swap trial move increases. We compare, at constant temperature and pressure, the Gibbs-NPT and Gibbs-NVT ensembles to analyze their performance differences and results consistency. As theoretically predicted, the agreement between the simulations implies that Gibbs-NVT can be used to validate Gibbs-NPT predictions when experimental data is not available. © 2013 Elsevier Inc.
Bias-correction in vector autoregressive models
DEFF Research Database (Denmark)
Engsted, Tom; Pedersen, Thomas Quistgaard
2014-01-01
We analyze the properties of various methods for bias-correcting parameter estimates in both stationary and non-stationary vector autoregressive models. First, we show that two analytical bias formulas from the existing literature are in fact identical. Next, based on a detailed simulation study......, we show that when the model is stationary this simple bias formula compares very favorably to bootstrap bias-correction, both in terms of bias and mean squared error. In non-stationary models, the analytical bias formula performs noticeably worse than bootstrapping. Both methods yield a notable...... improvement over ordinary least squares. We pay special attention to the risk of pushing an otherwise stationary model into the non-stationary region of the parameter space when correcting for bias. Finally, we consider a recently proposed reduced-bias weighted least squares estimator, and we find...
Graphs: Associated Markov Chains
2012-01-01
In this research paper, weighted / unweighted, directed / undirected graphs are associated with interesting Discrete Time Markov Chains (DTMCs) as well as Continuous Time Markov Chains (CTMCs). The equilibrium / transient behaviour of such Markov chains is studied. Also entropy dynamics (Shannon entropy) of certain structured Markov chains is investigated. Finally certain structured graphs and the associated Markov chains are studied.
DEFF Research Database (Denmark)
Hobolth, Asger; Stone, Eric
2009-01-01
Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging fr...
Kepler AutoRegressive Planet Search: Motivation & Methodology
Caceres, Gabriel; Feigelson, Eric; Jogesh Babu, G.; Bahamonde, Natalia; Bertin, Karine; Christen, Alejandra; Curé, Michel; Meza, Cristian
2015-08-01
The Kepler AutoRegressive Planet Search (KARPS) project uses statistical methodology associated with autoregressive (AR) processes to model Kepler lightcurves in order to improve exoplanet transit detection in systems with high stellar variability. We also introduce a planet-search algorithm to detect transits in time-series residuals after application of the AR models. One of the main obstacles in detecting faint planetary transits is the intrinsic stellar variability of the host star. The variability displayed by many stars may have autoregressive properties, wherein later flux values are correlated with previous ones in some manner. Auto-Regressive Moving-Average (ARMA) models, Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH), and related models are flexible, phenomenological methods used with great success to model stochastic temporal behaviors in many fields of study, particularly econometrics. Powerful statistical methods are implemented in the public statistical software environment R and its many packages. Modeling involves maximum likelihood fitting, model selection, and residual analysis. These techniques provide a useful framework to model stellar variability and are used in KARPS with the objective of reducing stellar noise to enhance opportunities to find as-yet-undiscovered planets. Our analysis procedure consisting of three steps: pre-processing of the data to remove discontinuities, gaps and outliers; ARMA-type model selection and fitting; and transit signal search of the residuals using a new Transit Comb Filter (TCF) that replaces traditional box-finding algorithms. We apply the procedures to simulated Kepler-like time series with known stellar and planetary signals to evaluate the effectiveness of the KARPS procedures. The ARMA-type modeling is effective at reducing stellar noise, but also reduces and transforms the transit signal into ingress/egress spikes. A periodogram based on the TCF is constructed to concentrate the signal
Autoregressive description of biological phenomena
Morariu, Vasile V; Pop, Alexadru; Soltuz, Stefan M; Buimaga-Iarinca, Luiza; Zainea, Oana
2008-01-01
Many natural phenomena can be described by power-laws. A closer look at various experimental data reveals more or less significant deviations from a 1/f spectrum. We exemplify such cases with phenomena offered by molecular biology, cell biophysics, and cognitive psychology. Some of these cases can be described by first order autoregressive (AR) models or by higher order AR models which are short range correlation models. The calculations are checked against astrophysical data which were fitted to a an AR model by a different method. We found that our fitting method of the data give similar results for the astrhophysical data and therefore applied the method for examples mentioned above. Our results show that such phenomena can be described by first or higher order of AR models. Therefore such examples are described by short range correlation properties while they can be easily confounded with long range correlation phenomena.
Jalayer, Fatemeh; Ebrahimian, Hossein
2014-05-01
Introduction The first few days elapsed after the occurrence of a strong earthquake and in the presence of an ongoing aftershock sequence are quite critical for emergency decision-making purposes. Epidemic Type Aftershock Sequence (ETAS) models are used frequently for forecasting the spatio-temporal evolution of seismicity in the short-term (Ogata, 1988). The ETAS models are epidemic stochastic point process models in which every earthquake is a potential triggering event for subsequent earthquakes. The ETAS model parameters are usually calibrated a priori and based on a set of events that do not belong to the on-going seismic sequence (Marzocchi and Lombardi 2009). However, adaptive model parameter estimation, based on the events in the on-going sequence, may have several advantages such as, tuning the model to the specific sequence characteristics, and capturing possible variations in time of the model parameters. Simulation-based methods can be employed in order to provide a robust estimate for the spatio-temporal seismicity forecasts in a prescribed forecasting time interval (i.e., a day) within a post-main shock environment. This robust estimate takes into account the uncertainty in the model parameters expressed as the posterior joint probability distribution for the model parameters conditioned on the events that have already occurred (i.e., before the beginning of the forecasting interval) in the on-going seismic sequence. The Markov Chain Monte Carlo simulation scheme is used herein in order to sample directly from the posterior probability distribution for ETAS model parameters. Moreover, the sequence of events that is going to occur during the forecasting interval (and hence affecting the seismicity in an epidemic type model like ETAS) is also generated through a stochastic procedure. The procedure leads to two spatio-temporal outcomes: (1) the probability distribution for the forecasted number of events, and (2) the uncertainty in estimating the
Metastability of exponentially perturbed Markov chains
Institute of Scientific and Technical Information of China (English)
陈大岳; 冯建峰; 钱敏平
1996-01-01
A family of irreducible Markov chains on a finite state space is considered as an exponential perturbation of a reducible Markov chain. This is a generalization of the Freidlin-Wentzell theory, motivated by studies of stochastic Ising models, neural network and simulated annealing. It is shown that the metastability is a universal feature for this wide class of Markov chains. The metastable states are simply those recurrent states of the reducible Markov chain. Higher level attractors, related attractive basins and their pyramidal structure are analysed. The logarithmic asymptotics of the hitting time of various sets are estimated. The hitting time over its mean converges in law to the unit exponential distribution.
Markov processes and controlled Markov chains
Filar, Jerzy; Chen, Anyue
2002-01-01
The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South Ameri...
Single-Index Additive Vector Autoregressive Time Series Models
LI, YEHUA
2009-09-01
We study a new class of nonlinear autoregressive models for vector time series, where the current vector depends on single-indexes defined on the past lags and the effects of different lags have an additive form. A sufficient condition is provided for stationarity of such models. We also study estimation of the proposed model using P-splines, hypothesis testing, asymptotics, selection of the order of the autoregression and of the smoothing parameters and nonlinear forecasting. We perform simulation experiments to evaluate our model in various settings. We illustrate our methodology on a climate data set and show that our model provides more accurate yearly forecasts of the El Niño phenomenon, the unusual warming of water in the Pacific Ocean. © 2009 Board of the Foundation of the Scandinavian Journal of Statistics.
Energy Technology Data Exchange (ETDEWEB)
Kadoura, Ahmad; Sun, Shuyu, E-mail: shuyu.sun@kaust.edu.sa; Salama, Amgad
2014-08-01
Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system's potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide.
Kadoura, Ahmad Salim
2014-08-01
Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system\\'s potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide. © 2014 Elsevier Inc.
Random Walk Smooth Transition Autoregressive Models
2004-01-01
This paper extends the family of smooth transition autoregressive (STAR) models by proposing a specification in which the autoregressive parameters follow random walks. The random walks in the parameters can capture structural change within a regime switching framework, but in contrast to the time varying STAR (TV-STAR) speciifcation recently introduced by Lundbergh et al (2003), structural change in our random walk STAR (RW-STAR) setting follows a stochastic process rather than a determinist...
Alfaro, Michael E; Zoller, Stefan; Lutzoni, François
2003-02-01
Bayesian Markov chain Monte Carlo sampling has become increasingly popular in phylogenetics as a method for both estimating the maximum likelihood topology and for assessing nodal confidence. Despite the growing use of posterior probabilities, the relationship between the Bayesian measure of confidence and the most commonly used confidence measure in phylogenetics, the nonparametric bootstrap proportion, is poorly understood. We used computer simulation to investigate the behavior of three phylogenetic confidence methods: Bayesian posterior probabilities calculated via Markov chain Monte Carlo sampling (BMCMC-PP), maximum likelihood bootstrap proportion (ML-BP), and maximum parsimony bootstrap proportion (MP-BP). We simulated the evolution of DNA sequence on 17-taxon topologies under 18 evolutionary scenarios and examined the performance of these methods in assigning confidence to correct monophyletic and incorrect monophyletic groups, and we examined the effects of increasing character number on support value. BMCMC-PP and ML-BP were often strongly correlated with one another but could provide substantially different estimates of support on short internodes. In contrast, BMCMC-PP correlated poorly with MP-BP across most of the simulation conditions that we examined. For a given threshold value, more correct monophyletic groups were supported by BMCMC-PP than by either ML-BP or MP-BP. When threshold values were chosen that fixed the rate of accepting incorrect monophyletic relationship as true at 5%, all three methods recovered most of the correct relationships on the simulated topologies, although BMCMC-PP and ML-BP performed better than MP-BP. BMCMC-PP was usually a less biased predictor of phylogenetic accuracy than either bootstrapping method. BMCMC-PP provided high support values for correct topological bipartitions with fewer characters than was needed for nonparametric bootstrap.
Dynamic Bandwidth Provisioning Using Markov Chain Based on RSVP
2013-09-01
Cambridge University Press,2008. [20] P. Bremaud, Markov Chains : Gibbs Fields, Monte Carlo Simulation and Queues, New York, NY, Springer Science...is successful. Qualnet, a simulation platform for the wireless environment is used to simulate the algorithm (integration of Markov chain ...in Qualnet, the simulation platform used. 16 THIS PAGE INTENTIONALLY LEFT BLANK 17 III. GENERAL DISCUSSION OF MARKOV CHAIN ALGORITHM AND RSVP
King, Martin D; Crowder, Martin J; Hand, David J; Harris, Neil G; Williams, Stephen R; Obrenovitch, Tihomir P; Gadian, David G
2003-06-01
Markov chain Monte Carlo simulation was used in a reanalysis of the longitudinal data obtained by Harris et al. (J Cereb Blood Flow Metab 20:28-36) in a study of the direct current (DC) potential and apparent diffusion coefficient (ADC) responses to focal ischemia. The main purpose was to provide a formal analysis of the temporal relationship between the ADC and DC responses, to explore the possible involvement of a common latent (driving) process. A Bayesian nonlinear hierarchical random coefficients model was adopted. DC and ADC transition parameter posterior probability distributions were generated using three parallel Markov chains created using the Metropolis algorithm. Particular attention was paid to the within-subject differences between the DC and ADC time course characteristics. The results show that the DC response is biphasic, whereas the ADC exhibits monophasic behavior, and that the two DC components are each distinguishable from the ADC response in their time dependencies. The DC and ADC changes are not, therefore, driven by a common latent process. This work demonstrates a general analytical approach to the multivariate, longitudinal data-processing problem that commonly arises in stroke and other biomedical research.
Operational modal analysis by updating autoregressive model
Vu, V. H.; Thomas, M.; Lakis, A. A.; Marcouiller, L.
2011-04-01
This paper presents improvements of a multivariable autoregressive (AR) model for applications in operational modal analysis considering simultaneously the temporal response data of multi-channel measurements. The parameters are estimated by using the least squares method via the implementation of the QR factorization. A new noise rate-based factor called the Noise rate Order Factor (NOF) is introduced for use in the effective selection of model order and noise rate estimation. For the selection of structural modes, an orderwise criterion called the Order Modal Assurance Criterion (OMAC) is used, based on the correlation of mode shapes computed from two successive orders. Specifically, the algorithm is updated with respect to model order from a small value to produce a cost-effective computation. Furthermore, the confidence intervals of each natural frequency, damping ratio and mode shapes are also computed and evaluated with respect to model order and noise rate. This method is thus very effective for identifying the modal parameters in case of ambient vibrations dealing with modern output-only modal analysis. Simulations and discussions on a steel plate structure are presented, and the experimental results show good agreement with the finite element analysis.
Directory of Open Access Journals (Sweden)
Kevin McNally
2012-01-01
Full Text Available There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure.
McNally, Kevin; Cotton, Richard; Cocker, John; Jones, Kate; Bartels, Mike; Rick, David; Price, Paul; Loizou, George
2012-01-01
There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure.
Monaco, James Peter; Madabhushi, Anant
2011-07-01
The ability of classification systems to adjust their performance (sensitivity/specificity) is essential for tasks in which certain errors are more significant than others. For example, mislabeling cancerous lesions as benign is typically more detrimental than mislabeling benign lesions as cancerous. Unfortunately, methods for modifying the performance of Markov random field (MRF) based classifiers are noticeably absent from the literature, and thus most such systems restrict their performance to a single, static operating point (a paired sensitivity/specificity). To address this deficiency we present weighted maximum posterior marginals (WMPM) estimation, an extension of maximum posterior marginals (MPM) estimation. Whereas the MPM cost function penalizes each error equally, the WMPM cost function allows misclassifications associated with certain classes to be weighted more heavily than others. This creates a preference for specific classes, and consequently a means for adjusting classifier performance. Realizing WMPM estimation (like MPM estimation) requires estimates of the posterior marginal distributions. The most prevalent means for estimating these--proposed by Marroquin--utilizes a Markov chain Monte Carlo (MCMC) method. Though Marroquin's method (M-MCMC) yields estimates that are sufficiently accurate for MPM estimation, they are inadequate for WMPM. To more accurately estimate the posterior marginals we present an equally simple, but more effective extension of the MCMC method (E-MCMC). Assuming an identical number of iterations, E-MCMC as compared to M-MCMC yields estimates with higher fidelity, thereby 1) allowing a far greater number and diversity of operating points and 2) improving overall classifier performance. To illustrate the utility of WMPM and compare the efficacies of M-MCMC and E-MCMC, we integrate them into our MRF-based classification system for detecting cancerous glands in (whole-mount or quarter) histological sections of the prostate.
Quantum Markov fields on graphs
2009-01-01
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on $C^*$-algebras defined by general graphs. As examples of generalized d-Markov chains, we construct the entangled Markov fields on tree graphs. The concrete examples of generalized d-Markov chains on Cayley trees are also investigated.
Relative survival multistate Markov model.
Huszti, Ella; Abrahamowicz, Michal; Alioum, Ahmadou; Binquet, Christine; Quantin, Catherine
2012-02-10
Prognostic studies often have to deal with two important challenges: (i) separating effects of predictions on different 'competing' events and (ii) uncertainty about cause of death. Multistate Markov models permit multivariable analyses of competing risks of, for example, mortality versus disease recurrence. On the other hand, relative survival methods help estimate disease-specific mortality risks even in the absence of data on causes of death. In this paper, we propose a new Markov relative survival (MRS) model that attempts to combine these two methodologies. Our MRS model extends the existing multistate Markov piecewise constant intensities model to relative survival modeling. The intensity of transitions leading to death in the MRS model is modeled as the sum of an estimable excess hazard of mortality from the disease of interest and an 'offset' defined as the expected hazard of all-cause 'natural' mortality obtained from relevant life-tables. We evaluate the new MRS model through simulations, with a design based on registry-based prognostic studies of colon cancer. Simulation results show almost unbiased estimates of prognostic factor effects for the MRS model. We also applied the new MRS model to reassess the role of prognostic factors for mortality in a study of colorectal cancer. The MRS model considerably reduces the bias observed with the conventional Markov model that does not permit accounting for unknown causes of death, especially if the 'true' effects of a prognostic factor on the two types of mortality differ substantially.
A Markov-based Curbside Parking Model and Simulations%基于马尔科夫链的停车寻位模型与仿真
Institute of Scientific and Technical Information of China (English)
田琼; 杨丽; 罗婷
2015-01-01
本文在经典的环形城市模型上，基于马尔科夫链建立解析的路边停车寻位模型。分别从系统和驾驶者两个角度，对寻位竞争队列进行描述，依据其马尔科夫特性，推导出停车寻位距离概率密度函数，发现传统的二项分布假设不能反映寻位车辆间的竞争车位行为，揭示了寻位车辆间的竞争是已有理论低估了停车难的原因之一。在数理分析基础上，提出环形城市路边停车仿真模型及算法，仿真结果验证了理论模型的结论，并发现车位被连续占用也是低估停车难问题的另一个主要原因。研究结果有助于加深对路边停车行为的认识，为制定相关车辆停车政策提供依据。%Referring to the classic circular city model, a curbside parking model based on the Markov chain theory is formulated. According to its Markov properties, the cruising competition queue is depicted through the viewpoints of the system and drivers, respectively. Consequently, the probability density function of the searching distance is derived, which proves that the traditional binomial distribution is limited in describing the competition behaviors between drivers. Then, a simulation algorithm is established to verify the theoretical results of the Markov model and find that besides the competition behavior, the continuously-parking phenomenon is another major reason for difficult curbside parking. The finding extends our knowledge of curbside parking and can be helpful in designing the curbside parking policies.
Markov stochasticity coordinates
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method-termed Markov Stochasticity Coordinates-is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
MAXIMUM LIKELIHOOD ESTIMATION FOR PERIODIC AUTOREGRESSIVE MOVING AVERAGE MODELS.
Vecchia, A.V.
1985-01-01
A useful class of models for seasonal time series that cannot be filtered or standardized to achieve second-order stationarity is that of periodic autoregressive moving average (PARMA) models, which are extensions of ARMA models that allow periodic (seasonal) parameters. An approximation to the exact likelihood for Gaussian PARMA processes is developed, and a straightforward algorithm for its maximization is presented. The algorithm is tested on several periodic ARMA(1, 1) models through simulation studies and is compared to moment estimation via the seasonal Yule-Walker equations. Applicability of the technique is demonstrated through an analysis of a seasonal stream-flow series from the Rio Caroni River in Venezuela.
Modified Testing for Structural Changes in Autoregressive Processes
Institute of Scientific and Technical Information of China (English)
Hao JIN; Zheng TIAN; Yun Feng YANG
2011-01-01
In this paper, we consider the problem of detecting for structural changes in the autoregressive processes including AR(p) process. In performing a test, we employ the conventional residual CUSUM of squares test (RCUSQ) statistic. The RCUSQ test is based on the subsampiing method introduced by Jach and Kokoszka [J. Methodology and Computing in Applied Probability 25(2004)]. It is shown that under regularity conditions, the asymptotic distribution of the test statistic is the function of a standard Brownian bridge. Simulation results as to AR(1)process and an example of real data analysis axe provided for illustration.
Gong, Wenfeng; Yuan, Li; Fan, Wenyi; Stott, Philip
2015-02-01
There have been rapid population and accelerating urban growth with associated changes in land use and soil degradation in northeast China, an important grain-producing region. The development of integrated use of remote sensing, geographic information systems, and combined cellular automata- Markov models has provided new means of assessing changes in land use and land cover, and has enabled projection of trajectories into the future. We applied such techniques to the prefecture-level city of Harbin, the tenth largest city in China. We found that there had been significant losses of the land uses termed "cropland", "grassland", "wetland", and "floodplain" in favour of "built-up land" and lesser transformations from "floodplain" to "forestland" and "water body" over the 18-year period. However, the transition was not a simple process but a complex network of changes, interchanges, and multiple transitions. In the absence of effective land use policies, projection of past trajectories into a balance state in the future would result in the decline of cropland from 65.6% to 46.9% and the increase of built-up area from 7.7% to 23.0% relative to the total area of the prefecture in 1989. It also led to the virtual elimination of land use types such as unused wetland and floodplain.
Directory of Open Access Journals (Sweden)
J. A. Vrugt
2011-04-01
Full Text Available Formal and informal Bayesian approaches are increasingly being used to treat forcing, model structural, parameter and calibration data uncertainty, and summarize hydrologic prediction uncertainty. This requires posterior sampling methods that approximate the (evolving posterior distribution. We recently introduced the DiffeRential Evolution Adaptive Metropolis (DREAM algorithm, an adaptive Markov Chain Monte Carlo (MCMC method that is especially designed to solve complex, high-dimensional and multimodal posterior probability density functions. The method runs multiple chains in parallel, and maintains detailed balance and ergodicity. Here, I present the latest algorithmic developments, and introduce a discrete sampling variant of DREAM that samples the parameter space at fixed points. The development of this new code, DREAM(D, has been inspired by the existing class of integer optimization problems, and emerging class of experimental design problems. Such non-continuous parameter estimation problems are of considerable theoretical and practical interest. The theory developed herein is applicable to DREAM(ZS (Vrugt et al., 2011 and MT-DREAM(ZS (Laloy and Vrugt, 2011 as well. Two case studies involving a sudoku puzzle and rainfall – runoff model calibration problem are used to illustrate DREAM(D.
Testing for vector autoregressive dynamics under heteroskedasticity
C.M. Hafner (Christian); H. Herwartz
2002-01-01
textabstractIn this paper we introduce a bootstrap procedure to test parameter restrictions in vector autoregressive models which is robust in cases of conditionally heteroskedastic error terms. The adopted wild bootstrap method does not require any parametric specification of the volatility process
Bayesian Vector Autoregressions with Stochastic Volatility
Uhlig, H.F.H.V.S.
1996-01-01
This paper proposes a Bayesian approach to a vector autoregression with stochastic volatility, where the multiplicative evolution of the precision matrix is driven by a multivariate beta variate.Exact updating formulas are given to the nonlinear filtering of the precision matrix.Estimation of the au
Oracle Inequalities for High Dimensional Vector Autoregressions
DEFF Research Database (Denmark)
Callot, Laurent; Kock, Anders Bredahl
This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order...
Forecasting with periodic autoregressive time series models
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard)
1999-01-01
textabstractThis paper is concerned with forecasting univariate seasonal time series data using periodic autoregressive models. We show how one should account for unit roots and deterministic terms when generating out-of-sample forecasts. We illustrate the models for various quarterly UK consumption
Bayesian Analyses of Nonhomogeneous Autoregressive Processes
1986-09-01
random coefficient autoregressive processes have a wide applicability in the analysis of economic, sociological, biological and industrial data...1980). Approximate Bayesian Methods. Trabajos Estadistica , Vol. 32, pp. 223-237. LIU, L. M. and G. C. TIAO (1980). Random Coefficient First
The Integration Order of Vector Autoregressive Processes
DEFF Research Database (Denmark)
Franchi, Massimo
We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2...
Schuurman, N K; Grasman, R P P P; Hamaker, E L
2016-01-01
Multilevel autoregressive models are especially suited for modeling between-person differences in within-person processes. Fitting these models with Bayesian techniques requires the specification of prior distributions for all parameters. Often it is desirable to specify prior distributions that have negligible effects on the resulting parameter estimates. However, the conjugate prior distribution for covariance matrices-the Inverse-Wishart distribution-tends to be informative when variances are close to zero. This is problematic for multilevel autoregressive models, because autoregressive parameters are usually small for each individual, so that the variance of these parameters will be small. We performed a simulation study to compare the performance of three Inverse-Wishart prior specifications suggested in the literature, when one or more variances for the random effects in the multilevel autoregressive model are small. Our results show that the prior specification that uses plug-in ML estimates of the variances performs best. We advise to always include a sensitivity analysis for the prior specification for covariance matrices of random parameters, especially in autoregressive models, and to include a data-based prior specification in this analysis. We illustrate such an analysis by means of an empirical application on repeated measures data on worrying and positive affect.
To center or not to center? Investigating inertia with a multilevel autoregressive model
Directory of Open Access Journals (Sweden)
Ellen L. Hamaker
2015-01-01
Full Text Available Whether level 1 predictors should be centered per cluster has received considerable attention in the multilevel literature. While most agree that there is no one preferred approach, it has also been argued that cluster mean centering is desirable when the within-cluster slope and the between-cluster slope are expected to deviate, and the main interest is in the within-cluster slope. However, we show in a series of simulations that if one has a multilevel autoregressive model in which the level 1 predictor is the lagged outcome variable (i.e., the outcome variable at the previous occasion, cluster mean centering will in general lead to a downward bias in the parameter estimate of the within-cluster slope (i.e., the autoregressive relationship. This is particularly relevant if the main question is whether there is on average an autoregressive effect. Nonetheless, we show that if the main interest is in estimating the effect of a level 2 predictor on the autoregressive parameter (i.e., a cross-level interaction, cluster mean centering should be preferred over other forms of centering. Hence, researchers should be clear on what is considered the main goal of their study, and base their choice of centering method on this when using a multilevel autoregressive model.
A Study of Wind Statistics Through Auto-Regressive and Moving-Average (ARMA) Modeling
Institute of Scientific and Technical Information of China (English)
尹彰; 周宗仁
2001-01-01
Statistical properties of winds near the Taichung Harbour are investigated. The 26 years′incomplete data of wind speeds, measured on an hourly basis, are used as reference. The possibility of imputation using simulated results of the Auto-Regressive (AR), Moving-Average (MA), and/or Auto-Regressive and Moving-Average (ARMA) models is studied. Predictions of the 25-year extreme wind speeds based upon the augmented data are compared with the original series. Based upon the results, predictions of the 50- and 100-year extreme wind speeds are then made.
Directory of Open Access Journals (Sweden)
Knuiman Matthew
2008-06-01
Full Text Available Abstract Background Treatments for coronary heart disease (CHD have evolved rapidly over the last 15 years with considerable change in the number and effectiveness of both medical and surgical treatments. This period has seen the rapid development and uptake of statin drugs and coronary artery revascularization procedures (CARPs that include Coronary Artery Bypass Graft procedures (CABGs and Percutaneous Coronary Interventions (PCIs. It is difficult in an era of such rapid change to accurately forecast requirements for treatment services such as CARPs. In a previous paper we have described and outlined the use of a Markov Monte Carlo simulation model for analyzing and predicting the requirements for CARPs for the population of Western Australia (Mannan et al, 2007. In this paper, we expand on the use of this model for forecasting CARPs in Western Australia with a focus on the lack of adequate performance of the (standard model for forecasting CARPs in a period during the mid 1990s when there were considerable changes to CARP technology and implementation policy and an exploration and demonstration of how the standard model may be adapted to achieve better performance. Methods Selected key CARP event model probabilities are modified based on information relating to changes in the effectiveness of CARPs from clinical trial evidence and an awareness of trends in policy and practice of CARPs. These modified model probabilities and the ones obtained by standard methods are used as inputs in our Markov simulation model. Results The projected numbers of CARPs in the population of Western Australia over 1995–99 only improve marginally when modifications to model probabilities are made to incorporate an increase in effectiveness of PCI procedures. However, the projected numbers improve substantially when, in addition, further modifications are incorporated that relate to the increased probability of a PCI procedure and the reduced probability of a CABG
Search for periodicities in experimental data using an autoregression data model
Belashev, B Z
2001-01-01
To process data obtained during interference experiments in high-energy physics, methods of spectral analysis are employed. Methods of spectral analysis, in which an autoregression model of experimental data is used, such as the maximum entropy technique as well as Pisarenko and Prony's method, are described. To show the potentials of the methods, experimental and simulated hummed data are discussed as an example.
Grabski
2014-01-01
Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. Clearly defines the properties and
Energy Technology Data Exchange (ETDEWEB)
Glaser, R E; Johannesson, G; Sengupta, S; Kosovic, B; Carle, S; Franz, G A; Aines, R D; Nitao, J J; Hanley, W G; Ramirez, A L; Newmark, R L; Johnson, V M; Dyer, K M; Henderson, K A; Sugiyama, G A; Hickling, T L; Pasyanos, M E; Jones, D A; Grimm, R J; Levine, R A
2004-03-11
Accurate prediction of complex phenomena can be greatly enhanced through the use of data and observations to update simulations. The ability to create these data-driven simulations is limited by error and uncertainty in both the data and the simulation. The stochastic engine project addressed this problem through the development and application of a family of Markov Chain Monte Carlo methods utilizing importance sampling driven by forward simulators to minimize time spent search very large state spaces. The stochastic engine rapidly chooses among a very large number of hypothesized states and selects those that are consistent (within error) with all the information at hand. Predicted measurements from the simulator are used to estimate the likelihood of actual measurements, which in turn reduces the uncertainty in the original sample space via a conditional probability method called Bayesian inferencing. This highly efficient, staged Metropolis-type search algorithm allows us to address extremely complex problems and opens the door to solving many data-driven, nonlinear, multidimensional problems. A key challenge has been developing representation methods that integrate the local details of real data with the global physics of the simulations, enabling supercomputers to efficiently solve the problem. Development focused on large-scale problems, and on examining the mathematical robustness of the approach in diverse applications. Multiple data types were combined with large-scale simulations to evaluate systems with {approx}{sup 10}20,000 possible states (detecting underground leaks at the Hanford waste tanks). The probable uses of chemical process facilities were assessed using an evidence-tree representation and in-process updating. Other applications included contaminant flow paths at the Savannah River Site, locating structural flaws in buildings, improving models for seismic travel times systems used to monitor nuclear proliferation, characterizing the source
Energy Technology Data Exchange (ETDEWEB)
Saldanha Filho, Paulo Carlos
1998-02-01
Stochastic simulation has been employed in petroleum reservoir characterization as a modeling tool able to reconcile information from several different sources. It has the ability to preserve the variability of the modeled phenomena and permits transference of geological knowledge to numerical models of flux, whose predictions on reservoir constitute the main basis for reservoir management decisions. Several stochastic models have been used and/or suggested, depending on the nature of the phenomena to be described. Markov Random Fields (MRFs) appear as an alternative for the modeling of discrete variables, mainly reservoirs with mosaic architecture of facies. In this dissertation, the reader is introduced to the stochastic modeling by MRFs in a generic sense. The main aspects of the technique are reviewed. MRF Conceptual Background is described: its characterization through the Markovian property and the equivalence to Gibbs distributions. The framework for generic modeling of MRFs is described. The classical models of Ising and Potts-Strauss are specific in this context and are related to models of Ising and Potts-Strauss are specific in this context and are related to models used in petroleum reservoir characterization. The problem of parameter estimation is discussed. The maximum pseudolikelihood estimators for some models are presented. Estimators for two models useful for reservoir characterization are developed, and represent a new contribution to the subject. Five algorithms for the Conditional Simulation of MRFs are described: the Metropolis algorithm, the algorithm of German and German (Gibbs sampler), the algorithm of Swendsen-Wang, the algorithm of Wolff, and the algorithm of Flinn. Finally, examples of simulation for some of the models discussed are presented, along with their implications on the modelling of petroleum reservoirs. (author)
Nishizawa, Manami; Nishizawa, Kazuhisa
2002-12-01
To study the mechanisms for local evolutionary changes in DNA sequences involving slippage-type insertions and deletions, an alignment approach is explored that can consider the posterior probabilities of alignment models. Various patterns of insertion and deletion that can link the ancestor and descendant sequences are proposed and evaluated by simulation and compared by the Markov chain Monte Carlo (MCMC) method. Analyses of pseudogenes reveal that the introduction of the parameters that control the probability of slippage-type events markedly augments the probability of the observed sequence evolution, arguing that a cryptic involvement of slippage occurrences is manifested as insertions and deletions of short nucleotide segments. Strikingly, approximately 80% of insertions in human pseudogenes and approximately 50% of insertions in murids pseudogenes are likely to be caused by the slippage-mediated process, as represented by BC in ABCD --> ABCBCD. We suggest that, in both human and murids, even very short repetitive motifs, such as CAGCAG, CACACA, and CCCC, have approximately 10- to 15-fold susceptibility to insertions and deletions, compared to nonrepetitive sequences. Our protocol, namely, indel-MCMC, thus seems to be a reasonable approach for statistical analyses of the early phase of microsatellite evolution.
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Badawi A
2012-04-01
Full Text Available Soroush Mortaz*, Christine Wessman*, Ross Duncan, Rachel Gray, Alaa Badawi Office of Biotechnology Genomics and Population Health, Public Health Agency of Canada, Toronto, Ontario, Canada*Both authors contributed equally to this workBackground: Type 2 diabetes mellitus (T2DM is a major global health problem. An estimated 20%–50% of diabetic subjects in Canada are currently undiagnosed, and around 20%–30% have already developed complications. Screening for high blood glucose levels can identify people with prediabetic conditions and permit introduction of timely and effective prevention. This study examines the benefit of screening for impaired fasting glucose (IFG and T2DM. If intervention is introduced at this prediabetic stage, it can be most effective in delaying the onset and complications of T2DM.Methods: Using a Markov model simulation, we compare the cost-effectiveness of screening for prediabetes (IFG and T2DM with the strategy of no screening. An initial cohort of normoglycemic, prediabetic, or undiagnosed diabetic adults with one or more T2DM risk factors was used to model the strategies mentioned over a 10-year period. Subjects without known prediabetes or diabetes are screened every 3 years and persons with prediabetes were tested for diabetes on an annual basis. The model weighs the increase in quality-adjusted life-years (QALYs associated with early detection of prediabetes and earlier diagnosis of T2DM due to lifestyle intervention and early treatment in asymptomatic subjects.Results: Costs for each QALY gained were $2281 for conventional screening compared with $2890 for no screening. Thus, in this base-case analysis, conventional screening with a frequency of once every 3 years was favored over no screening. Furthermore, conventional screening was more favorable compared with no screening over a wide range of willingness-to-pay thresholds. Changing the frequency of screening did not affect the overall results. Screening
Fitting Hidden Markov Models to Psychological Data
Directory of Open Access Journals (Sweden)
Ingmar Visser
2002-01-01
Full Text Available Markov models have been used extensively in psychology of learning. Applications of hidden Markov models are rare however. This is partially due to the fact that comprehensive statistics for model selection and model assessment are lacking in the psychological literature. We present model selection and model assessment statistics that are particularly useful in applying hidden Markov models in psychology. These statistics are presented and evaluated by simulation studies for a toy example. We compare AIC, BIC and related criteria and introduce a prediction error measure for assessing goodness-of-fit. In a simulation study, two methods of fitting equality constraints are compared. In two illustrative examples with experimental data we apply selection criteria, fit models with constraints and assess goodness-of-fit. First, data from a concept identification task is analyzed. Hidden Markov models provide a flexible approach to analyzing such data when compared to other modeling methods. Second, a novel application of hidden Markov models in implicit learning is presented. Hidden Markov models are used in this context to quantify knowledge that subjects express in an implicit learning task. This method of analyzing implicit learning data provides a comprehensive approach for addressing important theoretical issues in the field.
Schoups, G.H.W.; Vrugt, J.A.; Fenicia, F.; Van de Giesen, N.C.
2010-01-01
Conceptual rainfall‐runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first‐order, explicit, fixed‐step integration methods leads to computationally cheap simulation models that are e
Schoups, G.; Vrugt, J.A.; Fenicia, F.; van de Giesen, N.C.
2010-01-01
Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are e
Generalization of Brownian Motion with Autoregressive Increments
Fendick, Kerry
2011-01-01
This paper introduces a generalization of Brownian motion with continuous sample paths and stationary, autoregressive increments. This process, which we call a Brownian ray with drift, is characterized by three parameters quantifying distinct effects of drift, volatility, and autoregressiveness. A Brownian ray with drift, conditioned on its state at the beginning of an interval, is another Brownian ray with drift over the interval, and its expected path over the interval is a ray with a slope that depends on the conditioned state. This paper shows how Brownian rays can be applied in finance for the analysis of queues or inventories and the valuation of options. We model a queue's net input process as a superposition of Brownian rays with drift and derive the transient distribution of the queue length conditional on past queue lengths and on past states of the individual Brownian rays comprising the superposition. The transient distributions of Regulated Brownian Motion and of the Regulated Brownian Bridge are...
Detrended Fluctuation Analysis of Autoregressive Processes
Morariu, V V; Vamos, C; Soltuz, S
2007-01-01
Autoregressive processes (AR) have typical short-range memory. Detrended Fluctuation Analysis (DFA) was basically designed to reveal long range correlation in non stationary processes. However DFA can also be regarded as a suitable method to investigate both long-range and short range correlation in non-stationary and stationary systems. Applying DFA to AR processes can help understanding the non uniform correlation structure of such processes. We systematically investigated a first order autoregressive model AR(1) by DFA and established the relationship between the interaction constant of AR(1) and the DFA correlation exponent. The higher the interaction constant the higher is the short range correlation exponent. They are exponentially related. The investigation was extended to AR(2) processes. The presence of a distant positive interaction in addition to a near by interaction will increase the correlation exponent and the range of correlation while the effect of a distant negative interaction will decrease...
Abdulla, Parosh Aziz; Mayr, Richard
2007-01-01
We consider qualitative and quantitative verification problems for infinite-state Markov chains. We call a Markov chain decisive w.r.t. a given set of target states F if it almost certainly eventually reaches either F or a state from which F can no longer be reached. While all finite Markov chains are trivially decisive (for every set F), this also holds for many classes of infinite Markov chains. Infinite Markov chains which contain a finite attractor are decisive w.r.t. every set F. In particular, this holds for probabilistic lossy channel systems (PLCS). Furthermore, all globally coarse Markov chains are decisive. This class includes probabilistic vector addition systems (PVASS) and probabilistic noisy Turing machines (PNTM). We consider both safety and liveness problems for decisive Markov chains, i.e., the probabilities that a given set of states F is eventually reached or reached infinitely often, respectively. 1. We express the qualitative problems in abstract terms for decisive Markov chains, and show...
DEFF Research Database (Denmark)
Justesen, Jørn
2005-01-01
A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly.......A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly....
Generalization error bounds for stationary autoregressive models
McDonald, Daniel J; Schervish, Mark
2011-01-01
We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that the stationarity assumption alone lets us treat the estimation of AR models as a regularized kernel regression without the need to further regularize the model arbitrarily. We thereby bound the Rademacher complexity of AR models and apply existing Rademacher complexity results to characterize the predictive risk of AR models. We demonstrate our methods by predicting interest rate movements.
Ristad, E S; Ristad, Eric Sven; Thomas, Robert G.
1996-01-01
A statistical language model assigns probability to strings of arbitrary length. Unfortunately, it is not possible to gather reliable statistics on strings of arbitrary length from a finite corpus. Therefore, a statistical language model must decide that each symbol in a string depends on at most a small, finite number of other symbols in the string. In this report we propose a new way to model conditional independence in Markov models. The central feature of our nonuniform Markov model is that it makes predictions of varying lengths using contexts of varying lengths. Experiments on the Wall Street Journal reveal that the nonuniform model performs slightly better than the classic interpolated Markov model. This result is somewhat remarkable because both models contain identical numbers of parameters whose values are estimated in a similar manner. The only difference between the two models is how they combine the statistics of longer and shorter strings. Keywords: nonuniform Markov model, interpolated Markov m...
Autoregressive cascades on random networks
Iyer, Srikanth K.; Vaze, Rahul; Narasimha, Dheeraj
2016-04-01
A network cascade model that captures many real-life correlated node failures in large networks via load redistribution is studied. The considered model is well suited for networks where physical quantities are transmitted, e.g., studying large scale outages in electrical power grids, gridlocks in road networks, and connectivity breakdown in communication networks, etc. For this model, a phase transition is established, i.e., existence of critical thresholds above or below which a small number of node failures lead to a global cascade of network failures or not. Theoretical bounds are obtained for the phase transition on the critical capacity parameter that determines the threshold above and below which cascade appears or disappears, respectively, that are shown to closely follow numerical simulation results.
Dodani, Sheel C.; Kiss, Gert; Cahn, Jackson K. B.; Su, Ye; Pande, Vijay S.; Arnold, Frances H.
2016-05-01
The dynamic motions of protein structural elements, particularly flexible loops, are intimately linked with diverse aspects of enzyme catalysis. Engineering of these loop regions can alter protein stability, substrate binding and even dramatically impact enzyme function. When these flexible regions are unresolvable structurally, computational reconstruction in combination with large-scale molecular dynamics simulations can be used to guide the engineering strategy. Here we present a collaborative approach that consists of both experiment and computation and led to the discovery of a single mutation in the F/G loop of the nitrating cytochrome P450 TxtE that simultaneously controls loop dynamics and completely shifts the enzyme's regioselectivity from the C4 to the C5 position of L-tryptophan. Furthermore, we find that this loop mutation is naturally present in a subset of homologous nitrating P450s and confirm that these uncharacterized enzymes exclusively produce 5-nitro-L-tryptophan, a previously unknown biosynthetic intermediate.
[Decision analysis in radiology using Markov models].
Golder, W
2000-01-01
Markov models (Multistate transition models) are mathematical tools to simulate a cohort of individuals followed over time to assess the prognosis resulting from different strategies. They are applied on the assumption that persons are in one of a finite number of states of health (Markov states). Each condition is given a transition probability as well as an incremental value. Probabilities may be chosen constant or varying over time due to predefined rules. Time horizon is divided into equal increments (Markov cycles). The model calculates quality-adjusted life expectancy employing real-life units and values and summing up the length of time spent in each health state adjusted for objective outcomes and subjective appraisal. This sort of modeling prognosis for a given patient is analogous to utility in common decision trees. Markov models can be evaluated by matrix algebra, probabilistic cohort simulation and Monte Carlo simulation. They have been applied to assess the relative benefits and risks of a limited number of diagnostic and therapeutic procedures in radiology. More interventions should be submitted to Markov analyses in order to elucidate their cost-effectiveness.
Fuzzy Markov chains: uncertain probabilities
2002-01-01
We consider finite Markov chains where there are uncertainties in some of the transition probabilities. These uncertainties are modeled by fuzzy numbers. Using a restricted fuzzy matrix multiplication we investigate the properties of regular, and absorbing, fuzzy Markov chains and show that the basic properties of these classical Markov chains generalize to fuzzy Markov chains.
Directory of Open Access Journals (Sweden)
Mehdi Javanbakht
Full Text Available The aim of this study was to estimate the economic burden of diabetes mellitus (DM in Iran from 2009 to 2030.A Markov micro-simulation (MM model was developed to predict the DM population size and associated economic burden. Age- and sex-specific prevalence and incidence of diagnosed and undiagnosed DM were derived from national health surveys. A systematic review was performed to identify the cost of diabetes in Iran and the mean annual direct and indirect costs of patients with DM were estimated using a random-effect Bayesian meta-analysis. Face, internal, cross and predictive validity of the MM model were assessed by consulting an expert group, performing sensitivity analysis (SA and comparing model results with published literature and national survey reports. Sensitivity analysis was also performed to explore the effect of uncertainty in the model.We estimated 3.78 million cases of DM (2.74 million diagnosed and 1.04 million undiagnosed in Iran in 2009. This number is expected to rise to 9.24 million cases (6.73 million diagnosed and 2.50 million undiagnosed by 2030. The mean annual direct and indirect costs of patients with DM in 2009 were US$ 556 (posterior standard deviation, 221 and US$ 689 (619, respectively. Total estimated annual cost of DM was $3.64 (2009 US$ billion (including US$1.71 billion direct and US$1.93 billion indirect costs in 2009 and is predicted to increase to $9.0 (in 2009 US$ billion (including US$4.2 billion direct and US$4.8 billion indirect costs by 2030.The economic burden of DM in Iran is predicted to increase markedly in the coming decades. Identification and implementation of effective strategies to prevent and manage DM should be considered as a public health priority.
Robust Burg estimation of stationary autoregressive mixtures covariance
Decurninge, Alexis; Barbaresco, Frédéric
2015-01-01
Burg estimators are classically used for the estimation of the autocovariance of a stationary autoregressive process. We propose to consider scale mixtures of stationary autoregressive processes, a non-Gaussian extension of the latter. The traces of such processes are Spherically Invariant Random Vectors (SIRV) with a constraint on the scatter matrix due to the autoregressive model. We propose adaptations of the Burg estimators to the considered models and their associated robust versions based on geometrical considerations.
Identifying regime shifts in Indian stock market: A Markov switching approach
Wasim, Ahmad; Bandi, Kamaiah
2011-01-01
Seeking for the existence of bull and bear regimes in the Indian stock market, a two state Markov switching autoregressive model (MS (2)-AR (2)) is used to identify bull and bear market regimes. The model predicts that Indian stock market will remain under bull regime with very high probability compared to bear regime. The results also identify the bear phases during all major global economic crises including recent US sub-prime (2008) and European debt crisis (2010). The paper concludes that...
Multi-fidelity modelling via recursive co-kriging and Gaussian–Markov random fields
Perdikaris, P.; Venturi, D.; Royset, J. O.; Karniadakis, G. E.
2015-01-01
We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account multi-fidelity in models, such as direct numerical simulations versus empirical formulae, as well as multi-fidelity in the probability space (e.g. sparse grids versus tensor product multi-element probabilistic collocation). We are able to construct response surfaces of complex dynamical systems by blending multiple information sources via auto-regressive stochastic modelling. A computationally efficient machine learning framework is developed based on multi-level recursive co-kriging with sparse precision matrices of Gaussian–Markov random fields. The effectiveness of the new algorithms is demonstrated in numerical examples involving a prototype problem in risk-averse design, regression of random functions, as well as uncertainty quantification in fluid mechanics involving the evolution of a Burgers equation from a random initial state, and random laminar wakes behind circular cylinders. PMID:26345079
Autoregressive model selection with simultaneous sparse coefficient estimation
Sang, Hailin
2011-01-01
In this paper we propose a sparse coefficient estimation procedure for autoregressive (AR) models based on penalized conditional maximum likelihood. The penalized conditional maximum likelihood estimator (PCMLE) thus developed has the advantage of performing simultaneous coefficient estimation and model selection. Mild conditions are given on the penalty function and the innovation process, under which the PCMLE satisfies a strong consistency, local $N^{-1/2}$ consistency, and oracle property, respectively, where N is sample size. Two penalty functions, least absolute shrinkage and selection operator (LASSO) and smoothly clipped average deviation (SCAD), are considered as examples, and SCAD is shown to have better performances than LASSO. A simulation study confirms our theoretical results. At the end, we provide an application of our method to a historical price data of the US Industrial Production Index for consumer goods, and the result is very promising.
Modeling of non-stationary autoregressive alpha-stable processe
National Aeronautics and Space Administration — In the literature, impulsive signals are mostly modeled by symmetric alpha-stable processes. To represent their temporal dependencies, usually autoregressive models...
Directory of Open Access Journals (Sweden)
R.J. Boys
2002-01-01
Full Text Available This paper describes a Bayesian approach to determining the order of a finite state Markov chain whose transition probabilities are themselves governed by a homogeneous finite state Markov chain. It extends previous work on homogeneous Markov chains to more general and applicable hidden Markov models. The method we describe uses a Markov chain Monte Carlo algorithm to obtain samples from the (posterior distribution for both the order of Markov dependence in the observed sequence and the other governing model parameters. These samples allow coherent inferences to be made straightforwardly in contrast to those which use information criteria. The methods are illustrated by their application to both simulated and real data sets.
Massey, J. L.
1975-01-01
A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.
Elbourne, A.; de Haan, J.
2009-01-01
Using the vector autoregressive methodology, we present estimates of monetary transmission for five new EU member countries in Central and Eastern Europe with more or less flexible exchange rates. We select sample periods to estimate over the longest possible period that can be considered as a singl
Problem signatures from enhanced vector autoregressive modeling
Andriamanalimanana, Bruno R.; Sengupta, Saumen S.
2001-09-01
The work reported in this paper concerns the enhancement of mutivariate autoregressive (AR) models with geometric shape analysis data and stochastic causal relations. The study aims at producing numerical signatures characterizing operating problems, from multivariate time series of data collected in an application and operating environment domain. Since the information content of an AR model does not appear sufficient to characterize observed vector values fully, both geometric and stochastic modeling techniques are applied to refine causal inferences further. The specific application domain used for this study is real-time network traffic monitoring. However, other domains utilizing vector models might benefit as well. A partial Java implementation is being used for experimentation.
Chain binomial models and binomial autoregressive processes.
Weiss, Christian H; Pollett, Philip K
2012-09-01
We establish a connection between a class of chain-binomial models of use in ecology and epidemiology and binomial autoregressive (AR) processes. New results are obtained for the latter, including expressions for the lag-conditional distribution and related quantities. We focus on two types of chain-binomial model, extinction-colonization and colonization-extinction models, and present two approaches to parameter estimation. The asymptotic distributions of the resulting estimators are studied, as well as their finite-sample performance, and we give an application to real data. A connection is made with standard AR models, which also has implications for parameter estimation.
ENSO Prediction using Vector Autoregressive Models
Chapman, D. R.; Cane, M. A.; Henderson, N.; Lee, D.; Chen, C.
2013-12-01
A recent comparison (Barnston et al, 2012 BAMS) shows the ENSO forecasting skill of dynamical models now exceeds that of statistical models, but the best statistical models are comparable to all but the very best dynamical models. In this comparison the leading statistical model is the one based on the Empirical Model Reduction (EMR) method. Here we report on experiments with multilevel Vector Autoregressive models using only sea surface temperatures (SSTs) as predictors. VAR(L) models generalizes Linear Inverse Models (LIM), which are a VAR(1) method, as well as multilevel univariate autoregressive models. Optimal forecast skill is achieved using 12 to 14 months of prior state information (i.e 12-14 levels), which allows SSTs alone to capture the effects of other variables such as heat content as well as seasonality. The use of multiple levels allows the model advancing one month at a time to perform at least as well for a 6 month forecast as a model constructed to explicitly forecast 6 months ahead. We infer that the multilevel model has fully captured the linear dynamics (cf. Penland and Magorian, 1993 J. Climate). Finally, while VAR(L) is equivalent to L-level EMR, we show in a 150 year cross validated assessment that we can increase forecast skill by improving on the EMR initialization procedure. The greatest benefit of this change is in allowing the prediction to make effective use of information over many more months.
Partridge, D.G.; Vrugt, J.A.; Tunved, P.; Ekman, A.M.L.; Struthers, H.; Sooroshian, A.
2012-01-01
This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov chain Monte Carlo (MCMC) algorithm to an adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools t
Lehman, Li-wei H.; Nemati, Shamim; Mark, Roger G.
2016-01-01
In a critical care setting, shock and resuscitation endpoints are often defined based on arterial blood pressure values. Patient-specific fluctuations and interactions between heart rate (HR) and blood pressure (BP), however, may provide additional prognostic value to stratify individual patients’ risks for adverse outcomes at different blood pressure targets. In this work, we use the switching autoregressive (SVAR) dynamics inferred from the multivariate vital sign time series to stratify mortality risks of intensive care units (ICUs) patients receiving vasopressor treatment. We model vital sign observations as generated from latent states from an autoregressive Hidden Markov Model (AR-HMM) process, and use the proportion of time patients stayed in different latent states to predict outcome. We evaluate the performance of our approach using minute-by-minute HR and mean arterial BP (MAP) of an ICU patient cohort while on vasopressor treatment. Our results indicate that the bivariate HR/MAP dynamics (AUC 0.74 [0.64, 0.84]) contain additional prognostic information beyond the MAP values (AUC 0.53 [0.42, 0.63]) in mortality prediction. Further, HR/MAP dynamics achieved better performance among a subgroup of patients in a low MAP range (median MAP < 65 mmHg) while on pressors. A realtime implementation of our approach may provide clinicians a tool to quantify the effectiveness of interventions and to inform treatment decisions. PMID:27774489
A General Representation Theorem for Integrated Vector Autoregressive Processes
DEFF Research Database (Denmark)
Franchi, Massimo
We study the algebraic structure of an I(d) vector autoregressive process, where d is restricted to be an integer. This is useful to characterize its polynomial cointegrating relations and its moving average representation, that is to prove a version of the Granger representation theorem valid...... for I(d) vector autoregressive processes...
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Knuiman Matthew
2010-01-01
Full Text Available Abstract Background The population incidence of coronary heart disease (CHD has been declining in Australia and many other countries. This decline has been due to reduced population levels of risk factors for CHD and improved medical care for those at higher risk of CHD. However, there are signs that there may be a slowing down or even reversal in the decline of CHD incidence due to the 'obesity epidemic' and other factors and this will have implications for the requirements for surgical treatments for those with CHD. Methods Using a validated Markov simulation model applied to the population of Western Australia, different CHD incidence trend scenarios were developed to explore the effect of changing CHD incidence on requirements for coronary artery bypass graft (CABG and percutaneous coronary interventions (PCI, together known as coronary artery revascularization procedures (CARPs. Results The most dominant component of CHD incidence is the risk of CHD hospital admission for those with no history of CHD and if this risk leveled off and the trends in all other risks continued unchanged, then the projected numbers of CABGs and PCIs are only minimally changed. Further, the changes in the projected numbers remained small even when this risk was increased by 20 percent (although it is an unlikely scenario. However, when the other CHD incidence components that had also been declining, namely, the risk of CABG and that of CHD death for those with no history of CHD, were also projected to level off as these were declining in 1998-2000 and the risk of PCI for those with no history of CHD (which was already increasing was projected to further increase by 5 percent, it had a substantial effect on the projected numbers of CARPs. Conclusion There needs to be dramatic changes to several CHD incidence components before it has a substantial impact on the projected requirements for CARPs. Continued monitoring of CHD incidence and also the mix of initial
Directory of Open Access Journals (Sweden)
Yu Zhao
2013-01-01
Full Text Available In the study, we discussed the generalized autoregressive conditional heteroskedasticity model and enhanced it with wavelet transform to evaluate the daily returns for 1/4/2002-30/12/2011 period in Brent oil market. We proposed discrete wavelet transform generalized autoregressive conditional heteroskedasticity model to increase the forecasting performance of the generalized autoregressive conditional heteroskedasticity model. Our new approach can overcome the defect of generalized autoregressive conditional heteroskedasticity family models which can’t describe the detail and partial features of times series and retain the advantages of them at the same time. Comparing with the generalized autoregressive conditional heteroskedasticity model, the new approach significantly improved forecast results and greatly reduces conditional variances.
Directory of Open Access Journals (Sweden)
Wararit PANICHKITKOSOLKUL
2012-09-01
Full Text Available Guttman and Tiao [1], and Chang [2] showed that the effect of outliers may cause serious bias in estimating autocorrelations, partial correlations, and autoregressive moving average parameters (cited in Chang et al. [3]. This paper presents a modified weighted symmetric estimator for a Gaussian first-order autoregressive AR(1 model with additive outliers. We apply the recursive median adjustment based on an exponentially weighted moving average (EWMA to the weighted symmetric estimator of Park and Fuller [4]. We consider the following estimators: the weighted symmetric estimator (, the recursive mean adjusted weighted symmetric estimator ( proposed by Niwitpong [5], the recursive median adjusted weighted symmetric estimator ( proposed by Panichkitkosolkul [6], and the weighted symmetric estimator using adjusted recursive median based on EWMA (. Using Monte Carlo simulations, we compare the mean square error (MSE of estimators. Simulation results have shown that the proposed estimator, , provides a MSE lower than those of , and for almost all situations.
Markov bridges, bisection and variance reduction
DEFF Research Database (Denmark)
Asmussen, Søren; Hobolth, Asger
Time-continuous Markov jump processes is a popular modelling tool in disciplines ranging from computational finance and operations research to human genetics and genomics. The data is often sampled at discrete points in time, and it can be useful to simulate sample paths between the datapoints....... In this paper we firstly consider the problem of generating sample paths from a continuous-time Markov chain conditioned on the endpoints using a new algorithm based on the idea of bisection. Secondly we study the potential of the bisection algorithm for variance reduction. In particular, examples are presented...... where the methods of stratification, importance sampling and quasi Monte Carlo are investigated....
El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar
2014-11-01
Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.
Institute of Scientific and Technical Information of China (English)
袁修开; 吕震宙; 许鑫
2011-01-01
For the implicit limit state function usually encountered in an engineering reliability analysis and design, the Support Vector Machine (SVM) reliability analysis method is proposed on fast Markov chain simulation. In the proposed method, Markov chain is used to simulate the samples in the importance region defined by the limit state function, and the surrogate model is obtained by using these samples to train a SVM.Since Markov chain can adaptively simulate the samples of the importance region, and the candidate states but not Markov states are used as the training samples, the proposed method can well approximate the limit state equation in the region contributing to the failure probability significantly, and can utilize the information provided by Markov chain simulation sufficiently. In addition, the gradual change on variance in a simulation process is adopted to improve the quality of the Markov chain samples. Moreover, the proposed method uses the SVM regression method and classification method to construct the surrogate model, which can minimize the risk in approximating the limit state equation, and thus approximate the failure probability with a high precision. Finally numerical and engineering examples illustrate that the proposed method owns good performance in calculating efficiency and precision.%针对实际工程中可靠性分析设计的极限状态方程为隐式的情况,提出了一种基于马尔科夫链模拟的支持向量机可靠性分析方法.所提方法采用改进的马尔科夫链来产生极限状态重要区域上的样本点,再采用支持向量机方法求得相应的函数替代模型来进行可靠性分析.由于马尔科夫链能够自适应的模拟极限状态重要失效区域附近的样本,并且由于采用马尔科夫链备选样本点而非状态点作为训练样本,因而所提方法能够高效快速逼近对失效概率贡献较大区域的极限状态方程,并且充分利用了模拟过程产生的有用信
Empirical Markov Chain Monte Carlo Bayesian analysis of fMRI data.
de Pasquale, F; Del Gratta, C; Romani, G L
2008-08-01
In this work an Empirical Markov Chain Monte Carlo Bayesian approach to analyse fMRI data is proposed. The Bayesian framework is appealing since complex models can be adopted in the analysis both for the image and noise model. Here, the noise autocorrelation is taken into account by adopting an AutoRegressive model of order one and a versatile non-linear model is assumed for the task-related activation. Model parameters include the noise variance and autocorrelation, activation amplitudes and the hemodynamic response function parameters. These are estimated at each voxel from samples of the Posterior Distribution. Prior information is included by means of a 4D spatio-temporal model for the interaction between neighbouring voxels in space and time. The results show that this model can provide smooth estimates from low SNR data while important spatial structures in the data can be preserved. A simulation study is presented in which the accuracy and bias of the estimates are addressed. Furthermore, some results on convergence diagnostic of the adopted algorithm are presented. To validate the proposed approach a comparison of the results with those from a standard GLM analysis, spatial filtering techniques and a Variational Bayes approach is provided. This comparison shows that our approach outperforms the classical analysis and is consistent with other Bayesian techniques. This is investigated further by means of the Bayes Factors and the analysis of the residuals. The proposed approach applied to Blocked Design and Event Related datasets produced reliable maps of activation.
Markov chains for testing redundant software
White, Allan L.; Sjogren, Jon A.
1988-01-01
A preliminary design for a validation experiment has been developed that addresses several problems unique to assuring the extremely high quality of multiple-version programs in process-control software. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process-control testing, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level using confidence intervals obtained for the transition probabilities during the experiment. An example demonstrating the method is provided.
DEFF Research Database (Denmark)
Pinson, Pierre; Madsen, Henrik
2012-01-01
optimized is based on penalized maximum likelihood, with exponential forgetting of past observations. MSAR models are then employed for one-step-ahead point forecasting of 10 min resolution time series of wind power at two large offshore wind farms. They are favourably compared against persistence...
DEFF Research Database (Denmark)
Pinson, Pierre; Madsen, Henrik
optimized is based on penalized maximum-likelihood, with exponential forgetting of past observations. MSAR models are then employed for 1-step-ahead point forecasting of 10-minute resolution time-series of wind power at two large offshore wind farms. They are favourably compared against persistence and Auto...
Turner, Sean; Galelli, Stefano; Wilcox, Karen
2015-04-01
Water reservoir systems are often affected by recurring large-scale ocean-atmospheric anomalies, known as teleconnections, that cause prolonged periods of climatological drought. Accurate forecasts of these events -- at lead times in the order of weeks and months -- may enable reservoir operators to take more effective release decisions to improve the performance of their systems. In practice this might mean a more reliable water supply system, a more profitable hydropower plant or a more sustainable environmental release policy. To this end, climate indices, which represent the oscillation of the ocean-atmospheric system, might be gainfully employed within reservoir operating models that adapt the reservoir operation as a function of the climate condition. This study develops a Stochastic Dynamic Programming (SDP) approach that can incorporate climate indices using a Hidden Markov Model. The model simulates the climatic regime as a hidden state following a Markov chain, with the state transitions driven by variation in climatic indices, such as the Southern Oscillation Index. Time series analysis of recorded streamflow data reveals the parameters of separate autoregressive models that describe the inflow to the reservoir under three representative climate states ("normal", "wet", "dry"). These models then define inflow transition probabilities for use in a classic SDP approach. The key advantage of the Hidden Markov Model is that it allows conditioning the operating policy not only on the reservoir storage and the antecedent inflow, but also on the climate condition, thus potentially allowing adaptability to a broader range of climate conditions. In practice, the reservoir operator would effect a water release tailored to a specific climate state based on available teleconnection data and forecasts. The approach is demonstrated on the operation of a realistic, stylised water reservoir with carry-over capacity in South-East Australia. Here teleconnections relating
Model reduction methods for vector autoregressive processes
Brüggemann, Ralf
2004-01-01
1. 1 Objective of the Study Vector autoregressive (VAR) models have become one of the dominant research tools in the analysis of macroeconomic time series during the last two decades. The great success of this modeling class started with Sims' (1980) critique of the traditional simultaneous equation models (SEM). Sims criticized the use of 'too many incredible restrictions' based on 'supposed a priori knowledge' in large scale macroeconometric models which were popular at that time. Therefore, he advo cated largely unrestricted reduced form multivariate time series models, unrestricted VAR models in particular. Ever since his influential paper these models have been employed extensively to characterize the underlying dynamics in systems of time series. In particular, tools to summarize the dynamic interaction between the system variables, such as impulse response analysis or forecast error variance decompo sitions, have been developed over the years. The econometrics of VAR models and related quantities i...
Noise can speed convergence in Markov chains.
Franzke, Brandon; Kosko, Bart
2011-10-01
A new theorem shows that noise can speed convergence to equilibrium in discrete finite-state Markov chains. The noise applies to the state density and helps the Markov chain explore improbable regions of the state space. The theorem ensures that a stochastic-resonance noise benefit exists for states that obey a vector-norm inequality. Such noise leads to faster convergence because the noise reduces the norm components. A corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality. This leads to a noise-benefit algorithm that requires knowledge of the steady state. An alternative blind algorithm uses only past state information to achieve a weaker noise benefit. Simulations illustrate the predicted noise benefits in three well-known Markov models. The first model is a two-parameter Ehrenfest diffusion model that shows how noise benefits can occur in the class of birth-death processes. The second model is a Wright-Fisher model of genotype drift in population genetics. The third model is a chemical reaction network of zeolite crystallization. A fourth simulation shows a convergence rate increase of 64% for states that satisfy the theorem and an increase of 53% for states that satisfy the corollary. A final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles. Noise benefits tend to be sharpest in Markov models that do not converge quickly and that do not have strong absorbing states.
On Markov Chains and Filtrations
1997-01-01
In this paper we rederive some well known results for continuous time Markov processes that live on a finite state space.Martingale techniques are used throughout the paper. Special attention is paid to the construction of a continuous timeMarkov process, when we start from a discrete time Markov chain. The Markov property here holds with respect tofiltrations that need not be minimal.
A new Markov Binomial distribution
Leda D. Minkova; Omey, Edward
2011-01-01
In this paper, we introduce a two state homogeneous Markov chain and define a geometric distribution related to this Markov chain. We define also the negative binomial distribution similar to the classical case and call it NB related to interrupted Markov chain. The new binomial distribution is related to the interrupted Markov chain. Some characterization properties of the Geometric distributions are given. Recursion formulas and probability mass functions for the NB distribution and the new...
Autoregression of Quasi-Stationary Time Series (Invited)
Meier, T. M.; Küperkoch, L.
2009-12-01
Autoregression is a model based tool for spectral analysis and prediction of time series. It has the potential to increase the resolution of spectral estimates. However, the validity of the assumed model has to be tested. Here we review shortly methods for the determination of the parameters of autoregression and summarize properties of autoregressive prediction and autoregressive spectral analysis. Time series with a limited number of dominant frequencies varying slowly in time (quasi-stationary time series) may well be described by a time-dependent autoregressive model of low order. An algorithm for the estimation of the autoregression parameters in a moving window is presented. Time-varying dominant frequencies are estimated. The comparison to results obtained by Fourier transform based methods and the visualization of the time dependent normalized prediction error are essential for quality assessment of the results. The algorithm is applied to synthetic examples as well as to mircoseism and tremor. The sensitivity of the results to the choice of model and filter parameters is discussed. Autoregressive forward prediction offers the opportunity to detect body wave phases in seismograms and to determine arrival times automatically. Examples are shown for P- and S-phases at local and regional distances. In order to determine S-wave arrival times the autoregressive model is extended to multi-component recordings. For the detection of significant temporal changes in waveforms, the choice of the model appears to be less crucial compared to spectral analysis. Temporal changes in frequency, amplitude, phase, and polarisation are detectable by autoregressive prediction. Quality estimates of automatically determined onset times may be obtained from the slope of the absolute prediction error as a function of time and the signal-to-noise ratio. Results are compared to manual readings.
DEFF Research Database (Denmark)
Kohlenbach, Ulrich Wilhelm
2002-01-01
We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive real number is positive is underivable in E-HA + AC. Since allows one to formalize (atl eastl arge parts of) Bishop's constructive mathematics, this makes it unlikely that WMP can be proved within the...
Institute of Scientific and Technical Information of China (English)
Zhao Haijun; Ma Yan; Huang Xiaohong; Su Yujie
2008-01-01
Predicting heartbeat message arrival time is crucial for the quality of failure detection service over internet. However, internet dynamic characteristics make it very difficult to understand message behavior and accurately predict heartbeat arrival time. To solve this problem, a novel black-box model is proposed to predict the next heartbeat arrival time. Heartbeat arrival time is modeled as auto-regressive process, heartbeat sending time is modeled as exogenous variable, the model's coefficients are estimated based on the sliding window of observations and this result is used to predict the next heartbeat arrival time. Simulation shows that this adaptive auto-regressive exogenous (ARX) model can accurately capture heartbeat arrival dynamics and minimize prediction error in different network environments.
Smith, R. M.
1991-01-01
Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.
Dealing with Multiple Solutions in Structural Vector Autoregressive Models.
Beltz, Adriene M; Molenaar, Peter C M
2016-01-01
Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior.
On nonlinear Markov chain Monte Carlo
Andrieu, Christophe; Doucet, Arnaud; Del Moral, Pierre; 10.3150/10-BEJ307
2011-01-01
Let $\\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for simulating from a probability measure $\\pi\\in\\mathscr{P}(E)$. Nonlinear Markov kernels (see [Feynman--Kac Formulae: Genealogical and Interacting Particle Systems with Applications (2004) Springer]) $K:\\mathscr{P}(E)\\times E\\rightarrow\\mathscr{P}(E)$ can be constructed to, in some sense, improve over MCMC methods. However, such nonlinear kernels cannot be simulated exactly, so approximations of the nonlinear kernels are constructed using auxiliary or potentially self-interacting chains. Several nonlinear kernels are presented and it is demonstrated that, under some conditions, the associated approximations exhibit a strong law of large numbers; our proof technique is via the Poisson equation and Foster--Lyapunov conditions. We investigate the performance of our approximations with some simulations.
On robust forecasting of autoregressive time series under censoring
Kharin, Y.; Badziahin, I.
2009-01-01
Problems of robust statistical forecasting are considered for autoregressive time series observed under distortions generated by interval censoring. Three types of robust forecasting statistics are developed; meansquare risk is evaluated for the developed forecasting statistics. Numerical results are given.
Modeling non-Gaussian time-varying vector autoregressive process
National Aeronautics and Space Administration — We present a novel and general methodology for modeling time-varying vector autoregressive processes which are widely used in many areas such as modeling of chemical...
Estimation of Time Varying Autoregressive Symmetric Alpha Stable
National Aeronautics and Space Administration — In this work, we present a novel method for modeling time-varying autoregressive impulsive signals driven by symmetric alpha stable distributions. The proposed...
Institute of Scientific and Technical Information of China (English)
周亚平; 刘剑宇; 殷保群; 奚宏生
2005-01-01
给出半Markov过程(Semi-Markov Processes)性能势基于一条样本轨道的仿真算法,从并行仿真的角度,将已有Markov过程的性能势理论推广到半Markov过程,使该理论具有更加广泛的应用范围.并将该性能势与等价的Markov过程的性能势进行比较,表明了两者的一致性.
Autoregressive bispectrum characteristics of magneto-rheometer
Institute of Scientific and Technical Information of China (English)
黄宜坚; 陈丙三; 蒋雨燕
2008-01-01
The operating principle of measuring rheological properties of magnetorheological(MR) fluid was expounded by means of a new rheometer with double driving discs rotating at the same speed in the opposite directions.The constitutive equation of MR fluid was established with theoretical analysis from experimental data.The conventional power spectrum approach was unable to detect the existence of quadratic phase coupling for dynamic rheological measurement.Bispectrum analysis is emerging as a new powerful technique in signal processing,which can describe nonlinear coupling,restrain Gaussian noise and reserve phase component.An autoregressive(AR) model of the third order cumulant,the bispectra and bispectral contours were utilized for analyzing the dynamic characteristics of the MR rheometer by merely using the sampled output torque signals when a zero mean non-Gaussian white noise interferes with the rotary disc system.The measurement and analysis process based on virtual instruments were automatically controlled by computer in this paper.The experimental and theoretical results show that rheological properties and dynamic characteristics of MR fluid can be measured with this double disc rheometer.
Energy Technology Data Exchange (ETDEWEB)
Nicoulaud-Gouin, V.; Giacalone, M.; Gonze, M.A. [Institut de Radioprotection et de Surete Nucleaire-PRP-ENV/SERIS/LM2E (France); Martin-Garin, A.; Garcia-Sanchez, L. [IRSN-PRP-ENV/SERIS/L2BT (France)
2014-07-01
, distinguishes instantaneous (K{sub d}1) and first-order kinetics of sorption and desorption processes (λ{sub fix}, λ{sub rem}), each having potentially a limited sorption capacity. A Soil-Plant Deposition Model describing the weeds contamination in {sup 137}Cs, {sup 134}Cs and {sup 131}I, with in situ measures in the Fukushima prefecture (Gonze et al. submitted to this conference). This model considers two foliage pools and a root pool, and describes foliar biomass growth with a Verhulst model. One prerequisite for calibration is model identifiability. Here, we showed that there are not unique parameter values corresponding to a data set. However, sharp distributions were found when several data sets were involved. One numerical difficulty of Markov Chains is to check convergence. It was here examined with Raftery and Lewis diagnostic, Gelman and Rubin plots, and simulation trails. Failing to converge may indicate that the model is not adapted to the observations. The Bayes factor was used to decide between competing models, which applies even if they are not nested. For most data series, EK model was preferable to the nested K{sub d} approach. An Empirical Dynamical Model -consisting of two exponential functions- was compared to the Soil-Plant Deposition Model, by distinguishing site-specific parameters and invariant parameters between stations, in order to study the goodness-of-fit of the Soil-Plant Deposition Model. (authors)
Institute of Scientific and Technical Information of China (English)
马耀庭; 张新龙
2014-01-01
为了研究帧时隙 ALOHA防碰撞算法性能，应用马尔科夫链模型对该算法标签识别过程进行数学分析，得到成功识别出的标签数量的状态转移概率矩阵。用蒙特卡罗统计方法模拟这一过程，对马尔科夫链模型求解，得到了标签数量、时隙数和成功识别率之间的关系曲线。%In order to study the performance of the frame slotted ALOHA anti-collision algorithm,by use of the Markov Model,a mathematical analysis was done to the tag identification process of this algorithm and a state transition probability matrix is thus obtained for the successful identification of the number of tags.By using the Monte-Carlo method to simulate this process,the solution of the Markov Chain Model was worked out and the relationship curve between the number of tags, the number of slots and the rate of successful recognition was obtained.
Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions
Directory of Open Access Journals (Sweden)
Samuel Livingstone
2014-06-01
Full Text Available Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond statistics. A full exposition of Markov chains and their use in Monte Carlo simulation for statistical inference and molecular dynamics is provided, with particular emphasis on methods based on Langevin diffusions. After this, geometric concepts in Markov chain Monte Carlo are introduced. A full derivation of the Langevin diffusion on a Riemannian manifold is given, together with a discussion of the appropriate Riemannian metric choice for different problems. A survey of applications is provided, and some open questions are discussed.
Generalized Markov branching models
Li, Junping
2005-01-01
In this thesis, we first considered a modified Markov branching process incorporating both state-independent immigration and resurrection. After establishing the criteria for regularity and uniqueness, explicit expressions for the extinction probability and mean extinction time are presented. The criteria for recurrence and ergodicity are also established. In addition, an explicit expression for the equilibrium distribution is presented.\\ud \\ud We then moved on to investigate the basic proper...
Generalized Markov branching models
Li, Junping
2005-01-01
In this thesis, we first considered a modified Markov branching process incorporating both state-independent immigration and resurrection. After establishing the criteria for regularity and uniqueness, explicit expressions for the extinction probability and mean extinction time are presented. The criteria for recurrence and ergodicity are also established. In addition, an explicit expression for the equilibrium distribution is presented. We then moved on to investigate the basic proper...
Lee, Duncan; Rushworth, Alastair; Sahu, Sujit K
2014-06-01
Estimation of the long-term health effects of air pollution is a challenging task, especially when modeling spatial small-area disease incidence data in an ecological study design. The challenge comes from the unobserved underlying spatial autocorrelation structure in these data, which is accounted for using random effects modeled by a globally smooth conditional autoregressive model. These smooth random effects confound the effects of air pollution, which are also globally smooth. To avoid this collinearity a Bayesian localized conditional autoregressive model is developed for the random effects. This localized model is flexible spatially, in the sense that it is not only able to model areas of spatial smoothness, but also it is able to capture step changes in the random effects surface. This methodological development allows us to improve the estimation performance of the covariate effects, compared to using traditional conditional auto-regressive models. These results are established using a simulation study, and are then illustrated with our motivating study on air pollution and respiratory ill health in Greater Glasgow, Scotland in 2011. The model shows substantial health effects of particulate matter air pollution and nitrogen dioxide, whose effects have been consistently attenuated by the currently available globally smooth models.
Temperature scaling method for Markov chains.
Crosby, Lonnie D; Windus, Theresa L
2009-01-22
The use of ab initio potentials in Monte Carlo simulations aimed at investigating the nucleation kinetics of water clusters is complicated by the computational expense of the potential energy determinations. Furthermore, the common desire to investigate the temperature dependence of kinetic properties leads to an urgent need to reduce the expense of performing simulations at many different temperatures. A method is detailed that allows a Markov chain (obtained via Monte Carlo) at one temperature to be scaled to other temperatures of interest without the need to perform additional large simulations. This Markov chain temperature-scaling (TeS) can be generally applied to simulations geared for numerous applications. This paper shows the quality of results which can be obtained by TeS and the possible quantities which may be extracted from scaled Markov chains. Results are obtained for a 1-D analytical potential for which the exact solutions are known. Also, this method is applied to water clusters consisting of between 2 and 5 monomers, using Dynamical Nucleation Theory to determine the evaporation rate constant for monomer loss. Although ab initio potentials are not utilized in this paper, the benefit of this method is made apparent by using the Dang-Chang polarizable classical potential for water to obtain statistical properties at various temperatures.
Institute of Scientific and Technical Information of China (English)
尹文也; 何伟基; 顾国华; 陈钱
2014-01-01
To reconstruct the target shape distribution in the distance, full waveform analysis algorithm is utilized by extracting and analyzing the number of the peaks, the time of the peak maximum and other parameters. A novel fast full waveform analysis algorithm (simulated tempering Markov chain Monte Carlo algorithm, STMCMC) is proposed, which is able to process the waveform data automatically. For the different types of the parameters, simulated tempering strategy and the Metropolis strategy are presented. In simulated tempering strategy, due to the demand of speed or accuracy, active intervention tempering is used to control the process of solving the vector parameters. On the other hand, the Metropolis strategy is adopted for non-vector parameters to reduce computation amount. Both the strategies are based on Markov chain algorithm, and meanwhile can hold the convergence of the Markov chain, which makes the STMCMC algorithm robust.%针对传统的全波形分析方法不能快速自动处理全波形数据的缺点，提出了一种模拟回火马尔可夫链蒙特卡罗全波形分析法，用于求解全波形数据中的波峰数和峰值位置等参量。该方法采用Metropolis更新策略求解波峰数量和噪声两个参量，以达到快速求解的目的；而峰值位置和波峰幅值则采用改进的模拟回火策略求解，通过添加的主动干预回火步骤实现对参量更新过程的有效探测，以满足对速度或运算收敛性的要求。模拟回火马尔可夫链蒙特卡罗全波形分析方法以马尔可夫算法为基础，仍保持马氏链的收敛性，从而保证本方法具有良好的鲁棒性，实现对全波形数据的自动化处理。
Wang, Guofeng; Liu, Chang; Cui, Yinhu
2012-09-01
Feature extraction plays an important role in the clustering analysis. In this paper an integrated Autoregressive (AR)/Autoregressive Conditional Heteroscedasticity (ARCH) model is proposed to characterize the vibration signal and the model coefficients are adopted as feature vectors to realize clustering diagnosis of rolling element bearings. The main characteristic is that the AR item and ARCH item are interrelated with each other so that it can depict the excess kurtosis and volatility clustering information in the vibration signal more accurately in comparison with two-stage AR/ARCH model. To testify the correctness, four kinds of bearing signals are adopted for parametric modeling by using the integrated and two-stage AR/ARCH model. The variance analysis of the model coefficients shows that the integrated AR/ARCH model can get more concentrated distribution. Taking these coefficients as feature vectors, K means based clustering is utilized to realize the automatic classification of bearing fault status. The results show that the proposed method can get more accurate results in comparison with two-stage model and discrete wavelet decomposition.
Markov Chains For Testing Redundant Software
White, Allan L.; Sjogren, Jon A.
1990-01-01
Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
Institute of Scientific and Technical Information of China (English)
罗钢; 石东源; 陈金富; 吴小珊
2014-01-01
准确、合理地构建间歇性电源的发电功率模型对于电力系统的仿真分析与计算具有重要意义。提出了一种风光发电功率时间序列模拟的单变量与多变量马尔科夫链蒙特卡罗(Markov chain Monte Carlo，MCMC)仿真方法。该模型针对风电场与光伏电站等多种类型的间歇性电源，构建发电功率时间序列的马尔科夫链，采用Gibbs抽样技术实现了单变量或多变量的时间序列模拟。不仅全面地分析了不同类型间歇性电源马尔科夫过程的特征与影响因素，并且在 MCMC方法中考虑了多变量之间的相互联系，使模型能够适应多组间歇性电源彼此间存在相关性的情形。对德国2家电力公司控制区域内的风电场、光伏电站进行仿真模拟，通过统计特征参数的对比分析，验证了所提模型的有效性。%Constructing a model of generated power for intermittent power source accurately and reasonably is of great significance for power system simulation and analysis. A single- and multi-variable Markov chain Monte Carlo (MCMC) method to simulate time series of wind and photovoltaic (PV) power is proposed. Aiming to many types of intermittent power source such as wind farms and PV generation stations, the proposed model constructs Markov chain for time series of generated power and utilizing Gibbs sampling the single- or multi-variable time series simulation is realized. Not only the features and impacting factors of Markov processes for different types of intermittent power sources are overall analyzed, and in the MCMC method the interrelation among multi-variables is considered, thus the proposed model can adapt to the condition that there are interrelations among multi sets of intermittent power sources. The wind farms and PV power plants located in the control areas of two power companies in Germany are simulated, and through the comparative analysis on statistical feature parameters the validity of
Institute of Scientific and Technical Information of China (English)
Xiaoyun MO; Jieming ZHOU; Hui OU; Xiangqun YANG
2013-01-01
Given a new Double-Markov risk model DM =(μ,Q,v,H; Y,Z) and Double-Markov risk process U ={U(t),t ≥ 0}.The ruin or survival problem is addressed.Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained.Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained.The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.
Auto-Regressive Models of Non-Stationary Time Series with Finite Length
Institute of Scientific and Technical Information of China (English)
FEI Wanchun; BAI Lun
2005-01-01
To analyze and simulate non-stationary time series with finite length, the statistical characteristics and auto-regressive (AR) models of non-stationary time series with finite length are discussed and studied. A new AR model called the time varying parameter AR model is proposed for solution of non-stationary time series with finite length. The auto-covariances of time series simulated by means of several AR models are analyzed. The result shows that the new AR model can be used to simulate and generate a new time series with the auto-covariance same as the original time series. The size curves of cocoon filaments regarded as non-stationary time series with finite length are experimentally simulated. The simulation results are significantly better than those obtained so far, and illustrate the availability of the time varying parameter AR model. The results are useful for analyzing and simulating non-stationary time series with finite length.
Mixture latent autoregressive models for longitudinal data
Bartolucci, Francesco; Pennoni, Fulvia
2011-01-01
Many relevant statistical and econometric models for the analysis of longitudinal data include a latent process to account for the unobserved heterogeneity between subjects in a dynamic fashion. Such a process may be continuous (typically an AR(1)) or discrete (typically a Markov chain). In this paper, we propose a model for longitudinal data which is based on a mixture of AR(1) processes with different means and correlation coefficients, but with equal variances. This model belongs to the class of models based on a continuous latent process, and then it has a natural interpretation in many contexts of application, but it is more flexible than other models in this class, reaching a goodness-of-fit similar to that of a discrete latent process model, with a reduced number of parameters. We show how to perform maximum likelihood estimation of the proposed model by the joint use of an Expectation-Maximisation algorithm and a Newton-Raphson algorithm, implemented by means of recursions developed in the hidden Mark...
Spectral Analysis of Markov Chains
2007-01-01
The paper deals with the problem of a statistical analysis of Markov chains connected with the spectral density. We present the expressions for the function of spectral density. These expressions may be used to estimate the parameter of the Markov chain.
A complex autoregressive model and application to monthly temperature forecasts
Directory of Open Access Journals (Sweden)
X. Gu
2005-11-01
Full Text Available A complex autoregressive model was established based on the mathematic derivation of the least squares for the complex number domain which is referred to as the complex least squares. The model is different from the conventional way that the real number and the imaginary number are separately calculated. An application of this new model shows a better forecast than forecasts from other conventional statistical models, in predicting monthly temperature anomalies in July at 160 meteorological stations in mainland China. The conventional statistical models include an autoregressive model, where the real number and the imaginary number are separately disposed, an autoregressive model in the real number domain, and a persistence-forecast model.
A Score Type Test for General Autoregressive Models in Time Series
Institute of Scientific and Technical Information of China (English)
Jian-hong Wu; Li-xing Zhu
2007-01-01
This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.
A Mixture Innovation Heterogeneous Autoregressive Model for Structural Breaks and Long Memory
DEFF Research Database (Denmark)
Nonejad, Nima
We propose a flexible model to describe nonlinearities and long-range dependence in time series dynamics. Our model is an extension of the heterogeneous autoregressive model. Structural breaks occur through mixture distributions in state innovations of linear Gaussian state space models. Monte...... Carlo simulations evaluate the properties of the estimation procedures. Results show that the proposed model is viable and flexible for purposes of forecasting volatility. Model uncertainty is accounted for by employing Bayesian model averaging. Bayesian model averaging provides very competitive...... forecasts compared to any single model specification. It provides further improvements when we average over nonlinear specifications....
Recursive Least Squares Estimator with Multiple Exponential Windows in Vector Autoregression
Institute of Scientific and Technical Information of China (English)
Hong-zhi An; Zhi-guo Li
2002-01-01
In the parameter tracking of time-varying systems, the ordinary method is weighted least squares with the rectangular window or the exponential window. In this paper we propose a new kind of sliding window called the multiple exponential window, and then use it to fit time-varying Gaussian vector autoregressive models. The asymptotic bias and covariance of the estimator of the parameter for time-invariant models are also derived. Simulation results show that the multiple exponential windows have better parameter tracking effect than rectangular windows and exponential ones.
Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity
Directory of Open Access Journals (Sweden)
Isao Ishida
2015-01-01
Full Text Available We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500 and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility.
Directory of Open Access Journals (Sweden)
D. G. Partridge
2012-03-01
Full Text Available This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov chain Monte Carlo (MCMC algorithm to an adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools to investigate the global sensitivity of a cloud model to input aerosol physiochemical parameters. Using numerically generated cloud droplet number concentration (CDNC distributions (i.e. synthetic data as cloud observations, this inverse modelling framework is shown to successfully estimate the correct calibration parameters, and their underlying posterior probability distribution.
The employed analysis method provides a new, integrative framework to evaluate the global sensitivity of the derived CDNC distribution to the input parameters describing the lognormal properties of the accumulation mode aerosol and the particle chemistry. To a large extent, results from prior studies are confirmed, but the present study also provides some additional insights. There is a transition in relative sensitivity from very clean marine Arctic conditions where the lognormal aerosol parameters representing the accumulation mode aerosol number concentration and mean radius and are found to be most important for determining the CDNC distribution to very polluted continental environments (aerosol concentration in the accumulation mode >1000 cm^{−3} where particle chemistry is more important than both number concentration and size of the accumulation mode.
The competition and compensation between the cloud model input parameters illustrates that if the soluble mass fraction is reduced, the aerosol number concentration, geometric standard deviation and mean radius of the accumulation mode must increase in order to achieve the same CDNC distribution.
This study demonstrates that inverse modelling provides a flexible, transparent and
Simulation of M/M/m Queuing Model Based on Markov State Transition Process%基于马尔科夫状态转移过程的M/M/m排队模型仿真
Institute of Scientific and Technical Information of China (English)
曹永荣; 韩瑞霞; 胡伟
2012-01-01
马尔科夫链是研究排队系统的主要方法,本文在现有M/M/m排队理论和排队系统仿真理论基础上,利用Matlab建立基于马尔科夫状态转移过程的M/M/m排队模型仿真程序.仿真程序在产生初始化参数设定后,利用时钟推进法来模拟空闲服务台和繁忙服务台情况下的服务流程,最后通过M/M/m模型特征描述的仿真计算,获得平均等待时间(E[W])、平均停机时间(E[ DT])、平均排队队长E[ Q]、系统中的平均客户数(E[L])和可能延迟的概率((Ⅱ))5项重要的特征描述.模拟次数设定为20 000次,模拟客户服务率和客户到达率相同,服务台在3～6个的排队系统,并将仿真结果与理论值以及Queue2.0的模拟结果相比较.最终结果显示E[W]、[DT]和H3项最重要指标的仿真结果和理论值都极为相近,误差范围小,本研究将为优先权排队系统的仿真研究提供理论依据.%Markov chain is the main method for the study of queuing systems. This paper integrates the existing theories of M/M/m queuing system and theories of queuing system simulation, and builds simulation program of M/M/m Queuing Model according to the Markov state transition process using Matlab. The simulation process is as follows. First of all, simulation program initializes the parameter settings, such as service time, the interval of customer arrival, the number of server etc. Secondly, promotes the program used time clock which is based on the arrival time of customers and the end time of service. Thirdly, simulates the free servers and busy servers process when a customer arrived, and recodes the corresponding data. Finally, calculate the M/M/m model's characterized descriptions , included in the average down time (E[ DT] ) , the average waiting time (E[ W]), the average number of queuing customer (E[(Q])＞ the average number of customers in the queuing system( E[ L]) and delay probability (Ⅱ) , based on the simulation formula. Sets the
Markov chains theory and applications
Sericola, Bruno
2013-01-01
Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the
Ivkovic, Stefan
2015-01-01
In this thesis we will consider Markov operators on cones . More precisely, we let X equipped with certain norm be a real Banach space, K in X be a closed, normal cone with nonempty interior, e in Int (K) be an order unit. A bounded, linear operator T from X into X is a Markov operator w.r.t. K and e if K is invariant under T and e is fixed by T. We consider then the adjoint of T, T* and homogeneous, discrete time Markov system given by u_k+1 = T*(u_k), k = 0,1,2 where u_0(x) is nonnegative f...
Representation of cointegrated autoregressive processes with application to fractional processes
DEFF Research Database (Denmark)
Johansen, Søren
2009-01-01
We analyse vector autoregressive processes using the matrix valued characteristic polynomial. The purpose of this paper is to give a survey of the mathematical results on inversion of a matrix polynomial in case there are unstable roots, to study integrated and cointegrated processes. The new...
Unit Root Vector Autoregression with volatility Induced Stationarity
DEFF Research Database (Denmark)
Rahbek, Anders; Nielsen, Heino Bohn
stationarity despite such unit-roots. Specifically, the model bridges vector autoregressions and multivariate ARCH models in which residuals are replaced by levels lagged. An empirical illustration using recent US term structure data is given in which the individual interest rates have unit roots, have...
Unit root vector autoregression with volatility induced stationarity
DEFF Research Database (Denmark)
Rahbek, Anders; Nielsen, Heino Bohn
stationarity despite such unit-roots. Specifically, the model bridges vector autoregressions and multivariate ARCH models in which residuals are replaced by levels lagged. An empirical illustration using recent US term structure data is given in which the individual interest rates have unit roots, have...
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß...
Temporal aggregation in a periodically integrated autoregressive process
Ph.H.B.F. Franses (Philip Hans); H.P. Boswijk (Peter)
1996-01-01
textabstractA periodically integrated autoregressive process for a time series which is observed S times per year assumes the presence of S - 1 cointegration relations between the annual series containing the seasonal observations, with the additional feature that these relations are different acros
Automating Vector Autoregression on Electronic Patient Diary Data
Emerencia, Ando Celino; Krieke, Lian van der; Bos, Elisabeth H.; de Jonge, Peter; Petkov, Nicolai; Aiello, Marco
2016-01-01
Finding the best vector autoregression model for any dataset, medical or otherwise, is a process that, to this day, is frequently performed manually in an iterative manner requiring a statistical expertize and time. Very few software solutions for automating this process exist, and they still requir
The correlation structure of spatial autoregressions on graphs
Martellosio, F.
2006-01-01
This paper studies the correlation structure of spatial autoregressions defined over arbitrary configurations of observational units. We derive a number of new properties of the models and provide new interpretations of some of their known properties. A little graph theory helps to clarify how the c
Nonlinear autoregressive models with heavy-tailed innovation
Institute of Scientific and Technical Information of China (English)
JIN; Yang; AN; Hongzhi
2005-01-01
In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlJnear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.
Likelihood Inference for a Nonstationary Fractional Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial...
Testing exact rational expectations in cointegrated vector autoregressive models
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
1999-01-01
This paper considers the testing of restrictions implied by rational expectations hypotheses in a cointegrated vector autoregressive model for I(1) variables. If the rational expectations involve one-step-ahead observations only and the coefficients are known, an explicit parameterization...
Limit theorems for bifurcating integer-valued autoregressive processes
Blandin, Vassili
2012-01-01
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with the quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.
CICAAR - Convolutive ICA with an Auto-Regressive Inverse Model
DEFF Research Database (Denmark)
Dyrholm, Mads; Hansen, Lars Kai
2004-01-01
We invoke an auto-regressive IIR inverse model for convolutive ICA and derive expressions for the likelihood and its gradient. We argue that optimization will give a stable inverse. When there are more sensors than sources the mixing model parameters are estimated in a second step by least squares...
Temporal aggregation in first order cointegrated vector autoregressive
DEFF Research Database (Denmark)
la Cour, Lisbeth Funding; Milhøj, Anders
2006-01-01
of aggregation on the adjustment coefficient in cointegrated systems. We study only first order vector autoregressive processes for n dimensional time series Xt, and we illustrate the theory by a two dimensional and a four dimensional model for prices of various grades of gasoline....
Temporal aggregation in first order cointegrated vector autoregressive models
DEFF Research Database (Denmark)
La Cour, Lisbeth Funding; Milhøj, Anders
of aggregation on the adjustment coefficient in cointegrated systems. We study only first order vector autoregressive processes for n dimensional time series Xt, and we illustrate the theory by a two dimensional and a four dimensional model for prices of various grades of gasoline...
Least squares estimation in a simple random coefficient autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Lange, Theis
2013-01-01
The question we discuss is whether a simple random coefficient autoregressive model with infinite variance can create the long swings, or persistence, which are observed in many macroeconomic variables. The model is defined by yt=stρyt−1+εt,t=1,…,n, where st is an i.i.d. binary variable with p=P(...
The cointegrated vector autoregressive model with general deterministic terms
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive model X(t)= Z(t) + Y(t), where Z(t) belongs to a large class...
Compressing redundant information in Markov chains
2006-01-01
Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is hence defined and tested on some classical problems.
a Markov-Process Inspired CA Model of Highway Traffic
Wang, Fa; Li, Li; Hu, Jian-Ming; Ji, Yan; Ma, Rui; Jiang, Rui
To provide a more accurate description of the driving behaviors especially in car-following, namely a Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process whose stationary distribution corresponds to the observed gap distribution. This new model provides a microscopic simulation explanation for the governing interaction forces (potentials) between the queuing vehicles, which cannot be directly measurable for traffic flow applications. The agreement between empirical observations and simulation results suggests the soundness of this new approach.
Dynamic modeling of presence of occupants using inhomogeneous Markov chains
DEFF Research Database (Denmark)
Andersen, Philip Hvidthøft Delff; Iversen, Anne; Madsen, Henrik;
2014-01-01
on time of day, and by use of a filter of the observations it is able to capture per-employee sequence dynamics. Simulations using this method are compared with simulations using homogeneous Markov chains and show far better ability to reproduce key properties of the data. The method is based...... on inhomogeneous Markov chains with where the transition probabilities are estimated using generalized linear models with polynomials, B-splines, and a filter of passed observations as inputs. For treating the dispersion of the data series, a hierarchical model structure is used where one model is for low presence...
Institute of Scientific and Technical Information of China (English)
李磊; 杨瑞科; 赵振维
2012-01-01
Based on the N-State Markov chain model established by Markov theory,the rain attenuation time series about Changchun and Xinxiang areas are simulated and the complementary cumulative distributions obtained by the simulatived and measured data at these areas are compared.The probability distribution about 50 simulative rain attenuation time series are compiled in statistics.The results agree with the results predicted by ITU-R model at 12.5 GHz and 92°Eorbital position of the geostationary satellite.Hence,the usability of this model is validated at partial areas in China.This research establishes a basis for the development of the rain fade mitigation techniques in communication and radar systems at Ku and above Ku band.%基于马尔科夫理论建立的N阶马尔科夫链模型,模拟了长春和新乡地区的降雨衰减时间序列,比较了长春和新乡地区单个模拟和实测雨衰时间序列的概率分布;分别统计了长春和新乡地区50组模拟雨衰时间序列的百分概率分布,并与国际电信联盟无线电通信研究组（ITU-R）提供的卫星轨道位置为92°E、频率为12.5GHz在线极化情况下长春和新乡雨区不同降雨衰减值下的时间百分概率进行了比较,一致性很好,从而验证了N阶马尔可夫链模型在中国部分地区的可用性。模拟结果对我国在Ku及以上频段通信卫星的抗衰落技术的发展具有重要的应用价值。
Mosavi, A. A.; Dickey, D.; Seracino, R.; Rizkalla, S.
2012-01-01
This paper presents a study for identifying damage locations in an idealized steel bridge girder using the ambient vibration measurements. A sensitive damage feature is proposed in the context of statistical pattern recognition to address the damage detection problem. The study utilizes an experimental program that consists of a two-span continuous steel beam subjected to ambient vibrations. The vibration responses of the beam are measured along its length under simulated ambient vibrations and different healthy/damage conditions of the beam. The ambient vibration is simulated using a hydraulic actuator, and damages are induced by cutting portions of the flange at two locations. Multivariate vector autoregressive models were fitted to the vibration response time histories measured at the multiple sensor locations. A sensitive damage feature is proposed for identifying the damage location by applying Mahalanobis distances to the coefficients of the vector autoregressive models. A linear discriminant criterion was used to evaluate the amount of variations in the damage features obtained for different sensor locations with respect to the healthy condition of the beam. The analyses indicate that the highest variations in the damage features were coincident with the sensors closely located to the damages. The presented method showed a promising sensitivity to identify the damage location even when the induced damage was very small.
Directory of Open Access Journals (Sweden)
D. G. Partridge
2011-07-01
Full Text Available This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov Chain Monte Carlo (MCMC algorithm to a pseudo-adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools to investigate the sensitivity of a cloud model to input aerosol physiochemical parameters. Using synthetic data as observed values of cloud droplet number concentration (CDNC distribution, this inverse modelling framework is shown to successfully converge to the correct calibration parameters.
The employed analysis method provides a new, integrative framework to evaluate the sensitivity of the derived CDNC distribution to the input parameters describing the lognormal properties of the accumulation mode and the particle chemistry. To a large extent, results from prior studies are confirmed, but the present study also provides some additional insightful findings. There is a clear transition from very clean marine Arctic conditions where the aerosol parameters representing the mean radius and geometric standard deviation of the accumulation mode are found to be most important for determining the CDNC distribution to very polluted continental environments (aerosol concentration in the accumulation mode >1000 cm^{−3} where particle chemistry is more important than both number concentration and size of the accumulation mode.
The competition and compensation between the cloud model input parameters illustrate that if the soluble mass fraction is reduced, both the number of particles and geometric standard deviation must increase and the mean radius of the accumulation mode must increase in order to achieve the same CDNC distribution.
For more polluted aerosol conditions, with a reduction in soluble mass fraction the parameter correlation becomes weaker and more non-linear over the range of possible solutions
A Markov Chain Estimator of Multivariate Volatility from High Frequency Data
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume; Lunde, Asger;
We introduce a multivariate estimator of financial volatility that is based on the theory of Markov chains. The Markov chain framework takes advantage of the discreteness of high-frequency returns. We study the finite sample properties of the estimation in a simulation study and apply...
Bibliometric Application of Markov Chains.
Pao, Miranda Lee; McCreery, Laurie
1986-01-01
A rudimentary description of Markov Chains is presented in order to introduce its use to describe and to predict authors' movements among subareas of the discipline of ethnomusicology. Other possible applications are suggested. (Author)
Entropy: The Markov Ordering Approach
Directory of Open Access Journals (Sweden)
Alexander N. Gorban
2010-05-01
Full Text Available The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant “additivity” properties: (i existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i and (ii are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order. The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally “most random” distributions.
Markov Chains and Chemical Processes
Miller, P. J.
1972-01-01
Views as important the relating of abstract ideas of modern mathematics now being taught in the schools to situations encountered in the sciences. Describes use of matrices and Markov chains to study first-order processes. (Author/DF)
Markov processes, semigroups and generators
Kolokoltsov, Vassili N
2011-01-01
This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for applications. This work does just that, and with the necessary mathematical rigor.
Markov chain solution of photon multiple scattering through turbid slabs.
Lin, Ying; Northrop, William F; Li, Xuesong
2016-11-14
This work introduces a Markov Chain solution to model photon multiple scattering through turbid slabs via anisotropic scattering process, i.e., Mie scattering. Results show that the proposed Markov Chain model agree with commonly used Monte Carlo simulation for various mediums such as medium with non-uniform phase functions and absorbing medium. The proposed Markov Chain solution method successfully converts the complex multiple scattering problem with practical phase functions into a matrix form and solves transmitted/reflected photon angular distributions by matrix multiplications. Such characteristics would potentially allow practical inversions by matrix manipulation or stochastic algorithms where widely applied stochastic methods such as Monte Carlo simulations usually fail, and thus enable practical diagnostics reconstructions such as medical diagnosis, spray analysis, and atmosphere sciences.
Institute of Scientific and Technical Information of China (English)
陈爱玲; 都金康
2014-01-01
以秦淮河流域为研究区,以2006和2009年ETM+图像土地覆盖分类结果为输入数据,采用CA-Markov模型,模拟预测研究区未来的土地覆盖格局。在模型建立过程中,通过Markov模型求出转移概率矩阵和转移面积矩阵,确定CA模型转换规则,限制CA模型迭代次数。利用CA-Markov模型模拟预测研究区2012和2018年土地覆盖格局,并采用2012年实际土地覆盖分类结果验证预测精度,得到2012年各土地覆盖类型栅格数预测误差均小于等于6.5%,空间位置预测精度达到76.5%。预测结果表明,2018年研究区水田比例将降为33.3%,不透水面比例将达31.1%,其中多数水田转变成为不透水面,南京城区、禄口镇、句容市、溧水县等城镇地区的不透水面明显扩张。该方法可以对秦淮河流域的土地覆盖动态监测以及可持续发展提供依据。%Based on the classified result of Landsat ETM+ remote sensing images of 2006 and 2009 , the paper simulated and forecasted land cover types of Qinhuai River Basin in the future by using the CA-Markov model. In the model-building process, the transition probability matrix and the transition area matrix were obtained through the Markov model, which determined the conversion rules and iterative times of the CA model. The land cover pattern of the study area in 2012 and 2018 was simulated and forecasted with the CA-Markov model. Then the forecast result was compared with the actual classified data of 2012 to verify the forecast accuracy. The raster number forecast error of each land cover type is not higher than 6. 5%, and the spatial location accuracy is 76. 5%. The forecast results show that the paddy field decreased to 33 . 3 % and the impervious surface reached 31 . 1 % of Qinhuai River Basin in 2018. Most of the paddy field converted into impervious surface. The impervious surface of urban areas expands obviously in such urban areas as Nanjing, Lukou, Jurong and Lishui. The methods can
Gaussian Markov random fields theory and applications
Rue, Havard
2005-01-01
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.
Dettmer, Jan; Dosso, Stan E
2012-10-01
This paper develops a trans-dimensional approach to matched-field geoacoustic inversion, including interacting Markov chains to improve efficiency and an autoregressive model to account for correlated errors. The trans-dimensional approach and hierarchical seabed model allows inversion without assuming any particular parametrization by relaxing model specification to a range of plausible seabed models (e.g., in this case, the number of sediment layers is an unknown parameter). Data errors are addressed by sampling statistical error-distribution parameters, including correlated errors (covariance), by applying a hierarchical autoregressive error model. The well-known difficulty of low acceptance rates for trans-dimensional jumps is addressed with interacting Markov chains, resulting in a substantial increase in efficiency. The trans-dimensional seabed model and the hierarchical error model relax the degree of prior assumptions required in the inversion, resulting in substantially improved (more realistic) uncertainty estimates and a more automated algorithm. In particular, the approach gives seabed parameter uncertainty estimates that account for uncertainty due to prior model choice (layering and data error statistics). The approach is applied to data measured on a vertical array in the Mediterranean Sea.
Weijs, Liesbeth; Yang, Raymond S H; Das, Krishna; Covaci, Adrian; Blust, Ronny
2013-05-01
Physiologically based pharmacokinetic (PBPK) modeling in marine mammals is a challenge because of the lack of parameter information and the ban on exposure experiments. To minimize uncertainty and variability, parameter estimation methods are required for the development of reliable PBPK models. The present study is the first to develop PBPK models for the lifetime bioaccumulation of p,p'-DDT, p,p'-DDE, and p,p'-DDD in harbor porpoises. In addition, this study is also the first to apply the Bayesian approach executed with Markov chain Monte Carlo simulations using two data sets of harbor porpoises from the Black and North Seas. Parameters from the literature were used as priors for the first "model update" using the Black Sea data set, the resulting posterior parameters were then used as priors for the second "model update" using the North Sea data set. As such, PBPK models with parameters specific for harbor porpoises could be strengthened with more robust probability distributions. As the science and biomonitoring effort progress in this area, more data sets will become available to further strengthen and update the parameters in the PBPK models for harbor porpoises as a species anywhere in the world. Further, such an approach could very well be extended to other protected marine mammals.
Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation.
Stathopoulos, Vassilios; Girolami, Mark A
2013-02-13
Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.
Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy
Abler, Daniel; Davies, Jim; Dosanjh, Manjit; Jena, Raj; Kirkby, Norman; Peach, Ken
2013-01-01
Decision-making processes in medicine rely increasingly on modelling and simulation techniques; they are especially useful when combining evidence from multiple sources. Markov models are frequently used to synthesize the available evidence for such simulation studies, by describing disease and treatment progress, as well as associated factors such as the treatment's effects on a patient's life and the costs to society. When the same decision problem is investigated by multiple stakeholders, differing modelling assumptions are often applied, making synthesis and interpretation of the results difficult. This paper proposes a standardized approach towards the creation of Markov models. It introduces the notion of ‘general Markov models’, providing a common definition of the Markov models that underlie many similar decision problems, and develops a language for their specification. We demonstrate the application of this language by developing a general Markov model for adverse event analysis in radiotherapy ...
Parameter Estimation for Generalized Brownian Motion with Autoregressive Increments
Fendick, Kerry
2011-01-01
This paper develops methods for estimating parameters for a generalization of Brownian motion with autoregressive increments called a Brownian ray with drift. We show that a superposition of Brownian rays with drift depends on three types of parameters - a drift coefficient, autoregressive coefficients, and volatility matrix elements, and we introduce methods for estimating each of these types of parameters using multidimensional times series data. We also cover parameter estimation in the contexts of two applications of Brownian rays in the financial sphere: queuing analysis and option valuation. For queuing analysis, we show how samples of queue lengths can be used to estimate the conditional expectation functions for the length of the queue and for increments in its net input and lost potential output. For option valuation, we show how the Black-Scholes-Merton formula depends on the price of the security on which the option is written through estimates not only of its volatility, but also of a coefficient ...
On Markov parameters in system identification
Phan, Minh; Juang, Jer-Nan; Longman, Richard W.
1991-01-01
A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.
Beef Supply Response Under Uncertainty: An Autoregressive Distributed Lag Model
Mbaga, Msafiri Daudi; Coyle, Barry T.
2003-01-01
This is the first econometric study of dynamic beef supply response to incorporate risk aversion or, more specifically, price variance. Autoregressive distributed lag (ADL) models are estimated for cow-calf and feedlot operations using aggregate data for Alberta. In all cases, output price variance has a negative impact on output supply and investment. Moreover, the impacts of expected price on supply response are greater in magnitude and significance than in risk-neutral models.
A NEW TEST FOR NORMALITY IN LINEAR AUTOREGRESSIVE MODELS
Institute of Scientific and Technical Information of China (English)
CHEN Min; WU Guofu; Gemai Chen
2002-01-01
A nonparametric test for normality of linear autoregressive time series isproposed in this paper. The test is based on the best one-step forecast in mean squarewith time reverse. Some asymptotic theory is developed for the test, and it is shown thatthe test is easy to use and has good powers. The empirical percentage points to conductthe test in practice are provided and three examples using real data are included.
Asymptotic results for bifurcating random coefficient autoregressive processes
Blandin, Vassili
2012-01-01
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.
Robust estimation of nonstationary, fractionally integrated, autoregressive, stochastic volatility
Mark J. Jensen
2015-01-01
Empirical volatility studies have discovered nonstationary, long-memory dynamics in the volatility of the stock market and foreign exchange rates. This highly persistent, infinite variance - but still mean reverting - behavior is commonly found with nonparametric estimates of the fractional differencing parameter d, for financial volatility. In this paper, a fully parametric Bayesian estimator, robust to nonstationarity, is designed for the fractionally integrated, autoregressive, stochastic ...
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2010-01-01
the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions. We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including...... d and b, and prove that they converge in distribution. We use the results to prove consistency of the maximum likelihood estimator for d,b in a large compact subset of {1/2...
Efficient maximum likelihood parameterization of continuous-time Markov processes
McGibbon, Robert T
2015-01-01
Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce an maximum likelihood estimator for constructing such models from data observed at a finite time interval. This estimator is drastically more efficient than prior approaches, enables the calculation of deterministic confidence intervals in all model parameters, and can easily enforce important physical constraints on the models such as detailed balance. We demonstrate and discuss the advantages of these models over existing discrete-time Markov models for the analysis of molecular dynamics simulations.
Automating Vector Autoregression on Electronic Patient Diary Data.
Emerencia, Ando Celino; van der Krieke, Lian; Bos, Elisabeth H; de Jonge, Peter; Petkov, Nicolai; Aiello, Marco
2016-03-01
Finding the best vector autoregression model for any dataset, medical or otherwise, is a process that, to this day, is frequently performed manually in an iterative manner requiring a statistical expertize and time. Very few software solutions for automating this process exist, and they still require statistical expertize to operate. We propose a new application called Autovar, for the automation of finding vector autoregression models for time series data. The approach closely resembles the way in which experts work manually. Our proposal offers improvements over the manual approach by leveraging computing power, e.g., by considering multiple alternatives instead of choosing just one. In this paper, we describe the design and implementation of Autovar, we compare its performance against experts working manually, and we compare its features to those of the most used commercial solution available today. The main contribution of Autovar is to show that vector autoregression on a large scale is feasible. We show that an exhaustive approach for model selection can be relatively safe to use. This study forms an important step toward making adaptive, personalized treatment available and affordable for all branches of healthcare.
Markov Networks in Evolutionary Computation
Shakya, Siddhartha
2012-01-01
Markov networks and other probabilistic graphical modes have recently received an upsurge in attention from Evolutionary computation community, particularly in the area of Estimation of distribution algorithms (EDAs). EDAs have arisen as one of the most successful experiences in the application of machine learning methods in optimization, mainly due to their efficiency to solve complex real-world optimization problems and their suitability for theoretical analysis. This book focuses on the different steps involved in the conception, implementation and application of EDAs that use Markov networks, and undirected models in general. It can serve as a general introduction to EDAs but covers also an important current void in the study of these algorithms by explaining the specificities and benefits of modeling optimization problems by means of undirected probabilistic models. All major developments to date in the progressive introduction of Markov networks based EDAs are reviewed in the book. Hot current researc...
Markov chains and mixing times
Levin, David A; Wilmer, Elizabeth L
2009-01-01
This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of r
Markov Random Field Surface Reconstruction
DEFF Research Database (Denmark)
Paulsen, Rasmus Reinhold; Bærentzen, Jakob Andreas; Larsen, Rasmus
2010-01-01
) and knowledge about data (the observation model) in an orthogonal fashion. Local models that account for both scene-specific knowledge and physical properties of the scanning device are described. Furthermore, how the optimal distance field can be computed is demonstrated using conjugate gradients, sparse......A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaption of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior...
Markov Models for Handwriting Recognition
Plotz, Thomas
2011-01-01
Since their first inception, automatic reading systems have evolved substantially, yet the recognition of handwriting remains an open research problem due to its substantial variation in appearance. With the introduction of Markovian models to the field, a promising modeling and recognition paradigm was established for automatic handwriting recognition. However, no standard procedures for building Markov model-based recognizers have yet been established. This text provides a comprehensive overview of the application of Markov models in the field of handwriting recognition, covering both hidden
Quantile estimation for a non-geometric ergodic Markov chain
Ramirez-Nafarrate, Adrian; Muñoz, David F.
2013-10-01
Simulation has been successfully used for estimating performance measures (e.g. mean, variance and quantiles) of complex systems, such as queueing and inventory systems. However, parameter estimation using simulation may be a difficult task under some conditions. In this paper, we present a counterexample for which traditional simulation methods do not allow us to estimate the accuracy of the point estimators for the mean and risk performance measures for steady-state. The counterexample is based on a Markov chain with continuous state space and non-geometric ergodicity. The simulation of this Markov chain shows that neither multiple replications nor batch-based methodologies can produce asymptotically valid confidence intervals for the point estimators.
Ozone Concentration Prediction via Spatiotemporal Autoregressive Model With Exogenous Variables
Kamoun, W.; Senoussi, R.
2009-04-01
Forecast of environmental variables are nowadays of main concern for public health or agricultural management. In this context a large literature is devoted to spatio-temporal modelling of these variables using different statistical approaches. However, most of studies ignored the potential contribution of local (e.g. meteorological and/or geographical) covariables as well as the dynamical characteristics of observations. In this study, we present a spatiotemporal short term forecasting model for ozone concentration based on regularly observed covariables in predefined geographical sites. Our driving system simply combines a multidimensional second order autoregressive structured process with a linear regression model over influent exogenous factors and reads as follows: 2 q j Z (t) = A (Î&,cedil;D )Ã- [ αiZ(t- i)]+ B (Î&,cedil;D )Ã- [ βjX (t)]+ É(t) i=1 j=1 Z(t)=(Z1(t),â¦,Zn(t)) represents the vector of ozone concentration at time t of the n geographical sites, whereas Xj(t)=(X1j(t),â¦,Xnj(t)) denotes the jth exogenous variable observed over these sites. The nxn matrix functions A and B account for the spatial relationships between sites through the inter site distance matrix D and a vector parameter Î&.cedil; Multidimensional white noise É is assumed to be Gaussian and spatially correlated but temporally independent. A covariance structure of Z that takes account of noise spatial dependences is deduced under a stationary hypothesis and then included in the likelihood function. Statistical model and estimation procedure: Contrarily to the widely used choice of a {0,1}-valued neighbour matrix A, we put forward two more natural choices of exponential or power decay. Moreover, the model revealed enough stable to readily accommodate the crude observations without the usual tedious and somewhat arbitrarily variable transformations. Data set and preliminary analysis: In our case, ozone variable represents here the daily maximum ozone
On a Result for Finite Markov Chains
Kulathinal, Sangita; Ghosh, Lagnojita
2006-01-01
In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…
Consistency and Refinement for Interval Markov Chains
DEFF Research Database (Denmark)
Delahaye, Benoit; Larsen, Kim Guldstrand; Legay, Axel;
2012-01-01
Interval Markov Chains (IMC), or Markov Chains with probability intervals in the transition matrix, are the base of a classic specification theory for probabilistic systems [18]. The standard semantics of IMCs assigns to a specification the set of all Markov Chains that satisfy its interval...
Estimation and uncertainty of reversible Markov models
Trendelkamp-Schroer, Benjamin; Paul, Fabian; Noé, Frank
2015-01-01
Reversibility is a key concept in the theory of Markov models, simplified kinetic models for the conforma- tion dynamics of molecules. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model relies heavily on the reversibility property. The estimation of a reversible transition matrix from simulation data is therefore crucial to the successful application of the previously developed theory. In this work we discuss methods for the maximum likelihood estimation of transition matrices from finite simulation data and present a new algorithm for the estimation if reversibility with respect to a given stationary vector is desired. We also develop new methods for the Bayesian posterior inference of reversible transition matrices with and without given stationary vector taking into account the need for a suitable prior distribution preserving the meta-stable features of the observed process during posterior inference.
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...
Confluence reduction for Markov automata
Timmer, Mark; Pol, van de Jaco; Stoelinga, Mariëlle
2013-01-01
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models gener
Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains
Directory of Open Access Journals (Sweden)
Michael Krumin
2010-01-01
Full Text Available Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ‘‘hidden’’ Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method.
Goodness-of-fit tests for vector autoregressive models in time series
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The paper proposes and studies some diagnostic tools for checking the goodness-of-fit of general parametric vector autoregressive models in time series. The resulted tests are asymptotically chi-squared under the null hypothesis and can detect the alternatives converging to the null at a parametric rate. The tests involve weight functions,which provides us with the flexibility to choose scores for enhancing power performance,especially under directional alternatives. When the alternatives are not directional,we construct asymptotically distribution-free maximin tests for a large class of alternatives. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. The power performance is also investigated. In addition,when the sample size is small,a nonparametric Monte Carlo test approach for dependent data is proposed to improve the performance of the tests. The algorithm is easy to implement. Simulation studies and real applications are carried out for illustration.
Madurapperuma, Buddhika Dilhan
Mapping forest resources is useful for identifying threat patterns and monitoring changes associated with landscapes. Remote Sensing and Geographic Information Science techniques are effective tools used to identify and forecast forest resource threats such as exotic plant invasion, vulnerability to climate change, and land-use/cover change. This research focused on mapping abundance and distribution of Russian-olive using soil and land-use/cover data, evaluating historic land-use/cover change using mappable water-related indices addressing the primary loss of riparian arboreal ecosystems, and detecting year-to-year land-cover changes on forest conversion processes. Digital image processing techniques were used to detect the changes of arboreal ecosystems using ArcGIS ArcInfoRTM 9.3, ENVIRTM, and ENVIRTM EX platforms. Research results showed that Russian-olive at the inundated habitats of the Missouri River is abundant compared to terrestrial habitats in the Bismarck-Mandan Wildland Urban Interface. This could be a consequence of habitat quality of the floodplain, such as its silt loam and silty clay soil type, which favors Russian-olive regeneration. Russian-olive has close assemblage with cottonwood (Populus deltoides) and buffaloberry (Shepherdia argentea) trees at the lower elevations. In addition, the Russian-olive-cottonwood association correlated with low nitrogen, low pH, and high Fe, while Russian-olive- buffaloberry association occurred in highly eroded areas. The Devils Lake sub-watershed was selected to demonstrate how both land-use/cover modification and climatic variability have caused the vulnerability of arboreal ecosystems on the fringe to such changes. Land-cover change showed that the forest acreage declined from 9% to 1%, water extent increased from 13% to 25%, and cropland extent increased from 34% to 39% between 1992 and 2006. In addition, stochastic modeling was adapted to simulate how land-use/cover change influenced forest conversion to non
Stochastic seismic tomography by interacting Markov chains
Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe
2016-10-01
Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches, they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high-dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case, the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on importance resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non-linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper, the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a simulated annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet-based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.
Stochastic seismic tomography by interacting Markov chains
Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe
2016-07-01
Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on Importance Resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a Simulated Annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.
Multiensemble Markov models of molecular thermodynamics and kinetics.
Wu, Hao; Paul, Fabian; Wehmeyer, Christoph; Noé, Frank
2016-06-07
We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models-clustering of high-dimensional spaces and modeling of complex many-state systems-with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein-ligand binding model.
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.
Institute of Scientific and Technical Information of China (English)
王友生; 余新晓; 贺康宁; 李庆云; 张由松; 宋思铭
2011-01-01
To explore the law of land use change and driving force in Loess hilly-gully area in Jihe watershed, based on the land use data interpretation from remote sensing images in 1995 and 2008, the degree of dynamic change of land use type in Jihe watershed was analyzed by dynamic degree model and spatial analysis model, and distribution of land use spatial patterns in 2022 was forecast by using the CA-Markov model. The results showed that spatial analysis model not only took the conversion process into account but also the spatial expansion process of land use change, so it could more precisely measure the dynamic change rate of land use. The simulation result by the CA-Markov method indicated that, the value of Kappa coefficients of agreement in the whole watershed was 0.9515, and forecasting results were credible. From 2008 to 2022, except for grassland and unused land, trends of land use evolution as well as its rate will keep constant. That is, the area of slope farmland, grassland, water and unused land will continue to reduce in some degree, while terrace, forest land and settlements will present a increasing trend. Because the Loess hilly-gully is a serious soil erosion area, this research is helpful to reinforce the protection of land resource and to enforce the agro-forestry policies of reusing farmland for forestland and grassland, and it is meaningful to serve as a scientific basis for land planning and management.%为了探讨黄土丘陵沟壑区藉河流域的土地利用变化规律及驱动力,基于1995和2008年两期遥感影像解译得到的土地利用数据,通过土地利用动态度模型和空间测算模型对藉河流域土地利用类型的动态变化程度进行分析,并运用CA-Markov模型对2022年土地利用空间格局进行预测.结果表明,空间分析测算模型由于同时考虑了各土地利用类型的空间转移及新增过程,能更为准确地测算出各种土地利用类型的动态变化程度与速率；CA-Markov
An Extension of Cointegration to Fractional Autoregressive Processes
DEFF Research Database (Denmark)
Johansen, Søren
This paper contains an overview of some recent results on the statistical analysis of cofractional processes, see Johansen and Nielsen (2010b). We first give an brief summary of the analysis of cointegration in the vector autoregressive model and then show how this can be extended to fractional...... processes. The model allows the process X_{t} to be fractional of order d and cofractional of order d-b=0; that is, there exist vectors ß for which ß'X_{t} is fractional of order d-b. We analyse the Gaussian likelihood function to derive estimators and test statistics. The asymptotic properties are derived...
Optimal hedging with the cointegrated vector autoregressive model
DEFF Research Database (Denmark)
Gatarek, Lukasz; Johansen, Søren
We derive the optimal hedging ratios for a portfolio of assets driven by a Coin- tegrated Vector Autoregressive model (CVAR) with general cointegration rank. Our hedge is optimal in the sense of minimum variance portfolio. We consider a model that allows for the hedges to be cointegrated...... horizons, the hedge ratio should overweight the cointegration parameters rather then short-run correlation information. In the innite horizon, the hedge ratios shall be equal to the cointegrating vector. The hedge ratios for any intermediate portfolio holding period should be based on the weighted average...
Integer Valued Autoregressive Models for Tipping Bucket Rainfall Measurements
DEFF Research Database (Denmark)
Thyregod, Peter; Carstensen, Niels Jacob; Madsen, Henrik
1999-01-01
A new method for modelling the dynamics of rain sampled by a tipping bucket rain gauge is proposed. The considered models belong to the class of integer valued autoregressive processes. The models take the autocorelation and discrete nature of the data into account. A first order, a second order...... and a threshold model are presented together with methods to estimate the parameters of each model. The models are demonstrated to provide a good description of dt from actual rain events requiring only two to four parameters....
Autoregressive Spectral Estimation for Quasi-Periodic Oscillations
Institute of Scientific and Technical Information of China (English)
Li Chen; Ti-Pei Li
2005-01-01
Modern methods of spectral estimation based on parametric time-series models are useful tools in power spectral analysis. We apply the autoregressive (AR) model to study quasi-periodic oscillations (QPOs). An empirical formula to estimate the expectation and standard deviation of the noise AR power densities is derived, which can be used to estimate the statistical significance of an apparent QPO peak in an AR spectrum. An iterative adding-noise algorithm in AR spectral analysis is proposed and applied to studying QPOs in the X-ray binary Cir X-1.
AN EXPONENTIAL INEQUALITY FOR AUTOREGRESSIVE PROCESSES IN ADAPTIVE TRACKING
Institute of Scientific and Technical Information of China (English)
Bernard BERCU
2007-01-01
A wide range of literature concerning classical asymptotic properties for linear models with adaptive control is available, such as strong laws of large numbers or central limit theorems.Unfortunately, in contrast with the situation without control, it appears to be impossible to find sharp asymptotic or nonasymptotic properties such as large deviation principles or exponential inequalities.Our purpose is to provide a first step towards that direction by proving a very simple exponential inequality for the standard least squares estimator of the unknown parameter of Gaussian autoregressive process in adaptive tracking.
Limit theorems for bifurcating autoregressive processes with missing data
de Saporta, Benoîte; Marsalle, Laurence
2010-01-01
We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes when some of the data are missing. We model the process of observed data with a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the almost sure convergence of our estimators on the set of non-extinction of the Galton-Watson. We also prove a quadratic strong law and a central limit theorem.
Directory of Open Access Journals (Sweden)
Nandamudi Lankalapalli Vijaykumar
2012-12-01
Full Text Available Statecharts are a graphical representation to model reactive systems that respond to external or internal stimuli by changing the state of a given system. Statecharts can be seen as an extension of state-transition diagrams that allows modeling hierarchy, orthogonality, and interdependence. Due to their features to represent reactive systems, Statecharts have been adapted to represent and deal analytically with performance models (reactive systems whose performance is to be evaluated. An interesting feature present in Statecharts is to record the system's state, which cannot be represented in Markov models in a straightforward manner due to its "memory-less" property. The contributions of this paper are: show that Statecharts are a feasible alternative to specify a reactive system so that its performance can be evaluated by both analytical and simulation techniques; show that the inclusion of the memory representation in the Statecharts specification can indeed be made by both analytical and simulation techniques. The results of a case study of a manufacturing system show that the objectives are achieved.Statecharts representam graficamente sistemas reativos que respondem aos estímulos externos ou internos e mudam estados de um dado sistema. Statecharts estendem diagramas de estado com hierarquia, paralelismo e interdependência. Devido às suas características, eles foram adaptados para representar e tratar analiticamente modelos de desempenho (sistemas reativos cujo desempenho deve ser avaliado. Uma característica presente em Statecharts é registrar (ou memorizar um estado do sistema que não é possível representar numa forma direta em modelos Markovianos devido à sua propriedade de "sem memória". São duas as contribuições deste artigo: mostrar que Statecharts são viáveis para especificar sistemas reativos e avaliar o seu desempenho tanto por técnicas analíticas quanto por simulação; mostrar que a inclusão de representa
Institute of Scientific and Technical Information of China (English)
徐廷学; 杜峻名; 蓝天
2011-01-01
Aiming at the large error problem while using the general time series prediction for lower demand spare parts, this paper builds a prediction model based on Markove and Monte Carlo simulation. Based on the simulation model, this paper using MATLAB platform analyses the Markov property, combines Markov chain with Monte Carlo simulation, gives the algorithms to achieve the Monte Carlo simulation and application for analysis. The results show that, given the rate of spare parts to meet the case, according to the application of the model to predict the sequence of quarterly consumption of such demand in the coming one year, spare parts for the low demand forecast for reference.%针对低需求量备件采用一般的时间序列预测法误差较大的难题,构建基于马尔可夫与蒙特卡罗仿真的预测模型.分析备件需求量的马尔可夫性,将马尔可夫链与蒙特卡罗仿真相结合,在建立仿真模型的基础上,以MATLAB 为平台,给出利用计算机实现蒙特卡罗仿真的算法步骤,并应用实例进行分析.结果表明:在给定备件满足率的情况下,应用该模型可根据季度消耗量序列来预测该类备件未来1年的需求量,为低需求量备件的预测提供借鉴.
Evaluation of a vector autoregressive approach for downscaling
Salonen, Sebastian; Sauter, Tobias
2014-05-01
Statisical downscaling has become a well-established tool in regional and local impact assessments over the last few years. Robust and universal downscaling methods are required to reliably correct the spatial and temporal structures from coarse models. In this study we set up and evaluate the application of VAR-models for automated temperature and precipitation downscaling. VAR-models belong to the vectorial regression-techniques, that include autoregressive effects of the considered time series. They might be seen as an extension of univariate time-series analysis to multivariate perspective. Including autoregressive effects is one of the great advantages of this method, but also includes some pitfalls. Before the model can be applied the structure of the data must be carfully examined and require appropriate data preprocessing. We study in detail different preprocessing techniques and the possibility of the automatization. The proposed method has been applied and evaluated to temperature and precipitation data in the Rhineland region (Germany) and Svalbard. The large-scale atmospheric data are derived from ERA-40 as NCEP/NCAR reanalysis. These datasets offer the possibility to determine the applicability of VAR-models in a downscaling approach, their need for data-preparation techniques and the possibility of an automatization of an approach based on these models.
Morawietz, Martin; Xu, Chong-Yu; Gottschalk, Lars; Tallaksen, Lena
2010-05-01
A post-processor that accounts for the hydrologic uncertainty in a probabilistic streamflow forecast system is necessary to account for the uncertainty introduced by the hydrological model. In this study different variants of an autoregressive error model that can be used as a post-processor for short to medium range streamflow forecasts, are evaluated. The deterministic HBV model is used to form the basis for the streamflow forecast. The general structure of the error models then used as post-processor is a first order autoregressive model of the form dt = αdt-1 + σɛt where dt is the model error (observed minus simulated streamflow) at time t, α and σ are the parameters of the error model, and ɛt is the residual error described through a probability distribution. The following aspects are investigated: (1) Use of constant parameters α and σ versus the use of state dependent parameters. The state dependent parameters vary depending on the states of temperature, precipitation, snow water equivalent and simulated streamflow. (2) Use of a Standard Normal distribution for ɛt versus use of an empirical distribution function constituted through the normalized residuals of the error model in the calibration period. (3) Comparison of two different transformations, i.e. logarithmic versus square root, that are applied to the streamflow data before the error model is applied. The reason for applying a transformation is to make the residuals of the error model homoscedastic over the range of streamflow values of different magnitudes. Through combination of these three characteristics, eight variants of the autoregressive post-processor are generated. These are calibrated and validated in 55 catchments throughout Norway. The discrete ranked probability score with 99 flow percentiles as standardized thresholds is used for evaluation. In addition, a non-parametric bootstrap is used to construct confidence intervals and evaluate the significance of the results. The main
Markov chain approach to identifying Wiener systems
Institute of Scientific and Technical Information of China (English)
ZHAO WenXiao; CHEN HanFu
2012-01-01
Identification of the Wiener system composed of an infinite impulse response (IIR) linear subsystem followed by a static nonlinearity is considered.The recursive estimates for unknown coefficients of the linear subsystem and for the values of the nonlinear function at any fixed points are given by the stochastic approximation algorithms with expanding truncations (SAAWET).With the help of properties of the Markov chain connected with the linear subsystem,all estimates derived in the paper are proved to be strongly consistent.In comparison with the existing results on the topic,the method presented in the paper simplifies the convergence analysis and requires weaker conditions.A numerical example is given,and the simulation results are consistent with the theoretical analysis.
Recombination Processes and Nonlinear Markov Chains.
Pirogov, Sergey; Rybko, Alexander; Kalinina, Anastasia; Gelfand, Mikhail
2016-09-01
Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity between the recombining segments, several studies examined whether this could lead to the emergence of subspecies. Most of them simulated fixed-size Wright-Fisher populations, in which the genetic drift should be taken into account. Here, we use nonlinear Markov processes to describe a bacterial population evolving under mutation and recombination. We consider a population structure as a probability measure on the space of genomes. This approach implies the infinite population size limit, and thus, the genetic drift is not assumed. We prove that under these conditions, the emergence of subspecies is impossible.
Maximizing Entropy over Markov Processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2013-01-01
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... as a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...
Maximizing entropy over Markov processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2014-01-01
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...
Markov processes characterization and convergence
Ethier, Stewart N
2009-01-01
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists."[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference."-American Scientist"There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings."-Zentralblatt f?r Mathematik und ihre Grenzgebiete/Mathematics Abstracts"Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook."-Journal of Statistical PhysicsMarkov Proce...
Descriptive and predictive evaluation of high resolution Markov chain precipitation models
DEFF Research Database (Denmark)
Sørup, Hjalte Jomo Danielsen; Madsen, Henrik; Arnbjerg-Nielsen, Karsten
2012-01-01
. Continuous modelling of the Markov process proved attractive because of a marked decrease in the number of parameters. Inclusion of seasonality into the continuous Markov chain model proved difficult. Monte Carlo simulations with the models show that it is very difficult for all the model formulations...... to reproduce the time series on event level. Extreme events with short (10 min), medium (60 min) and long (12 h) durations were investigated because of their importance in urban hydrology. Both the descriptive likelihood based statistics and the predictive Monte Carlo simulation based statistics are valuable......A time series of tipping bucket recordings of very high temporal and volumetric resolution precipitation is modelled using Markov chain models. Both first and second‐order Markov models as well as seasonal and diurnal models are investigated and evaluated using likelihood based techniques...
Exact goodness-of-fit tests for Markov chains.
Besag, J; Mondal, D
2013-06-01
Goodness-of-fit tests are useful in assessing whether a statistical model is consistent with available data. However, the usual χ² asymptotics often fail, either because of the paucity of the data or because a nonstandard test statistic is of interest. In this article, we describe exact goodness-of-fit tests for first- and higher order Markov chains, with particular attention given to time-reversible ones. The tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple Monte Carlo sampling or by Markov chain Monte Carlo. They apply both to single and to multiple sequences and allow a free choice of test statistic. Three examples are given. The first concerns multiple sequences of dry and wet January days for the years 1948-1983 at Snoqualmie Falls, Washington State, and suggests that standard analysis may be misleading. The second one is for a four-state DNA sequence and lends support to the original conclusion that a second-order Markov chain provides an adequate fit to the data. The last one is six-state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first-order reversible Markov chain at 6 picosecond time steps.
Statistical significance test for transition matrices of atmospheric Markov chains
Vautard, Robert; Mo, Kingtse C.; Ghil, Michael
1990-01-01
Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.
Aperiodicity in one-way Markov cycles and repeat times of large earthquakes in faults
Tejedor, Alejandro; Pacheco, Amalio F
2011-01-01
A common use of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. Here it is proved that in {\\it any} one-way Markov cycle, the aperiodicity of the corresponding distribution of cycle lengths is always lower than one. This fact concurs with observations of large earthquakes in faults all over the world.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelly; Robert, Philippe
2012-01-01
If ($C_n$) a Markov chain on a discrete state space $S$, a Markov chain ($C_n, M_n$) on the product space $S \\times S$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain behaves like the original Markov chain and the second component changes only when both coo
Hidden Markov Model Based Automated Fault Localization for Integration Testing
Ge, Ning; NAKAJIMA, SHIN; Pantel, Marc
2013-01-01
International audience; Integration testing is an expensive activity in software testing, especially for fault localization in complex systems. Model-based diagnosis (MBD) provides various benefits in terms of scalability and robustness. In this work, we propose a novel MBD approach for the automated fault localization in integration testing. Our method is based on Hidden Markov Model (HMM) which is an abstraction of system's component to simulate component's behaviour. The core of this metho...
Markov and semi-Markov processes as a failure rate
Grabski, Franciszek
2016-06-01
In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.
Markov process functionals in finance and insurance
Institute of Scientific and Technical Information of China (English)
GENG Xian-min; LI Liang
2009-01-01
The Maxkov property of Maxkov process functionals which axe frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Maxkov property of some important Markov process functionals axe presented, the following conclusions are obtained: the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent incre-ments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Maxkov process being still a Maxkov process are given.
Markov and mixed models with applications
DEFF Research Database (Denmark)
Mortensen, Stig Bousgaard
the individual in almost any thinkable way. This project focuses on measuring the eects on sleep in both humans and animals. The sleep process is usually analyzed by categorizing small time segments into a number of sleep states and this can be modelled using a Markov process. For this purpose new methods...... for non-parametric estimation of Markov processes are proposed to give a detailed description of the sleep process during the night. Statistically the Markov models considered for sleep states are closely related to the PK models based on SDEs as both models share the Markov property. When the models...
A compositional framework for Markov processes
Baez, John C.; Fong, Brendan; Pollard, Blake S.
2016-03-01
We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs." One can build up a Markov process from smaller open pieces. This process is formalized by making open Markov processes into the morphisms of a dagger compact category. We show that the behavior of a detailed balanced open Markov process is determined by a principle of minimum dissipation, closely related to Prigogine's principle of minimum entropy production. Using this fact, we set up a functor mapping open detailed balanced Markov processes to open circuits made of linear resistors. We also describe how to "black box" an open Markov process, obtaining the linear relation between input and output data that holds in any steady state, including nonequilibrium steady states with a nonzero flow of probability through the system. We prove that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to Lagrangian relations between symplectic vector spaces. This allows us to compute the steady state behavior of an open detailed balanced Markov process from the behaviors of smaller pieces from which it is built. We relate this black box functor to a previously constructed black box functor for circuits.
Implementing Modifed Burg Algorithms in Multivariate Subset Autoregressive Modeling
Directory of Open Access Journals (Sweden)
A. Alexandre Trindade
2003-02-01
Full Text Available The large number of parameters in subset vector autoregressive models often leads one to procure fast, simple, and efficient alternatives or precursors to maximum likelihood estimation. We present the solution of the multivariate subset Yule-Walker equations as one such alternative. In recent work, Brockwell, Dahlhaus, and Trindade (2002, show that the Yule-Walker estimators can actually be obtained as a special case of a general recursive Burg-type algorithm. We illustrate the structure of this Algorithm, and discuss its implementation in a high-level programming language. Applications of the Algorithm in univariate and bivariate modeling are showcased in examples. Univariate and bivariate versions of the Algorithm written in Fortran 90 are included in the appendix, and their use illustrated.
Autoregressive modelling for rolling element bearing fault diagnosis
Al-Bugharbee, H.; Trendafilova, I.
2015-07-01
In this study, time series analysis and pattern recognition analysis are used effectively for the purposes of rolling bearing fault diagnosis. The main part of the suggested methodology is the autoregressive (AR) modelling of the measured vibration signals. This study suggests the use of a linear AR model applied to the signals after they are stationarized. The obtained coefficients of the AR model are further used to form pattern vectors which are in turn subjected to pattern recognition for differentiating among different faults and different fault sizes. This study explores the behavior of the AR coefficients and their changes with the introduction and the growth of different faults. The idea is to gain more understanding about the process of AR modelling for roller element bearing signatures and the relation of the coefficients to the vibratory behavior of the bearings and their condition.
Modeling shales and marls reflections by autoregression method
Malik, Umairia; Ching, Dennis Ling Chuan; Daud, Hanita; Januarisma, Vikri
2016-11-01
Seismic modeling is pervasive in exploring the subsurface structure. The propagation of elastic waves in homogenous medium has to be modeled to create synthetic seismograms. A numerical solution of partial differential equations describes the propagation phenomenon in elastic medium under the initial and boundary condition that is Clayton Engquist (CE). The subsurface discontinuities like fractures effect the seismic reflections that are used for subsurface imaging. A fractured velocity model with shales and marls sedimentary rocks is built and common depth point (CDP) seismograms with single shot are preprocessed by automatic gain control. The subsurface reflections are modeled by using the first-order autoregressive (AR(1)) model. A comparison of synthetic and real data AR model is made on the basis of average reflectivity, R2 and means square error (MSE). The real data has smaller average reflectivity, -1.80e-10, 93.966% explained variation i.e. R2 and 1.71e-07 minimum MSE.
Some Identification Problems in the Cointegrated Vector Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren
2010-01-01
The paper analyses some identification problems in the cointegrated vector autoregressive model. A criteria for identification by linear restrictions on individual relations is given. The asymptotic distribution of the estimators of a and ß is derived when they are identified by linear restrictions...... on ß , and when they are identified by linear restrictions on a . It it shown that, in the latter case, a component of is asymptotically Gaussian. Finally we discuss identification of shocks by introducing the contemporaneous and permanent effect of a shock and the distinction between permanent...... and transitory shocks, which allows one to identify permanent shocks from the long-run variance and transitory shocks from the short-run variance....
Stator Fault Detection in Induction Motors by Autoregressive Modeling
Directory of Open Access Journals (Sweden)
Francisco M. Garcia-Guevara
2016-01-01
Full Text Available This study introduces a novel methodology for early detection of stator short circuit faults in induction motors by using autoregressive (AR model. The proposed algorithm is based on instantaneous space phasor (ISP module of stator currents, which are mapped to α-β stator-fixed reference frame; then, the module is obtained, and the coefficients of the AR model for such module are estimated and evaluated by order selection criterion, which is used as fault signature. For comparative purposes, a spectral analysis of the ISP module by Discrete Fourier Transform (DFT is performed; a comparison of both methodologies is obtained. To demonstrate the suitability of the proposed methodology for detecting and quantifying incipient short circuit stator faults, an induction motor was altered to induce different-degree fault scenarios during experimentation.
Testing the Conditional Mean Function of Autoregressive Conditional Duration Models
DEFF Research Database (Denmark)
Hautsch, Nikolaus
function. The dynamic properties of the model as well as an assessment of the estimation quality is investigated in a Monte Carlo study. It is illustrated that the model is a useful approach to estimate conditional failure probabilities based on (persistent) serial dependent duration data which might......This paper proposes a dynamic proportional hazard (PH) model with non-specified baseline hazard for the modelling of autoregressive duration processes. A categorization of the durations allows us to reformulate the PH model as an ordered response model based on extreme value distributed errors....... In order to capture persistent serial dependence in the duration process, we extend the model by an observation driven ARMA dynamic based on generalized errors. We illustrate the maximum likelihood estimation of both the model parameters and discrete points of the underlying unspecified baseline survivor...
Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)
DEFF Research Database (Denmark)
Agosto, Arianna; Cavaliere, Guiseppe; Kristensen, Dennis;
in the analysis of the asympotic properties of the maximum-likelihood estimators of the models. The PARX class of models is used to analyse the time series properties of monthly corporate defaults in the US in the period 1982-2011 using financial and economic variables as exogeneous covariates. Results show......We develop a class of Poisson autoregressive models with additional covariates (PARX) that can be used to model and forecast time series of counts. We establish the time series properties of the models, including conditions for stationarity and existence of moments. These results are in turn used...... that our model is able to capture the time series dynamics of corporate defaults well, including the well-known default counts clustering found in data. Moreover, we find that while in general current defaults do indeed affect the probability of other firms defaulting in the future, in recent years...
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
2012-01-01
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters......likelihood estimators. To this end we prove weak convergence of the conditional likelihood as a continuous stochastic...... process in the parameters when errors are i.i.d. with suitable moment conditions and initial values are bounded. When the limit is deterministic this implies uniform convergence in probability of the conditional likelihood function. If the true value b0>1/2, we prove that the limit distribution of (ß...
Likelihood Inference for a Nonstationary Fractional Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
values Xº-n, n = 0, 1, ..., under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values......This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial...... are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to ?find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II...
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
values X0-n, n = 0, 1,...,under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values......This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d-b; where d ≥ b > 1/2 are parameters to be estimated. We model the data X1,...,XT given the initial...... are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II....
Parameter estimation in a spatial unit root autoregressive model
Baran, Sándor
2011-01-01
Spatial autoregressive model $X_{k,\\ell}=\\alpha X_{k-1,\\ell}+\\beta X_{k,\\ell-1}+\\gamma X_{k-1,\\ell-1}+\\epsilon_{k,\\ell}$ is investigated in the unit root case, that is when the parameters are on the boundary of the domain of stability that forms a tetrahedron with vertices $(1,1,-1), \\ (1,-1,1),\\ (-1,1,1)$ and $(-1,-1,-1)$. It is shown that the limiting distribution of the least squares estimator of the parameters is normal and the rate of convergence is $n$ when the parameters are in the faces or on the edges of the tetrahedron, while on the vertices the rate is $n^{3/2}$.
Autoregressive trispectrum and its slices analysis of magnetorheological damping device
Institute of Scientific and Technical Information of China (English)
陈丙三; 黄宜坚
2008-01-01
A combined magnetorheological damper combined with rubber spring and magnetorheological damper is addressed.This type of damping device has inherited the merits of rubber spring and the magnetorheological damper.The test damping device is made up of combined magnetorheological damper,amplitude controller,signal collecting device,computer software for dynamic analysis,etc.When a zeromean and non-Gaussian white noise interfere with the device,a time series autoregressive(AR) model is conducted by using the sampled experimental data.Trispectrum and its slices analysis are emerging as a new powerful technique in signal processing,which is put forward for investigating the dynamic characteristics of the magnetorheological vibrant device.The present of trispectrum and its slices analysis change with the variation of controllable working magnetic field of the damper correspondingly.It is indicated that AR trispectrum and its slices analysis methods are feasible and effective for investigation of magnetorheological vibrant device.
马尔科夫理论及其在预测中的应用综述%Review for Markov Theory and Its Application in the Forecast
Institute of Scientific and Technical Information of China (English)
黄麒元; 王致杰; 王东伟; 杜彬
2015-01-01
介绍了马尔科夫理论的发展进程。详细阐述了马尔科夫链算法的相关概念、原理和数学模型，并对基于马尔科夫状态转换的自回归模型进行了描述。说明算法在波动性预测研究中的应用现状，并着重体现了对电力系统状态预测的重要意义。充分考虑马尔科夫链的特征，对当前马尔科夫理论应用于新能源功率预测研究的未来发展趋势进行了展望。%The development of the theory of markov process is introduced. The concept, principle and mathematical model of markov chain is in detail elaborated. And the autoregressive model based on markov state transitions are described. Algorithm is explained in the application status of the volatility prediction research. And importance for power system state prediction is mainly reflected. Fully considering the characteristics of the markov chain, this paper discusses The trend of future development of the current markov theory applied to the new energy power prediction research.
Entropy Rate for Hidden Markov Chains with rare transitions
2010-01-01
We consider Hidden Markov Chains obtained by passing a Markov Chain with rare transitions through a noisy memoryless channel. We obtain asymptotic estimates for the entropy of the resulting Hidden Markov Chain as the transition rate is reduced to zero.
Noe, Frank; Prinz, Jan-Hendrik; Plattner, Nuria
2013-01-01
Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has therefore been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase- space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecula...
Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains.
Meyer, Denny; Forbes, Don; Clarke, Stephen R
2006-01-01
Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key PointsA comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition.The Markov assumption appears to be valid.However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play.Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes.
Inhomogeneous Markov point processes by transformation
DEFF Research Database (Denmark)
Jensen, Eva B. Vedel; Nielsen, Linda Stougaard
2000-01-01
We construct parametrized models for point processes, allowing for both inhomogeneity and interaction. The inhomogeneity is obtained by applying parametrized transformations to homogeneous Markov point processes. An interesting model class, which can be constructed by this transformation approach......, is that of exponential inhomogeneous Markov point processes. Statistical inference For such processes is discussed in some detail....
Modelling and analysis of Markov reward automata
Guck, Dennis; Timmer, Mark; Hatefi, Hassan; Ruijters, Enno; Stoelinga, Mariëlle
2014-01-01
Costs and rewards are important ingredients for many types of systems, modelling critical aspects like energy consumption, task completion, repair costs, and memory usage. This paper introduces Markov reward automata, an extension of Markov automata that allows the modelling of systems incorporating
Using Games to Teach Markov Chains
Johnson, Roger W.
2003-01-01
Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…
STATISTICS OF A CLASS OF MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
DENG Yingchun; CAO Xianbing
2004-01-01
In this paper we prove that the distributions of their sojourn time and hitting time at one special state for random walks which are allowed to be finite or infinite and Markov chains on star-graphs with discrete time can uniquely determine the probability distribution of the whole chains. This result also suggests a new statistical method for Markov chains.
Inferring animal densities from tracking data using Markov chains.
Directory of Open Access Journals (Sweden)
Hal Whitehead
Full Text Available The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.
Inferring animal densities from tracking data using Markov chains.
Whitehead, Hal; Jonsen, Ian D
2013-01-01
The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.
Offline and online detection of damage using autoregressive models and artificial neural networks
Omenzetter, Piotr; de Lautour, Oliver R.
2007-04-01
Developed to study long, regularly sampled streams of data, time series analysis methods are being increasingly investigated for the use of Structural Health Monitoring. In this research, Autoregressive (AR) models are used in conjunction with Artificial Neural Networks (ANNs) for damage detection, localisation and severity assessment. In the first reported experimental exercise, AR models were used offline to fit the acceleration time histories of a 3-storey test structure in undamaged and various damaged states when excited by earthquake motion simulated on a shake table. Damage was introduced into the structure by replacing the columns with those of a thinner thickness. Analytical models of the structure in both damaged and undamaged states were also developed and updated using experimental data in order to determine structural stiffness. The coefficients of AR models were used as damage sensitive features and input into an ANN to build a relationship between them and the remaining structural stiffness. In the second, analytical exercise, a system with gradually progressing damage was numerically simulated and acceleration AR models with exogenous inputs were identified recursively. A trained ANN was then required to trace the structural stiffness online. The results for the offline and online approach showed the efficiency of using AR coefficient as damage sensitive features and good performance of the ANNs for damage detection, localization and quantification.
Gutnisky, Diego A; Josić, Kresimir
2010-05-01
Experimental advances allowing for the simultaneous recording of activity at multiple sites have significantly increased our understanding of the spatiotemporal patterns in neural activity. The impact of such patterns on neural coding is a fundamental question in neuroscience. The simulation of spike trains with predetermined activity patterns is therefore an important ingredient in the study of potential neural codes. Such artificially generated spike trains could also be used to manipulate cortical neurons in vitro and in vivo. Here, we propose a method to generate spike trains with given mean firing rates and cross-correlations. To capture this statistical structure we generate a point process by thresholding a stochastic process that is continuous in space and discrete in time. This stochastic process is obtained by filtering Gaussian noise through a multivariate autoregressive (AR) model. The parameters of the AR model are obtained by a nonlinear transformation of the point-process correlations to the continuous-process correlations. The proposed method is very efficient and allows for the simulation of large neural populations. It can be optimized to the structure of spatiotemporal correlations and generalized to nonstationary processes and spatiotemporal patterns of local field potentials and spike trains.
A context dependent pair hidden Markov model for statistical alignment
Arribas-Gil, Ana
2011-01-01
This article proposes a novel approach to statistical alignment of nucleotide sequences by introducing a context dependent structure on the substitution process in the underlying evolutionary model. We propose to estimate alignments and context dependent mutation rates relying on the observation of two homologous sequences. The procedure is based on a generalized pair-hidden Markov structure, where conditional on the alignment path, the nucleotide sequences follow a Markov distribution. We use a stochastic approximation expectation maximization (saem) algorithm to give accurate estimators of parameters and alignments. We provide results both on simulated data and vertebrate genomes, which are known to have a high mutation rate from CG dinucleotide. In particular, we establish that the method improves the accuracy of the alignment of a human pseudogene and its functional gene.
Classification Using Markov Blanket for Feature Selection
DEFF Research Database (Denmark)
Zeng, Yifeng; Luo, Jian
2009-01-01
Selecting relevant features is in demand when a large data set is of interest in a classification task. It produces a tractable number of features that are sufficient and possibly improve the classification performance. This paper studies a statistical method of Markov blanket induction algorithm...... induction as a feature selection method. In addition, we point out an important assumption behind the Markov blanket induction algorithm and show its effect on the classification performance....... for filtering features and then applies a classifier using the Markov blanket predictors. The Markov blanket contains a minimal subset of relevant features that yields optimal classification performance. We experimentally demonstrate the improved performance of several classifiers using a Markov blanket...
Quantum Markov Chain Mixing and Dissipative Engineering
DEFF Research Database (Denmark)
Kastoryano, Michael James
2012-01-01
This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state...... of the system at the present point in time, but not on the history of events. Very many important processes in nature are of this type, therefore a good understanding of their behaviour has turned out to be very fruitful for science. Markov chains always have a non-empty set of limiting distributions...... (stationary states). The aim of Markov chain mixing is to obtain (upper and/or lower) bounds on the number of steps it takes for the Markov chain to reach a stationary state. The natural quantum extensions of these notions are density matrices and quantum channels. We set out to develop a general mathematical...
Markov state modeling of sliding friction
Pellegrini, F.; Landes, François P.; Laio, A.; Prestipino, S.; Tosatti, E.
2016-11-01
Markov state modeling (MSM) has recently emerged as one of the key techniques for the discovery of collective variables and the analysis of rare events in molecular simulations. In particular in biochemistry this approach is successfully exploited to find the metastable states of complex systems and their evolution in thermal equilibrium, including rare events, such as a protein undergoing folding. The physics of sliding friction and its atomistic simulations under external forces constitute a nonequilibrium field where relevant variables are in principle unknown and where a proper theory describing violent and rare events such as stick slip is still lacking. Here we show that MSM can be extended to the study of nonequilibrium phenomena and in particular friction. The approach is benchmarked on the Frenkel-Kontorova model, used here as a test system whose properties are well established. We demonstrate that the method allows the least prejudiced identification of a minimal basis of natural microscopic variables necessary for the description of the forced dynamics of sliding, through their probabilistic evolution. The steps necessary for the application to realistic frictional systems are highlighted.
Modeling of uncertain spectra through stochastic autoregressive systems
Wang, Yiwei; Wang, X. Q.; Mignolet, Marc P.; Yang, Shuchi; Chen, P. C.
2016-03-01
The focus of this investigation is on the formulation and validation of a modeling strategy of the uncertainty that may exist on the specification of the power spectral density of scalar stationary processes and on the spectral matrices of vector ones. These processes may, for example, be forces on a structure originating from natural phenomena which are coarsely modeled (i.e., with epistemic uncertainty) or are specified by parameters unknown (i.e., with aleatoric uncertainty) in the application considered. The propagation of the uncertainty, e.g., to the response of the structure, may be carried out provided that a stochastic model of the uncertainty in the power spectral density/matrix is available from which admissible samples can be efficiently generated. Such a stochastic model will be developed here through an autoregressive-based parameterization of the specified baseline power spectral density/matrix and of its random samples. Autoregressive (AR) models are particularly well suited for this parametrization since their spectra are known to converge to a broad class of spectra (all non-pathological spectra) as the AR order increases. Note that the characterization of these models is not achieved directly in terms of their coefficients but rather in terms of their reflection coefficients which lie (or their eigenvalues in the vector process case) in the domain [0,1) as a necessary and sufficient condition for stability. Maximum entropy concepts are then employed to formulate the distribution of the reflection coefficients in both scalar and vector process case leading to a small set of hyperparameters of the uncertain model. Depending on the information available, these hyperparameters could either be varied in a parametric study format to assess the effects of uncertainty or could be identified, e.g., in a maximum likelihood format, from observed data. The validation and assessment of these concepts is finally achieved on several examples including the
Hidden Markov Modeling for Weigh-In-Motion Estimation
Energy Technology Data Exchange (ETDEWEB)
Abercrombie, Robert K [ORNL; Ferragut, Erik M [ORNL; Boone, Shane [ORNL
2012-01-01
This paper describes a hidden Markov model to assist in the weight measurement error that arises from complex vehicle oscillations of a system of discrete masses. Present reduction of oscillations is by a smooth, flat, level approach and constant, slow speed in a straight line. The model uses this inherent variability to assist in determining the true total weight and individual axle weights of a vehicle. The weight distribution dynamics of a generic moving vehicle were simulated. The model estimation converged to within 1% of the true mass for simulated data. The computational demands of this method, while much greater than simple averages, took only seconds to run on a desktop computer.
DEFF Research Database (Denmark)
Kock, Anders Bredahl
2015-01-01
We show that the adaptive Lasso is oracle efficient in stationary and nonstationary autoregressions. This means that it estimates parameters consistently, selects the correct sparsity pattern, and estimates the coefficients belonging to the relevant variables at the same asymptotic efficiency...
DEFF Research Database (Denmark)
Teräsvirta, Timo; Yang, Yukai
We consider a nonlinear vector model called the logistic vector smooth transition autoregressive model. The bivariate single-transition vector smooth transition regression model of Camacho (2004) is generalised to a multivariate and multitransition one. A modelling strategy consisting...
Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas behind the Algorithm
Stewart, Wayne; Stewart, Sepideh
2014-01-01
For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…
Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model
de la Torre, Jimmy; Stark, Stephen; Chernyshenko, Oleksandr S.
2006-01-01
The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…
A fuzzy-autoregressive model of daily river flows
Greco, Roberto
2012-06-01
A model for the identification of daily river flows has been developed, consisting of the combination of an autoregressive model with a fuzzy inference system. The AR model is devoted to the identification of base flow, supposed to be described by linear laws. The fuzzy model identifies the surface runoff, by applying a small set of linguistic statements, deriving from the knowledge of the physical features of the nonlinear rainfall-runoff transformation, to the inflow entering the river basin. The model has been applied to the identification of the daily flow series of river Volturno at Cancello-Arnone (Southern Italy), with a drainage basin of around 5560 km2, observed between 1970 and 1974. The inflow was estimated on the basis of daily precipitations registered during the same years at six rain gauges located throughout the basin. The first two years were used for model training, the remaining three for the validation. The obtained results show that the proposed model provides good predictions of either low river flows or high floods, although the analysis of residuals, which do not turn out to be a white noise, indicates that the cause and effect relationship between rainfall and runoff is not completely identified by the model.
Sparse representation based image interpolation with nonlocal autoregressive modeling.
Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming
2013-04-01
Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.
Likelihood inference for a fractionally cointegrated vector autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X_{t} to be fractional of order d and cofractional of order d-b; that is, there exist vectors β for which β......′X_{t} is fractional of order d-b. The parameters d and b satisfy either d≥b≥1/2, d=b≥1/2, or d=d_{0}≥b≥1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2≤b≤d≤d_{1} for any d_{1}≥d_{0}. To this end, we consider the conditional likelihood as a stochastic...... process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of β is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We...
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß......'X(t) is fractional of order d-b. The parameters d and b satisfy either d=b=1/2, d=b=1/2, or d=d0=b=1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2=b=d=d1 for any d1=d0. To this end, we consider the conditional likelihood as a stochastic process...... in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of ß is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also find...
On the maximum-entropy/autoregressive modeling of time series
Chao, B. F.
1984-01-01
The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions.
An algebraic method for constructing stable and consistent autoregressive filters
Energy Technology Data Exchange (ETDEWEB)
Harlim, John, E-mail: jharlim@psu.edu [Department of Mathematics, the Pennsylvania State University, University Park, PA 16802 (United States); Department of Meteorology, the Pennsylvania State University, University Park, PA 16802 (United States); Hong, Hoon, E-mail: hong@ncsu.edu [Department of Mathematics, North Carolina State University, Raleigh, NC 27695 (United States); Robbins, Jacob L., E-mail: jlrobbi3@ncsu.edu [Department of Mathematics, North Carolina State University, Raleigh, NC 27695 (United States)
2015-02-15
In this paper, we introduce an algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth. By stable, we refer to the classical stability condition for the AR model. By consistent, we refer to the classical consistency constraints of Adams–Bashforth methods of order-two. One attractive feature of this algebraic method is that the model parameters can be obtained without directly knowing any training data set as opposed to many standard, regression-based parameterization methods. It takes only long-time average statistics as inputs. The proposed method provides a discretization time step interval which guarantees the existence of stable and consistent AR model and simultaneously produces the parameters for the AR models. In our numerical examples with two chaotic time series with different characteristics of decaying time scales, we find that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. These encouraging results are robust across wide ranges of discretization times, observation times, and observation noise variances. Finally, we also find that the proposed model produces an improved short-time prediction relative to the linear regression-based AR-models in forecasting a data set that characterizes the variability of the Madden–Julian Oscillation, a dominant tropical atmospheric wave pattern.
Revisiting Causality in Markov Chains
Shojaee, Abbas
2016-01-01
Identifying causal relationships is a key premise of scientific research. The growth of observational data in different disciplines along with the availability of machine learning methods offers the possibility of using an empirical approach to identifying potential causal relationships, to deepen our understandings of causal behavior and to build theories accordingly. Conventional methods of causality inference from observational data require a considerable length of time series data to capture cause-effect relationship. We find that potential causal relationships can be inferred from the composition of one step transition rates to and from an event. Also known as Markov chain, one step transition rates are a commonly available resource in different scientific disciplines. Here we introduce a simple, effective and computationally efficient method that we termed 'Causality Inference using Composition of Transitions CICT' to reveal causal structure with high accuracy. We characterize the differences in causes,...
MCMC simulation of GARCH model to forecast network traffic load
Directory of Open Access Journals (Sweden)
Akhter Raza Syed
2012-05-01
Full Text Available The performance of a computer network can be enhanced by increasing number of servers, upgrading the hardware, and gaining additional bandwidth but this solution require the huge amount to invest. In contrast to increasing the bandwidth and hardware resources, network traffic modeling play a significant role in enhancing the network performance. As the emphasis of telecommunication service providers shifted towards the high-speed networks providing integrated services at a prescribed Quality of Service (QoS, the role of accurate traffic models in network design and network simulation becomes ever more crucial. We analyze a traffic volume time series of internet requests made to a workstation. This series exhibits a long-range dependence and self-similarity in large time scale and exhibits multifractal in small time scale. In this paper, for this time series, we proposed Generalized Autoregressive Conditional Heteroscedastic, (GARCH model, and practical techniques for model fitting, Markov Chain Monte Carlo simulation and forecasting issues are demonstrated. The proposed model provides us simple and accurate approach for simulating internet data traffic patterns.
State Truncation for Large Markov Chains
Institute of Scientific and Technical Information of China (English)
JIANGLetian; XUGuozhi; ZHANGHao; YINGRendong
2003-01-01
One of the main issues to apply the Markov modeling method to reliability and availability analysis is the challenge called largeness, I.e., the explosive number of states, for a system with a large number of components.One method to quickly calculate the reliability of a sys-tem is to neglect ‘unimportant’ states in the Markov chain model. In this paper, based on a Markov model that is widely used in practical systems, a criterion of state trun-cation is presented.
Finite Markov processes and their applications
Iosifescu, Marius
2007-01-01
A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch
Uncertainty quantification for Markov chain models.
Meidani, Hadi; Ghanem, Roger
2012-12-01
Transition probabilities serve to parameterize Markov chains and control their evolution and associated decisions and controls. Uncertainties in these parameters can be associated with inherent fluctuations in the medium through which a chain evolves, or with insufficient data such that the inferential value of the chain is jeopardized. The behavior of Markov chains associated with such uncertainties is described using a probabilistic model for the transition matrices. The principle of maximum entropy is used to characterize the probability measure of the transition rates. The formalism is demonstrated on a Markov chain describing the spread of disease, and a number of quantities of interest, pertaining to different aspects of decision-making, are investigated.
Markov chains models, algorithms and applications
Ching, Wai-Ki; Ng, Michael K; Siu, Tak-Kuen
2013-01-01
This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods
Hidden Markov models estimation and control
Elliott, Robert J; Moore, John B
1995-01-01
As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filte
Siggiridou, Elsa; Kugiumtzis, Dimitris
2016-04-01
Granger causality has been used for the investigation of the inter-dependence structure of the underlying systems of multi-variate time series. In particular, the direct causal effects are commonly estimated by the conditional Granger causality index (CGCI). In the presence of many observed variables and relatively short time series, CGCI may fail because it is based on vector autoregressive models (VAR) involving a large number of coefficients to be estimated. In this work, the VAR is restricted by a scheme that modifies the recently developed method of backward-in-time selection (BTS) of the lagged variables and the CGCI is combined with BTS. Further, the proposed approach is compared favorably to other restricted VAR representations, such as the top-down strategy, the bottom-up strategy, and the least absolute shrinkage and selection operator (LASSO), in terms of sensitivity and specificity of CGCI. This is shown by using simulations of linear and nonlinear, low and high-dimensional systems and different time series lengths. For nonlinear systems, CGCI from the restricted VAR representations are compared with analogous nonlinear causality indices. Further, CGCI in conjunction with BTS and other restricted VAR representations is applied to multi-channel scalp electroencephalogram (EEG) recordings of epileptic patients containing epileptiform discharges. CGCI on the restricted VAR, and BTS in particular, could track the changes in brain connectivity before, during and after epileptiform discharges, which was not possible using the full VAR representation.
Siggiridou, Elsa
2015-01-01
Granger causality has been used for the investigation of the inter-dependence structure of the underlying systems of multi-variate time series. In particular, the direct causal effects are commonly estimated by the conditional Granger causality index (CGCI). In the presence of many observed variables and relatively short time series, CGCI may fail because it is based on vector autoregressive models (VAR) involving a large number of coefficients to be estimated. In this work, the VAR is restricted by a scheme that modifies the recently developed method of backward-in-time selection (BTS) of the lagged variables and the CGCI is combined with BTS. Further, the proposed approach is compared favorably to other restricted VAR representations, such as the top-down strategy, the bottom-up strategy, and the least absolute shrinkage and selection operator (LASSO), in terms of sensitivity and specificity of CGCI. This is shown by using simulations of linear and nonlinear, low and high-dimensional systems and different t...
Autoregressive Prediction with Rolling Mechanism for Time Series Forecasting with Small Sample Size
Directory of Open Access Journals (Sweden)
Zhihua Wang
2014-01-01
Full Text Available Reasonable prediction makes significant practical sense to stochastic and unstable time series analysis with small or limited sample size. Motivated by the rolling idea in grey theory and the practical relevance of very short-term forecasting or 1-step-ahead prediction, a novel autoregressive (AR prediction approach with rolling mechanism is proposed. In the modeling procedure, a new developed AR equation, which can be used to model nonstationary time series, is constructed in each prediction step. Meanwhile, the data window, for the next step ahead forecasting, rolls on by adding the most recent derived prediction result while deleting the first value of the former used sample data set. This rolling mechanism is an efficient technique for its advantages of improved forecasting accuracy, applicability in the case of limited and unstable data situations, and requirement of little computational effort. The general performance, influence of sample size, nonlinearity dynamic mechanism, and significance of the observed trends, as well as innovation variance, are illustrated and verified with Monte Carlo simulations. The proposed methodology is then applied to several practical data sets, including multiple building settlement sequences and two economic series.
A Ramp Cosine Cepstrum Model for the Parameter Estimation of Autoregressive Systems at Low SNR
Directory of Open Access Journals (Sweden)
Zhu Wei-Ping
2010-01-01
Full Text Available A new cosine cepstrum model-based scheme is presented for the parameter estimation of a minimum-phase autoregressive (AR system under low levels of signal-to-noise ratio (SNR. A ramp cosine cepstrum (RCC model for the one-sided autocorrelation function (OSACF of an AR signal is first proposed by considering both white noise and periodic impulse-train excitations. Using the RCC model, a residue-based least-squares optimization technique that guarantees the stability of the system is then presented in order to estimate the AR parameters from noisy output observations. For the purpose of implementation, the discrete cosine transform, which can efficiently handle the phase unwrapping problem and offer computational advantages as compared to the discrete Fourier transform, is employed. From extensive experimentations on AR systems of different orders, it is shown that the proposed method is capable of estimating parameters accurately and consistently in comparison to some of the existing methods for the SNR levels as low as −5 dB. As a practical application of the proposed technique, simulation results are also provided for the identification of a human vocal tract system using noise-corrupted natural speech signals demonstrating a superior estimation performance in terms of the power spectral density of the synthesized speech signals.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelly; Robert, Philippe
2009-01-01
Motivated by an original on-line page-ranking algorithm, starting from an arbitrary Markov chain $(C_n)$ on a discrete state space ${\\cal S}$, a Markov chain $(C_n,M_n)$ on the product space ${\\cal S}^2$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov
Hidden Markov models: the best models for forager movements?
Directory of Open Access Journals (Sweden)
Rocio Joo
Full Text Available One major challenge in the emerging field of movement ecology is the inference of behavioural modes from movement patterns. This has been mainly addressed through Hidden Markov models (HMMs. We propose here to evaluate two sets of alternative and state-of-the-art modelling approaches. First, we consider hidden semi-Markov models (HSMMs. They may better represent the behavioural dynamics of foragers since they explicitly model the duration of the behavioural modes. Second, we consider discriminative models which state the inference of behavioural modes as a classification issue, and may take better advantage of multivariate and non linear combinations of movement pattern descriptors. For this work, we use a dataset of >200 trips from human foragers, Peruvian fishermen targeting anchovy. Their movements were recorded through a Vessel Monitoring System (∼1 record per hour, while their behavioural modes (fishing, searching and cruising were reported by on-board observers. We compare the efficiency of hidden Markov, hidden semi-Markov, and three discriminative models (random forests, artificial neural networks and support vector machines for inferring the fishermen behavioural modes, using a cross-validation procedure. HSMMs show the highest accuracy (80%, significantly outperforming HMMs and discriminative models. Simulations show that data with higher temporal resolution, HSMMs reach nearly 100% of accuracy. Our results demonstrate to what extent the sequential nature of movement is critical for accurately inferring behavioural modes from a trajectory and we strongly recommend the use of HSMMs for such purpose. In addition, this work opens perspectives on the use of hybrid HSMM-discriminative models, where a discriminative setting for the observation process of HSMMs could greatly improve inference performance.
Bayesian posterior distributions without Markov chains.
Cole, Stephen R; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B
2012-03-01
Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.
A markov classification model for metabolic pathways
Directory of Open Access Journals (Sweden)
Mamitsuka Hiroshi
2010-01-01
Full Text Available Abstract Background This paper considers the problem of identifying pathways through metabolic networks that relate to a specific biological response. Our proposed model, HME3M, first identifies frequently traversed network paths using a Markov mixture model. Then by employing a hierarchical mixture of experts, separate classifiers are built using information specific to each path and combined into an ensemble prediction for the response. Results We compared the performance of HME3M with logistic regression and support vector machines (SVM for both simulated pathways and on two metabolic networks, glycolysis and the pentose phosphate pathway for Arabidopsis thaliana. We use AltGenExpress microarray data and focus on the pathway differences in the developmental stages and stress responses of Arabidopsis. The results clearly show that HME3M outperformed the comparison methods in the presence of increasing network complexity and pathway noise. Furthermore an analysis of the paths identified by HME3M for each metabolic network confirmed known biological responses of Arabidopsis. Conclusions This paper clearly shows HME3M to be an accurate and robust method for classifying metabolic pathways. HME3M is shown to outperform all comparison methods and further is capable of identifying known biologically active pathways within microarray data.
Directory of Open Access Journals (Sweden)
Bindu Abraham
2014-05-01
Full Text Available In this paper we analyze DAR(1/D/s Queue with Discrete Mittag-Leffler [DML(α] as marginal distribution. Simulation study of the sample path of the arrival process is conducted. For this queueing system, the stationary distribution of the system size and the waiting time distribution of an arbitrary packet is obtained with the help of matrix analytic methods and Markov regenerative theory. The quantitative effect of the stationary distribution on system size, waiting time and the autocorrelation function as well as the parameters of the input traffic is illustrated empirically. The model is applied to a real data on the passenger arrivals at a subway bus terminal in Santiago de Chile and is established that the model well suits this data.
Markov chains and decision processes for engineers and managers
Sheskin, Theodore J
2010-01-01
Markov Chain Structure and ModelsHistorical NoteStates and TransitionsModel of the WeatherRandom WalksEstimating Transition ProbabilitiesMultiple-Step Transition ProbabilitiesState Probabilities after Multiple StepsClassification of StatesMarkov Chain StructureMarkov Chain ModelsProblemsReferencesRegular Markov ChainsSteady State ProbabilitiesFirst Passage to a Target StateProblemsReferencesReducible Markov ChainsCanonical Form of the Transition MatrixTh
Observation uncertainty in reversible Markov chains.
Metzner, Philipp; Weber, Marcus; Schütte, Christof
2010-09-01
In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .
Generated dynamics of Markov and quantum processes
Janßen, Martin
2016-01-01
This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible. A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put in...
Generalized crested products of Markov chains
D'Angeli, Daniele
2010-01-01
We define a finite Markov chain, called generalized crested product, which naturally appears as a generalization of the first crested product of Markov chains. A complete spectral analysis is developed and the $k$-step transition probability is given. It is important to remark that this Markov chain describes a more general version of the classical Ehrenfest diffusion model. As a particular case, one gets a generalization of the classical Insect Markov chain defined on the ultrametric space. Finally, an interpretation in terms of representation group theory is given, by showing the correspondence between the spectral decomposition of the generalized crested product and the Gelfand pairs associated with the generalized wreath product of permutation groups.
Sparse multivariate autoregressive modeling for mild cognitive impairment classification.
Li, Yang; Wee, Chong-Yaw; Jie, Biao; Peng, Ziwen; Shen, Dinggang
2014-07-01
Brain connectivity network derived from functional magnetic resonance imaging (fMRI) is becoming increasingly prevalent in the researches related to cognitive and perceptual processes. The capability to detect causal or effective connectivity is highly desirable for understanding the cooperative nature of brain network, particularly when the ultimate goal is to obtain good performance of control-patient classification with biological meaningful interpretations. Understanding directed functional interactions between brain regions via brain connectivity network is a challenging task. Since many genetic and biomedical networks are intrinsically sparse, incorporating sparsity property into connectivity modeling can make the derived models more biologically plausible. Accordingly, we propose an effective connectivity modeling of resting-state fMRI data based on the multivariate autoregressive (MAR) modeling technique, which is widely used to characterize temporal information of dynamic systems. This MAR modeling technique allows for the identification of effective connectivity using the Granger causality concept and reducing the spurious causality connectivity in assessment of directed functional interaction from fMRI data. A forward orthogonal least squares (OLS) regression algorithm is further used to construct a sparse MAR model. By applying the proposed modeling to mild cognitive impairment (MCI) classification, we identify several most discriminative regions, including middle cingulate gyrus, posterior cingulate gyrus, lingual gyrus and caudate regions, in line with results reported in previous findings. A relatively high classification accuracy of 91.89 % is also achieved, with an increment of 5.4 % compared to the fully-connected, non-directional Pearson-correlation-based functional connectivity approach.
Stochastic relations foundations for Markov transition systems
Doberkat, Ernst-Erich
2007-01-01
Collecting information previously scattered throughout the vast literature, including the author's own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition systems. After an introduction to the basic mathematical tools from topology, measure theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the general
Chiang, Sharon; Guindani, Michele; Yeh, Hsiang J; Haneef, Zulfi; Stern, John M; Vannucci, Marina
2017-03-01
In this article a multi-subject vector autoregressive (VAR) modeling approach was proposed for inference on effective connectivity based on resting-state functional MRI data. Their framework uses a Bayesian variable selection approach to allow for simultaneous inference on effective connectivity at both the subject- and group-level. Furthermore, it accounts for multi-modal data by integrating structural imaging information into the prior model, encouraging effective connectivity between structurally connected regions. They demonstrated through simulation studies that their approach resulted in improved inference on effective connectivity at both the subject- and group-level, compared with currently used methods. It was concluded by illustrating the method on temporal lobe epilepsy data, where resting-state functional MRI and structural MRI were used. Hum Brain Mapp 38:1311-1332, 2017. © 2016 Wiley Periodicals, Inc.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The time-varying autoregressive (TVAR) modeling of a non-stationary signal is studied. In the proposed method, time-varying parametric identification of a non-stationary signal can be translated into a linear time-invariant problem by introducing a set of basic functions. Then, the parameters are estimated by using a recursive least square algorithm with a forgetting factor and an adaptive time-frequency distribution is achieved. The simulation results show that the proposed approach is superior to the short-time Fourier transform and Wigner distribution. And finally, the proposed method is applied to the fault diagnosis of a bearing, and the experiment result shows that the proposed method is effective in feature extraction.
Active Chemical Sensing With Partially Observable Markov Decision Processes
Gosangi, Rakesh; Gutierrez-Osuna, Ricardo
2009-05-01
We present an active-perception strategy to optimize the temperature program of metal-oxide sensors in real time, as the sensor reacts with its environment. We model the problem as a partially observable Markov decision process (POMDP), where actions correspond to measurements at particular temperatures, and the agent is to find a temperature sequence that minimizes the Bayes risk. We validate the method on a binary classification problem with a simulated sensor. Our results show that the method provides a balance between classification rate and sensing costs.
Partially observable Markov decision processes for risk-based screening
Mrozack, Alex; Liao, Xuejun; Skatter, Sondre; Carin, Lawrence
2016-05-01
A long-term goal for checked baggage screening in airports has been to include passenger information, or at least a predetermined passenger risk level, in the screening process. One method for including that information could be treating the checked baggage screening process as a system-of-systems. This would allow for an optimized policy builder, such as one trained using the methodology of partially observable Markov decision processes (POMDP), to navigate the different sensors available for screening. In this paper we describe the necessary steps to tailor a POMDP for baggage screening, as well as results of simulations for specific screening scenarios.
Hidden Markov Model Application to Transfer The Trader Online Forex Brokers
Directory of Open Access Journals (Sweden)
Farida Suharleni
2012-05-01
Full Text Available Hidden Markov Model is elaboration of Markov chain, which is applicable to cases that can’t directly observe. In this research, Hidden Markov Model is used to know trader’s transition to broker forex online. In Hidden Markov Model, observed state is observable part and hidden state is hidden part. Hidden Markov Model allows modeling system that contains interrelated observed state and hidden state. As observed state in trader’s transition to broker forex online is category 1, category 2, category 3, category 4, category 5 by condition of every broker forex online, whereas as hidden state is broker forex online Marketiva, Masterforex, Instaforex, FBS and Others. First step on application of Hidden Markov Model in this research is making construction model by making a probability of transition matrix (A from every broker forex online. Next step is making a probability of observation matrix (B by making conditional probability of five categories, that is category 1, category 2, category 3, category 4, category 5 by condition of every broker forex online and also need to determine an initial state probability (π from every broker forex online. The last step is using Viterbi algorithm to find hidden state sequences that is broker forex online sequences which is the most possible based on model and observed state that is the five categories. Application of Hidden Markov Model is done by making program with Viterbi algorithm using Delphi 7.0 software with observed state based on simulation data. Example: By the number of observation T = 5 and observed state sequences O = (2,4,3,5,1 is found hidden state sequences which the most possible with observed state O as following : where X1 = FBS, X2 = Masterforex, X3 = Marketiva, X4 = Others, and X5 = Instaforex.
Improved gene prediction by principal component analysis based autoregressive Yule-Walker method.
Roy, Manidipa; Barman, Soma
2016-01-10
Spectral analysis using Fourier techniques is popular with gene prediction because of its simplicity. Model-based autoregressive (AR) spectral estimation gives better resolution even for small DNA segments but selection of appropriate model order is a critical issue. In this article a technique has been proposed where Yule-Walker autoregressive (YW-AR) process is combined with principal component analysis (PCA) for reduction in dimensionality. The spectral peaks of DNA signal are used to detect protein-coding regions based on the 1/3 frequency component. Here optimal model order selection is no more critical as noise is removed by PCA prior to power spectral density (PSD) estimation. Eigenvalue-ratio is used to find the threshold between signal and noise subspaces for data reduction. Superiority of proposed method over fast Fourier Transform (FFT) method and autoregressive method combined with wavelet packet transform (WPT) is established with the help of receiver operating characteristics (ROC) and discrimination measure (DM) respectively.
Chattopadhyay, Goutami; 10.1140/epjp/i2012-12043-9
2012-01-01
This study reports a statistical analysis of monthly sunspot number time series and observes non homogeneity and asymmetry within it. Using Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series we generate autoregressive AR(p) and autoregressive moving average (ARMA(p,q)). Based on minimization of AIC we find 3 and 1 as the best values of p and q respectively. In the next phase, autoregressive neural network (AR-NN(3)) is generated by training a generalized feedforward neural network (GFNN). Assessing the model performances by means of Willmott's index of second order and coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).
Susanti, D.; Hartini, E.; Permana, A.
2017-01-01
Sale and purchase of the growing competition between companies in Indonesian, make every company should have a proper planning in order to win the competition with other companies. One of the things that can be done to design the plan is to make car sales forecast for the next few periods, it’s required that the amount of inventory of cars that will be sold in proportion to the number of cars needed. While to get the correct forecasting, on of the methods that can be used is the method of Adaptive Spline Threshold Autoregression (ASTAR). Therefore, this time the discussion will focus on the use of Adaptive Spline Threshold Autoregression (ASTAR) method in forecasting the volume of car sales in PT.Srikandi Diamond Motors using time series data.In the discussion of this research, forecasting using the method of forecasting value Adaptive Spline Threshold Autoregression (ASTAR) produce approximately correct.
A Note on the Properties of Generalised Separable Spatial Autoregressive Process
Directory of Open Access Journals (Sweden)
Mahendran Shitan
2009-01-01
Full Text Available Spatial modelling has its applications in many fields like geology, agriculture, meteorology, geography, and so forth. In time series a class of models known as Generalised Autoregressive (GAR has been introduced by Peiris (2003 that includes an index parameter δ. It has been shown that the inclusion of this additional parameter aids in modelling and forecasting many real data sets. This paper studies the properties of a new class of spatial autoregressive process of order 1 with an index. We will call this a Generalised Separable Spatial Autoregressive (GENSSAR Model. The spectral density function (SDF, the autocovariance function (ACVF, and the autocorrelation function (ACF are derived. The theoretical ACF and SDF plots are presented as three-dimensional figures.
Finding cis-regulatory modules in Drosophila using phylogenetic hidden Markov models
DEFF Research Database (Denmark)
Wong, Wendy S W; Nielsen, Rasmus
2007-01-01
of the increasing availability of comparative genomic data. RESULTS: We develop a method for finding regulatory modules in Eukaryotic species using phylogenetic data. Using computer simulations and analysis of real data, we show that the use of phylogenetic hidden Markov model can lead to an increase in accuracy...
Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R
DEFF Research Database (Denmark)
O'Connell, Jarad Michael; Højsgaard, Søren
2011-01-01
models only allow a geometrically distributed sojourn time in a given state, while hidden semi-Markov models extend this by allowing an arbitrary sojourn distribution. We demonstrate the software with simulation examples and an application involving the modelling of the ovarian cycle of dairy cows...
Performance Modeling of Communication Networks with Markov Chains
Mo, Jeonghoon
2010-01-01
This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMe and continuous time Markov chain (CTMe. We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probab
The Fracture Mechanical Markov Chain Fatigue Model Compared with Empirical Data
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
The applicability of the FMF-model (Fracture Mechanical Markov Chain Fatigue Model) introduced in Gansted, L., R. Brincker and L. Pilegaard Hansen (1991) is tested by simulations and compared with empirical data. Two sets of data have been used, the Virkler data (aluminium alloy) and data...... established at the Laboratory of Structural Engineering at Aalborg University, the AUC-data, (mild steel). The model, which is based on the assumption, that the crack propagation process can be described by a discrete Space Markov theory, is applicable to constant as well as random loading. It is shown...
DEFF Research Database (Denmark)
Hey, Jody; Nielsen, Rasmus
2007-01-01
Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint......In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte...
Quantum Markov Chain Mixing and Dissipative Engineering
DEFF Research Database (Denmark)
Kastoryano, Michael James
2012-01-01
This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state of the sy......This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state...... framework for studying quantum Markov chain mixing. We introduce two new distance measures into the quantum setting; the quantum $\\chi^2$-divergence and Hilbert's projective metric. With the help of these distance measures, we are able to derive some basic bounds on the the mixing times of quantum channels....... Finally, we consider three independent tasks of dissipative engineering: dissipatively preparing a maximally entangled state of two atoms trapped in an optical cavity, dissipative preparation of graph states, and dissipative quantum computing construction....
Stock Market Autoregressive Dynamics: A Multinational Comparative Study with Quantile Regression
Directory of Open Access Journals (Sweden)
Lili Li
2016-01-01
Full Text Available We study the nonlinear autoregressive dynamics of stock index returns in seven major advanced economies (G7 and China. The quantile autoregression model (QAR enables us to investigate the autocorrelation across the whole spectrum of return distribution, which provides more insightful conditional information on multinational stock market dynamics than conventional time series models. The relation between index return and contemporaneous trading volume is also investigated. While prior studies have mixed results on stock market autocorrelations, we find that the dynamics is usually state dependent. The results for G7 stock markets exhibit conspicuous similarities, but they are in manifest contrast to the findings on Chinese stock markets.
Directory of Open Access Journals (Sweden)
Fei Jin
2013-05-01
Full Text Available This paper studies the generalized spatial two stage least squares (GS2SLS estimation of spatial autoregressive models with autoregressive disturbances when there are endogenous regressors with many valid instruments. Using many instruments may improve the efficiency of estimators asymptotically, but the bias might be large in finite samples, making the inference inaccurate. We consider the case that the number of instruments K increases with, but at a rate slower than, the sample size, and derive the approximate mean square errors (MSE that account for the trade-offs between the bias and variance, for both the GS2SLS estimator and a bias-corrected GS2SLS estimator. A criterion function for the optimal K selection can be based on the approximate MSEs. Monte Carlo experiments are provided to show the performance of our procedure of choosing K.
Markov decision processes: a tool for sequential decision making under uncertainty.
Alagoz, Oguzhan; Hsu, Heather; Schaefer, Andrew J; Roberts, Mark S
2010-01-01
We provide a tutorial on the construction and evaluation of Markov decision processes (MDPs), which are powerful analytical tools used for sequential decision making under uncertainty that have been widely used in many industrial and manufacturing applications but are underutilized in medical decision making (MDM). We demonstrate the use of an MDP to solve a sequential clinical treatment problem under uncertainty. Markov decision processes generalize standard Markov models in that a decision process is embedded in the model and multiple decisions are made over time. Furthermore, they have significant advantages over standard decision analysis. We compare MDPs to standard Markov-based simulation models by solving the problem of the optimal timing of living-donor liver transplantation using both methods. Both models result in the same optimal transplantation policy and the same total life expectancies for the same patient and living donor. The computation time for solving the MDP model is significantly smaller than that for solving the Markov model. We briefly describe the growing literature of MDPs applied to medical decisions.
Formal Reasoning About Finite-State Discrete-Time Markov Chains in HOL
Institute of Scientific and Technical Information of China (English)
Liya Liu; Osman Hasan; Sofiène Tahar
2013-01-01
Markov chains are extensively used in modeling different aspects of engineering and scientific systems,such as performance of algorithms and reliability of systems.Different techniques have been developed for analyzing Markovian models,for example,Markov Chain Monte Carlo based simulation,Markov Analyzer,and more recently probabilistic modelchecking.However,these techniques either do not guarantee accurate analysis or are not scalable.Higher-order-logic theorem proving is a formal method that has the ability to overcome the above mentioned limitations.However,it is not mature enough to handle all sorts of Markovian models.In this paper,we propose a formalization of Discrete-Time Markov Chain (DTMC) that facilitates formal reasoning about time-homogeneous finite-state discrete-time Markov chain.In particular,we provide a formal verification on some of its important properties,such as joint probabilities,Chapman-Kolmogorov equation,reversibility property,using higher-order logic.To demonstrate the usefulness of our work,we analyze two applications:a simplified binary communication channel and the Automatic Mail Quality Measurement protocol.
Projected metastable Markov processes and their estimation with observable operator models
Energy Technology Data Exchange (ETDEWEB)
Wu, Hao, E-mail: hao.wu@fu-berlin.de; Prinz, Jan-Hendrik, E-mail: jan-hendrik.prinz@fu-berlin.de; Noé, Frank, E-mail: frank.noe@fu-berlin.de [DFG Research Center Matheon, Free University Berlin, Arnimallee 6, 14195 Berlin (Germany)
2015-10-14
The determination of kinetics of high-dimensional dynamical systems, such as macromolecules, polymers, or spin systems, is a difficult and generally unsolved problem — both in simulation, where the optimal reaction coordinate(s) are generally unknown and are difficult to compute, and in experimental measurements, where only specific coordinates are observable. Markov models, or Markov state models, are widely used but suffer from the fact that the dynamics on a coarsely discretized state spaced are no longer Markovian, even if the dynamics in the full phase space are. The recently proposed projected Markov models (PMMs) are a formulation that provides a description of the kinetics on a low-dimensional projection without making the Markovianity assumption. However, as yet no general way of estimating PMMs from data has been available. Here, we show that the observed dynamics of a PMM can be exactly described by an observable operator model (OOM) and derive a PMM estimator based on the OOM learning.
Uncovering and testing the fuzzy clusters based on lumped Markov chain in complex network.
Jing, Fan; Jianbin, Xie; Jinlong, Wang; Jinshuai, Qu
2013-01-01
Identifying clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. By means of a lumped Markov chain model of a random walker, we propose two novel ways of inferring the lumped markov transition matrix. Furthermore, some useful results are proposed based on the analysis of the properties of the lumped Markov process. To find the best partition of complex networks, a novel framework including two algorithms for network partition based on the optimal lumped Markovian dynamics is derived to solve this problem. The algorithms are constructed to minimize the objective function under this framework. It is demonstrated by the simulation experiments that our algorithms can efficiently determine the probabilities with which a node belongs to different clusters during the learning process and naturally supports the fuzzy partition. Moreover, they are successfully applied to real-world network, including the social interactions between members of a karate club.
First and second order semi-Markov chains for wind speed modeling
D'Amico, Guglielmo; Prattico, Flavio
2012-01-01
The increasing interest in renewable energy, particularly in wind, has given rise to the necessity of accurate models for the generation of good synthetic wind speed data. Markov chains are often used with this purpose but better models are needed to reproduce the statistical properties of wind speed data. We downloaded a database, freely available from the web, in which are included wind speed data taken from L.S.I. -Lastem station (Italy) and sampled every 10 minutes. With the aim of reproducing the statistical properties of this data we propose the use of three semi-Markov models. We generate synthetic time series for wind speed by means of Monte Carlo simulations. The time lagged autocorrelation is then used to compare statistical properties of the proposed models with those of real data and also with a synthetic time series generated though a simple Markov chain.
Markov dynamic models for long-timescale protein motion.
Chiang, Tsung-Han
2010-06-01
Molecular dynamics (MD) simulation is a well-established method for studying protein motion at the atomic scale. However, it is computationally intensive and generates massive amounts of data. One way of addressing the dual challenges of computation efficiency and data analysis is to construct simplified models of long-timescale protein motion from MD simulation data. In this direction, we propose to use Markov models with hidden states, in which the Markovian states represent potentially overlapping probabilistic distributions over protein conformations. We also propose a principled criterion for evaluating the quality of a model by its ability to predict long-timescale protein motions. Our method was tested on 2D synthetic energy landscapes and two extensively studied peptides, alanine dipeptide and the villin headpiece subdomain (HP-35 NleNle). One interesting finding is that although a widely accepted model of alanine dipeptide contains six states, a simpler model with only three states is equally good for predicting long-timescale motions. We also used the constructed Markov models to estimate important kinetic and dynamic quantities for protein folding, in particular, mean first-passage time. The results are consistent with available experimental measurements.
Coding with partially hidden Markov models
DEFF Research Database (Denmark)
Forchhammer, Søren; Rissanen, J.
1995-01-01
Partially hidden Markov models (PHMM) are introduced. They are a variation of the hidden Markov models (HMM) combining the power of explicit conditioning on past observations and the power of using hidden states. (P)HMM may be combined with arithmetic coding for lossless data compression. A general...... 2-part coding scheme for given model order but unknown parameters based on PHMM is presented. A forward-backward reestimation of parameters with a redefined backward variable is given for these models and used for estimating the unknown parameters. Proof of convergence of this reestimation is given....... The PHMM structure and the conditions of the convergence proof allows for application of the PHMM to image coding. Relations between the PHMM and hidden Markov models (HMM) are treated. Results of coding bi-level images with the PHMM coding scheme is given. The results indicate that the PHMM can adapt...
Chen, C; Lin, C-H; Long, Z; Chen, Q
2014-02-01
To quickly obtain information about airborne infectious disease transmission in enclosed environments is critical in reducing the infection risk to the occupants. This study developed a combined computational fluid dynamics (CFD) and Markov chain method for quickly predicting transient particle transport in enclosed environments. The method first calculated a transition probability matrix using CFD simulations. Next, the Markov chain technique was applied to calculate the transient particle concentration distributions. This investigation used three cases, particle transport in an isothermal clean room, an office with an underfloor air distribution system, and the first-class cabin of an MD-82 airliner, to validate the combined CFD and Markov chain method. The general trends of the particle concentrations vs. time predicted by the Markov chain method agreed with the CFD simulations for these cases. The proposed Markov chain method can provide faster-than-real-time information about particle transport in enclosed environments. Furthermore, for a fixed airflow field, when the source location is changed, the Markov chain method can be used to avoid recalculation of the particle transport equation and thus reduce computing costs.
Modelling and analysis of Markov reward automata (extended version)
Guck, Dennis; Timmer, Mark; Hatefi, Hassan; Ruijters, Enno; Stoelinga, Mariëlle
2014-01-01
Costs and rewards are important ingredients for cyberphysical systems, modelling critical aspects like energy consumption, task completion, repair costs, and memory usage. This paper introduces Markov reward automata, an extension of Markov automata that allows the modelling of systems incorporating
A Noether Theorem for Markov Processes
Baez, John C
2012-01-01
Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer holds, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state.
Markov decision processes in artificial intelligence
Sigaud, Olivier
2013-01-01
Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision problems under uncertainty as well as Reinforcement Learning problems. Written by experts in the field, this book provides a global view of current research using MDPs in Artificial Intelligence. It starts with an introductory presentation of the fundamental aspects of MDPs (planning in MDPs, Reinforcement Learning, Partially Observable MDPs, Markov games and the use of non-classical criteria). Then it presents more advanced research trends in the domain and gives some concrete examples using illustr
Markov Model Applied to Gene Evolution
Institute of Scientific and Technical Information of China (English)
季星来; 孙之荣
2001-01-01
The study of nucleotide substitution is very important both to our understanding of gene evolution and to reliable estimation of phylogenetic relationships. In this paper nucleotide substitution is assumed to be random and the Markov model is applied to the study of the evolution of genes. Then a non-linear optimization approach is proposed for estimating substitution in real sequences. This substitution is called the "Nucleotide State Transfer Matrix". One of the most important conclusions from this work is that gene sequence evolution conforms to the Markov process. Also, some theoretical evidences for random evolution are given from energy analysis of DNA replication.
Detecting Structural Breaks using Hidden Markov Models
DEFF Research Database (Denmark)
Ntantamis, Christos
Testing for structural breaks and identifying their location is essential for econometric modeling. In this paper, a Hidden Markov Model (HMM) approach is used in order to perform these tasks. Breaks are defined as the data points where the underlying Markov Chain switches from one state to another....... The estimation of the HMM is conducted using a variant of the Iterative Conditional Expectation-Generalized Mixture (ICE-GEMI) algorithm proposed by Delignon et al. (1997), that permits analysis of the conditional distributions of economic data and allows for different functional forms across regimes...
Markov processes an introduction for physical scientists
Gillespie, Daniel T
1991-01-01
Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.Key Features* A self-contained, prgamatic exposition of the needed elements of random variable theory* Logically integrated derviations of the Chapman-Kolmogorov e
Entropy production fluctuations of finite Markov chains
Jiang, Da-Quan; Qian, Min; Zhang, Fu-Xi
2003-09-01
For almost every trajectory segment over a finite time span of a finite Markov chain with any given initial distribution, the logarithm of the ratio of its probability to that of its time-reversal converges exponentially to the entropy production rate of the Markov chain. The large deviation rate function has a symmetry of Gallavotti-Cohen type, which is called the fluctuation theorem. Moreover, similar symmetries also hold for the rate functions of the joint distributions of general observables and the logarithmic probability ratio.
Institute of Scientific and Technical Information of China (English)
宋述芳; 吕震宙
2009-01-01
在小失效概率可靠性分析子集模拟法的基础上,提出基于马尔可夫蒙特卡罗(Markov Chain Monte Carlo,MCMC)子集模拟的可靠性灵敏度分析方法.在子集模拟的可靠性分析中,通过引入合理的中间失效事件将概率空间划分为一系列的子集,从而将小的失效概率表达为一系列易于模拟求解的较大条件失效概率乘积的形式,然后利用MCMC抽取条件样本点来估计条件失效概率.基于MCMC子集模拟的可靠性灵敏度分析,是将失效概率对基本变量分布参数的偏导数转化成条件失效概率对基本随机变量分布参数的偏导数.给出了偏导数通过MCMC模拟的条件样本点进行估计的原理和步骤,推导得出可靠性灵敏度分析的计算公式.利用简单数值算例和工程算例验证所提方法,算例结果表明:基于MCMC子集模拟的可靠性灵敏度分析方法有较高的计算效率和精度,对于高度非线性极限状态方程问题亦有很强的适应性.
AN IMPROVED MARKOV CHAIN MONTE CARLO METHOD FOR MIMO ITERATIVE DETECTION AND DECODING
Institute of Scientific and Technical Information of China (English)
Han Xiang; Wei Jibo
2008-01-01
Recently, a new soft-in soft-out detection algorithm based on the Markov Chain Monte Carlo (MCMC) simulation technique for Multiple-Input Multiple-Output (MIMO) systems is proposed,which is shown to perform significantly better than their sphere decoding counterparts with relatively low complexity. However, the MCMC simulator is likely to get trapped in a fixed state when the channel SNR is high, thus lots of repetitive samples are observed and the accuracy of A Posteriori Probability (APP) estimation deteriorates. To solve this problem, an improved version of MCMC simulator, named forced-dispersed MCMC algorithm is proposed. Based on the a posteriori variance of each bit, the Gibbs sampler is monitored. Once the trapped state is detected, the sample is dispersed intentionally according to the a posteriori variance. Extensive simulation shows that, compared with the existing solution, the proposed algorithm enables the markov chain to travel more states, which ensures a near-optimal performance.
Markov Chain Approximations to Singular Stable-like Processes
2012-01-01
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these chains to singular stable-like processes.
Using Markov State Models to Study Self-Assembly
Perkett, Matthew R
2014-01-01
Markov state models (MSMs) have been demonstrated to be a powerful method for computationally studying intramolecular processes such as protein folding and macromolecular conformational changes. In this article, we present a new approach to construct MSMs that is applicable to modeling a broad class of multi-molecular assembly reactions. Distinct structures formed during assembly are distinguished by their undirected graphs, which are defined by strong subunit interactions. Spatial inhomogeneities of free subunits are accounted for using a recently developed Gaussian-based signature. Simplifications to this state identification are also investigated. The feasibility of this approach is demonstrated on two different coarse-grained models for virus self-assembly. We find good agreement between the dynamics predicted by the MSMs and long, unbiased simulations, and that the MSMs can reduce overall simulation time by orders of magnitude.
Markov State Models for Rare Events in Molecular Dynamics
Directory of Open Access Journals (Sweden)
Marco Sarich
2013-12-01
Full Text Available Rare, but important, transition events between long-lived states are a key feature of many molecular systems. In many cases, the computation of rare event statistics by direct molecular dynamics (MD simulations is infeasible, even on the most powerful computers, because of the immensely long simulation timescales needed. Recently, a technique for spatial discretization of the molecular state space designed to help overcome such problems, so-called Markov State Models (MSMs, has attracted a lot of attention. We review the theoretical background and algorithmic realization of MSMs and illustrate their use by some numerical examples. Furthermore, we introduce a novel approach to using MSMs for the efficient solution of optimal control problems that appear in applications where one desires to optimize molecular properties by means of external controls.
Adaptive Algorithm for Estimation of Two-Dimensional Autoregressive Fields from Noisy Observations
Directory of Open Access Journals (Sweden)
Alimorad Mahmoudi
2014-01-01
Full Text Available This paper deals with the problem of two-dimensional autoregressive (AR estimation from noisy observations. The Yule-Walker equations are solved using adaptive steepest descent (SD algorithm. Performance comparisons are made with other existing methods to demonstrate merits of the proposed method.
Finite-Sample Bias Propagation in Autoregressive Estimation With the Yule–Walker Method
Broersen, P.M.T.
2009-01-01
The Yule-Walker (YW) method for autoregressive (AR) estimation uses lagged-product (LP) autocorrelation estimates to compute an AR parametric spectral model. The LP estimates only have a small triangular bias in the estimated autocorrelation function and are asymptotically unbiased. However, using t
Testing for rational bubbles in a co-explosive vector autoregression
DEFF Research Database (Denmark)
Engsted, Tom; Nielsen, Bent
We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable...
On the Oracle Property of the Adaptive LASSO in Stationary and Nonstationary Autoregressions
DEFF Research Database (Denmark)
Kock, Anders Bredahl
We show that the Adaptive LASSO is oracle efficient in stationary and non-stationary autoregressions. This means that it estimates parameters consistently, selects the correct sparsity pattern, and estimates the coefficients belonging to the relevant variables at the same asymptotic efficiency...
Global Hemispheric Temperatures and Co–Shifting: A Vector Shifting–Mean Autoregressive Analysis
DEFF Research Database (Denmark)
Holt, Matthew T.; Terasvirta, Timo
This paper examines local changes in annual temperature data for the northern and southern hemispheres (1850-2014) by using a multivariate generalisation of the shifting-mean autoregressive model of González and Teräsvirta (2008). Univariate models are first fitted to each series by using the Qui...
Forecasting the Levels of Vector Autoregressive Log-Transformed Time Series
M.A. Ariñ o; Ph.H.B.F. Franses (Philip Hans)
1996-01-01
textabstractIn this paper we give explicit expressions for the forecasts of levels of a vector time series when such forecasts are generated from (possibly cointegrated) vector autoregressions for the corresponding log-transformed time series. We also show that simply taking exponentials of forecast
A 'Maximum-Eigenvalue' test for the cointegration ranks in I(2) vector autoregressions
DEFF Research Database (Denmark)
Nielsen, Heino Bohn
2007-01-01
A maximum-eigenvalue test for the number of stochastic I(2) trends in a vector autoregression is suggested. The asymptotic distribution coincides with the distribution of the I(1) maximum-eigenvalue test. In two examples, the test reconciles empirical evidence with plausible economic scenarios...
de Vries, S O; Fidler, Vaclav; Kuipers, Wietze D; Hunink, Maria G M
1998-01-01
The purpose of this study was to develop a model that predicts the outcome of supervised exercise for intermittent claudication. The authors present an example of the use of autoregressive logistic regression for modeling observed longitudinal data. Data were collected from 329 participants in a six
Get Over It! A Multilevel Threshold Autoregressive Model for State-Dependent Affect Regulation
De Haan-Rietdijk, Silvia; Gottman, John M.; Bergeman, Cindy S.; Hamaker, Ellen L.
2014-01-01
Intensive longitudinal data provide rich information, which is best captured when specialized models are used in the analysis. One of these models is the multilevel autoregressive model, which psychologists have applied successfully to study affect regulation as well as alcohol use. A limitation of
Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility
DEFF Research Database (Denmark)
Cavaliere, Giuseppe; Rahbek, Anders Christian; Taylor, A. M. Robert
Many key macro-economic and …nancial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special...
Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility
DEFF Research Database (Denmark)
Cavaliere, Guiseppe; Rahbæk, Anders; Taylor, A.M. Robert
Many key macro-economic and financial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special...
Directory of Open Access Journals (Sweden)
Yang Lei
2012-10-01
Full Text Available Abstract Background Generalized Additive Model (GAM provides a flexible and effective technique for modelling nonlinear time-series in studies of the health effects of environmental factors. However, GAM assumes that errors are mutually independent, while time series can be correlated in adjacent time points. Here, a GAM with Autoregressive terms (GAMAR is introduced to fill this gap. Methods Parameters in GAMAR are estimated by maximum partial likelihood using modified Newton’s method, and the difference between GAM and GAMAR is demonstrated using two simulation studies and a real data example. GAMM is also compared to GAMAR in simulation study 1. Results In the simulation studies, the bias of the mean estimates from GAM and GAMAR are similar but GAMAR has better coverage and smaller relative error. While the results from GAMM are similar to GAMAR, the estimation procedure of GAMM is much slower than GAMAR. In the case study, the Pearson residuals from the GAM are correlated, while those from GAMAR are quite close to white noise. In addition, the estimates of the temperature effects are different between GAM and GAMAR. Conclusions GAMAR incorporates both explanatory variables and AR terms so it can quantify the nonlinear impact of environmental factors on health outcome as well as the serial correlation between the observations. It can be a useful tool in environmental epidemiological studies.
Optimal dividend distribution under Markov regime switching
Jiang, Z.; Pistorius, M.
2012-01-01
We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a determini
Estimating an Activity Driven Hidden Markov Model
Meyer, David A.; Shakeel, Asif
2015-01-01
We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent $\\textit{activity levels}$ that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of inferring human mobility on sub-daily time scales from, for example, mobile phone records.
Hidden Markov Models for Human Genes
DEFF Research Database (Denmark)
Baldi, Pierre; Brunak, Søren; Chauvin, Yves;
1997-01-01
We analyse the sequential structure of human genomic DNA by hidden Markov models. We apply models of widely different design: conventional left-right constructs and models with a built-in periodic architecture. The models are trained on segments of DNA sequences extracted such that they cover com...
Markov Random Fields on Triangle Meshes
DEFF Research Database (Denmark)
Andersen, Vedrana; Aanæs, Henrik; Bærentzen, Jakob Andreas;
2010-01-01
In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process labels...
Renewal characterization of Markov modulated Poisson processes
Directory of Open Access Journals (Sweden)
Marcel F. Neuts
1989-01-01
Full Text Available A Markov Modulated Poisson Process (MMPP M(t defined on a Markov chain J(t is a pure jump process where jumps of M(t occur according to a Poisson process with intensity λi whenever the Markov chain J(t is in state i. M(t is called strongly renewal (SR if M(t is a renewal process for an arbitrary initial probability vector of J(t with full support on P={i:λi>0}. M(t is called weakly renewal (WR if there exists an initial probability vector of J(t such that the resulting MMPP is a renewal process. The purpose of this paper is to develop general characterization theorems for the class SR and some sufficiency theorems for the class WR in terms of the first passage times of the bivariate Markov chain [J(t,M(t]. Relevance to the lumpability of J(t is also studied.
One-Counter Markov Decision Processes
Brazdil, T.; Brozek, V.; Etessami, K.; Kucera, A.; Wojtczak, D.K.; Charikar, M.
2010-01-01
We study the computational complexity of central analysis problems for One-Counter Markov Decision Processes (OC-MDPs), a class of finitely-presented, countable-state MDPs. OC-MDPs are equivalent to a controlled extension of (discrete-time) Quasi-Birth-Death processes (QBDs), a stochastic model stud
Shift ergodicity for stationary Markov processes
Institute of Scientific and Technical Information of China (English)
东金文
2001-01-01
In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our results provide partial answers to certain interesting problems in spin systems.
Quantitative timed analysis of interactive Markov chains
Guck, Dennis; Han, Tingting; Katoen, Joost-Pieter; Neuhausser, M.
2012-01-01
This paper presents new algorithms and accompanying tool support for analyzing interactive Markov chains (IMCs), a stochastic timed 1 1/2-player game in which delays are exponentially distributed. IMCs are compositional and act as semantic model for engineering formalisms such as AADL and dynamic fa
A Martingale Decomposition of Discrete Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard
We consider a multivariate time series whose increments are given from a homogeneous Markov chain. We show that the martingale component of this process can be extracted by a filtering method and establish the corresponding martingale decomposition in closed-form. This representation is useful fo...
Document Ranking Based upon Markov Chains.
Danilowicz, Czeslaw; Balinski, Jaroslaw
2001-01-01
Considers how the order of documents in information retrieval responses are determined and introduces a method that uses a probabilistic model of a document set where documents are regarded as states of a Markov chain and where transition probabilities are directly proportional to similarities between documents. (Author/LRW)
Markov Chain Estimation of Avian Seasonal Fecundity
To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...
Multi-dimensional quasitoeplitz Markov chains
Directory of Open Access Journals (Sweden)
Alexander N. Dudin
1999-01-01
Full Text Available This paper deals with multi-dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector-generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP-input, which operate in synchronous random environment.
Markov chains with quasitoeplitz transition matrix
Directory of Open Access Journals (Sweden)
Alexander M. Dukhovny
1989-01-01
Full Text Available This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.
Bayesian analysis of Markov point processes
DEFF Research Database (Denmark)
Berthelsen, Kasper Klitgaard; Møller, Jesper
2006-01-01
Recently Møller, Pettitt, Berthelsen and Reeves introduced a new MCMC methodology for drawing samples from a posterior distribution when the likelihood function is only specified up to a normalising constant. We illustrate the method in the setting of Bayesian inference for Markov point processes...
Evaluation of Usability Utilizing Markov Models
Penedo, Janaina Rodrigues; Diniz, Morganna; Ferreira, Simone Bacellar Leal; Silveira, Denis S.; Capra, Eliane
2012-01-01
Purpose: The purpose of this paper is to analyze the usability of a remote learning system in its initial development phase, using a quantitative usability evaluation method through Markov models. Design/methodology/approach: The paper opted for an exploratory study. The data of interest of the research correspond to the possible accesses of users…
Confluence reduction for Markov automata (extended version)
Timmer, M.; Pol, van de J.C.; Stoelinga, M.I.A.
2013-01-01
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models gener
Efficient Modelling and Generation of Markov Automata
Timmer, Mark; Katoen, Joost-Pieter; Pol, van de Jaco; Stoelinga, Mariëlle; Koutny, M.; Ulidowski, I.
2012-01-01
This paper introduces a framework for the efficient modelling and generation of Markov automata. It consists of (1) the data-rich process-algebraic language MAPA, allowing concise modelling of systems with nondeterminism, probability and Markovian timing; (2) a restricted form of the language, the M
Institute of Scientific and Technical Information of China (English)
刘培; 杜培军; 逄云峰
2012-01-01
针对遥感影像在定量描述土地覆盖和热环境分布方面的优越性,利用支持向量机（SVM）分类器对遥感影像进行分类,获取土地覆盖图,利用单窗算法反演获取地表温度。通过将元胞自动机和马尔科夫模型结合,构建CA_Markov模型对土地覆盖和热环境时空格局进行模拟与分析。采用定量景观指数和土地利用转移矩阵进一步挖掘了研究区空间信息,综合模拟与预测了土地覆盖和热环境时空变化特征。实验结果表明：利用遥感影像定量反演热环境特征时空分布与预测是可行的,CA_Markov模型能够有效地揭示和预测矿区土地覆盖变化和热环境演变趋势。%According to the merits of remotely sensed data in depicting regional land cover and thermal environment, multi-objective information processing was employed to remote sensing images to analyze and simulate land cover and thermal environment in mining areas. Support Vector Machine (SVM) classifier was used to classify remote sensing images and derive regional land cover maps, mono-window algorithm was used to retrieve land surface temperature from thermal infrared images. And land cover change and thermal environmental trends were simulated by CA_Markov mod- el. Quality landscape indexes and land use and land cover transfer matrixes were selected to analysis and assess the dynamic changes trend of different land cover types as well. The results demonstrate that it is signification and suitable to retrieval thermal environmental, evaluate and analyze its distribution and trend using remote sensing methods. CA_ Markov model is able to predict land cover and thermal environmental trends with good performance.
Upscaling of Mixing Processes using a Spatial Markov Model
Bolster, Diogo; Sund, Nicole; Porta, Giovanni
2016-11-01
The Spatial Markov model is a model that has been used to successfully upscale transport behavior across a broad range of spatially heterogeneous flows, with most examples to date coming from applications relating to porous media. In its most common current forms the model predicts spatially averaged concentrations. However, many processes, including for example chemical reactions, require an adequate understanding of mixing below the averaging scale, which means that knowledge of subscale fluctuations, or closures that adequately describe them, are needed. Here we present a framework, consistent with the Spatial Markov modeling framework, that enables us to do this. We apply and present it as applied to a simple example, a spatially periodic flow at low Reynolds number. We demonstrate that our upscaled model can successfully predict mixing by comparing results from direct numerical simulations to predictions with our upscaled model. To this end we focus on predicting two common metrics of mixing: the dilution index and the scalar dissipation. For both metrics our upscaled predictions very closely match observed values from the DNS. This material is based upon work supported by NSF Grants EAR-1351625 and EAR-1417264.
Grey-Markov Model for Road Accidents Forecasting
Institute of Scientific and Technical Information of China (English)
李相勇; 严余松; 蒋葛夫
2003-01-01
In order to improve the forecasting precision of road accidents, by introducing Markov chains forecasting method, a grey-Markov model for forecasting road accidents is established based on grey forecasting method. The model combines the advantages of both grey forecasting method and Markov chains forecasting method, overcomes the influence of random fluctuation data on forecasting precision and widens the application scope of the grey forecasting. An application example is conducted to evaluate the grey-Markov model, which shows that the precision of the grey-Markov model is better than that of grey model in forecasting road accidents.
POISSON LIMIT THEOREM FOR COUNTABLE MARKOV CHAINS IN MARKOVIAN ENVIRONMENTS
Institute of Scientific and Technical Information of China (English)
方大凡; 王汉兴; 唐矛宁
2003-01-01
A countable Markov chain in a Markovian environment is considered. A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved. In order to prove this theorem, the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the Markov chain in a Markovian environment is shown. It' s well-known that a Markov process in a Markovian environment is generally not a standard Markov chain, so an example of Poisson approximation for a process which is not a Markov process is given. On the other hand, when the environmental process degenerates to a constant sequence, a Poisson limit theorem for countable Markov chains, which is the generalization of Pitskel's result for finite Markov chains is obtained.
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.
Indian Academy of Sciences (India)
Long Zhang; Guoliang Xiong; Hesheng Liu; Huijun Zou; Weizhong Guo
2010-04-01
A parametric time-frequency representation is presented based on timevarying autoregressive model (TVAR), followed by applications to non-stationary vibration signal processing. The identiﬁcation of time-varying model coefﬁcients and the determination of model order, are addressed by means of neural networks and genetic algorithms, respectively. Firstly, a simulated signal which mimic the rotor vibration during run-up stages was processed for a comparative study on TVAR and other non-parametric time-frequency representations such as Short Time Fourier Transform, Continuous Wavelet Transform, Empirical Mode Decomposition, Wigner–Ville Distribution and Choi–Williams Distribution, in terms of their resolutions, accuracy, cross term suppression as well as noise resistance. Secondly, TVAR was applied to analyse non-stationary vibration signals collected from a rotor test rig during run-up stages, with an aim to extract fault symptoms under non-stationary operating conditions. Simulation and experimental results demonstrate that TVAR is an effective solution to non-stationary signal analysis and has strong capability in signal time-frequency feature extraction.
RANDOM TIMES TRANSFORMATION OF PROCESSES WITH MARKOV SKELETON%Markov 骨架过程的随机时变换
Institute of Scientific and Technical Information of China (English)
刘万荣; 刘再明; 侯振挺
2000-01-01
In this paper, random time transformations of processes with Markov skeleton are discussed. A class of random time transformations that transform a process with Markov skeleton into a process with Markov skeleton is given.%讨论了 Markov 骨架过程的随机时变换,给出了一类变换 Markov 骨架过程为Markov 骨架过程的随机时变换.
Markov modulated Poisson process models incorporating covariates for rainfall intensity.
Thayakaran, R; Ramesh, N I
2013-01-01
Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.
Deciding when to intervene: a Markov decision process approach.
Magni, P; Quaglini, S; Marchetti, M; Barosi, G
2000-12-01
The aim of this paper is to point out the difference between static and dynamic approaches to choosing the optimal time for intervention. The paper demonstrates that classical approaches, such as decision trees and influence diagrams, hardly cope with dynamic problems: they cannot simulate all the real-world strategies and consequently can only calculate suboptimal solutions. A dynamic formalism based on Markov decision processes (MPPs) is then proposed and applied to a medical problem: the prophylactic surgery in mild hereditary spherocytosis. The paper compares the proposed approach with a static approach on the same medical problem. The policy provided by the dynamic approach achieved significant gain over the static policy by delaying the intervention time in some categories of patients. The calculations are carried out with DT-Planner, a graphical decision aid specifically built for dealing with dynamic decision processes.
A Markov decision model for determining optimal outpatient scheduling.
Patrick, Jonathan
2012-06-01
Managing an efficient outpatient clinic can often be complicated by significant no-show rates and escalating appointment lead times. One method that has been proposed for avoiding the wasted capacity due to no-shows is called open or advanced access. The essence of open access is "do today's demand today". We develop a Markov Decision Process (MDP) model that demonstrates that a short booking window does significantly better than open access. We analyze a number of scenarios that explore the trade-off between patient-related measures (lead times) and physician- or system-related measures (revenue, overtime and idle time). Through simulation, we demonstrate that, over a wide variety of potential scenarios and clinics, the MDP policy does as well or better than open access in terms of minimizing costs (or maximizing profits) as well as providing more consistent throughput.
Reversible jump Markov chain Monte Carlo for deconvolution.
Kang, Dongwoo; Verotta, Davide
2007-06-01
To solve the problem of estimating an unknown input function to a linear time invariant system we propose an adaptive non-parametric method based on reversible jump Markov chain Monte Carlo (RJMCMC). We use piecewise polynomial functions (splines) to represent the input function. The RJMCMC algorithm allows the exploration of a large space of competing models, in our case the collection of splines corresponding to alternative positions of breakpoints, and it is based on the specification of transition probabilities between the models. RJMCMC determines: the number and the position of the breakpoints, and the coefficients determining the shape of the spline, as well as the corresponding posterior distribution of breakpoints, number of breakpoints, coefficients and arbitrary statistics of interest associated with the estimation problem. Simulation studies show that the RJMCMC method can obtain accurate reconstructions of complex input functions, and obtains better results compared with standard non-parametric deconvolution methods. Applications to real data are also reported.
HYDRA: a Java library for Markov Chain Monte Carlo
Directory of Open Access Journals (Sweden)
Gregory R. Warnes
2002-03-01
Full Text Available Hydra is an open-source, platform-neutral library for performing Markov Chain Monte Carlo. It implements the logic of standard MCMC samplers within a framework designed to be easy to use, extend, and integrate with other software tools. In this paper, we describe the problem that motivated our work, outline our goals for the Hydra pro ject, and describe the current features of the Hydra library. We then provide a step-by-step example of using Hydra to simulate from a mixture model drawn from cancer genetics, first using a variable-at-a-time Metropolis sampler and then a Normal Kernel Coupler. We conclude with a discussion of future directions for Hydra.
Sistem Bonus Malus sebagai Model Rantai Markov
Directory of Open Access Journals (Sweden)
- Supandi
2010-06-01
Full Text Available Sistem bonus-malus (BMS yang dibangun mempunyaiÂ tujuan untuk membuat premi yang dibayarkan oleh tertanggung sedekat mungkin dengan harapan terjadinya klaim setiap tahunnya. Bila kita ingin meneliti bagaimana efisiensi suatu BMS, kita harus melihat bagaimana premi itu bergantungÂ pada frekuensi klaim. Efisiensi sistem bonus-malus dicari melalui model Markovnya,Â yaitu dengan mencari distribusi stasioner dari rantai markov BMS-nya. Dalam paper ini BMS yang digunakan adalah BMS Brasil dan modifkasinya pada nilai preminya untuk keadaan bawah. Dari modifikasi ini akan dibahas pengaruh perubahan premi terhadapÂ efisiensi BMS tersebut. Kata kunci : BMS, rantai markov, stationer,Â efisiensi
Boundary value problems and Markov processes
Taira, Kazuaki
2009-01-01
This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called a Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel' boundary condition, on the boundary of the domain. Probabilistically, a Markovian particle moves both by jumps and continuously in the state space and it obeys the Ventcel' boundary condition, which consists of six terms corresponding to the diffusion along the boundary, the absorption phenomenon, the reflection phenomenon, the sticking (or viscosity) phenomenon, the jump phenomenon on the boundary, and the inward jump phenomenon from the boundary. In particular, second-order elliptic differential operators are called diffusion operators and describe analytically strong Markov pr...
Semigroups, boundary value problems and Markov processes
Taira, Kazuaki
2014-01-01
A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes ...
Probabilistic Reachability for Parametric Markov Models
DEFF Research Database (Denmark)
Hahn, Ernst Moritz; Hermanns, Holger; Zhang, Lijun
2011-01-01
Given a parametric Markov model, we consider the problem of computing the rational function expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression...... is computed. Afterwards, this expression is evaluated to a closed form function representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in the growth of the regular expression relative to the number...... of states (n(log n)).We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids this blow up in most practical cases. We give a detailed account of the approach, also extending to parametric...
Stochastic Dynamics through Hierarchically Embedded Markov Chains
Vasconcelos, Vítor V.; Santos, Fernando P.; Santos, Francisco C.; Pacheco, Jorge M.
2017-02-01
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects—such as mutations in evolutionary dynamics and a random exploration of choices in social systems—including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
Weak Markov Processes as Linear Systems
Gohm, Rolf
2012-01-01
A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter this is worked out systematically as a theory of representations of structure maps of a system by a weak process. We introduce subprocesses and quotient processes which can be described naturally by a suitable category of weak processes. A corresponding notion of cascade for processes induces a represented cascade of systems. We study the control theoretic notion of observability which turns out to be particularly interesting in connection with a cascade structure. As an application we gain new insights into stationary Markov chains where observability for the system is closely related to asymptotic completeness in the scattering theory of the chain. This motivates a general definition of asymptotic completeness in the category of weak processes.
A critical appraisal of Markov state models
Schütte, Ch.; Sarich, M.
2015-09-01
Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of attention recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecular sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well beyond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome.
MARKOV CHAIN PORTFOLIO LIQUIDITY OPTIMIZATION MODEL
Directory of Open Access Journals (Sweden)
Eder Oliveira Abensur
2014-05-01
Full Text Available The international financial crisis of September 2008 and May 2010 showed the importance of liquidity as an attribute to be considered in portfolio decisions. This study proposes an optimization model based on available public data, using Markov chain and Genetic Algorithms concepts as it considers the classic duality of risk versus return and incorporating liquidity costs. The work intends to propose a multi-criterion non-linear optimization model using liquidity based on a Markov chain. The non-linear model was tested using Genetic Algorithms with twenty five Brazilian stocks from 2007 to 2009. The results suggest that this is an innovative development methodology and useful for developing an efficient and realistic financial portfolio, as it considers many attributes such as risk, return and liquidity.
Nonlinear Markov Control Processes and Games
2012-11-15
further research we indicated possible extensions to state spaces with nontrivial geometry, to the controlled nonlinear quantum dynamic semigroups and...space nonlinear Markov semigroup is a one-parameter semigroup of (possibly nonlinear) transformations of the unit simplex in n-dimensional Euclidean...certain mixing property of nonlinear transition probabilities. In case of the semigroup parametrized by continuous time one defines its generator as the
Metrics for Finite Markov Decision Processes
Ferns, Norman; Panangaden, Prakash; Precup, Doina
2012-01-01
We present metrics for measuring the similarity of states in a finite Markov decision process (MDP). The formulation of our metrics is based on the notion of bisimulation for MDPs, with an aim towards solving discounted infinite horizon reinforcement learning tasks. Such metrics can be used to aggregate states, as well as to better structure other value function approximators (e.g., memory-based or nearest-neighbor approximators). We provide bounds that relate our metric distances to the opti...
Shift ergodicity for stationary Markov processes
Institute of Scientific and Technical Information of China (English)
CHEN; Jinwen(
2001-01-01
［1］Liggett, T. M., Interacting Particle Systems, New York: Springer-Verlag, 1985.［2］Andjel, E. D., Ergodic and mixing properties of equilibrium measures for Markov processes, Trans. of the AMS, 1990, 318:601－614.［3］Franchi, J., Asymptotic windings of ergodic diffusion, Stoch. Processes Appl., 1996, 62: 277－298.［4］Golden, K. , Goldstein, S., Lebowitz, J. L., Nash estimates and the asymptotic behavior of diffusion, Ann. Prob., 1988,16: 1127－1146.［5］Gordin. M. I., Lifsic, B. A. , The central limit theorem for stationary ergodic Markov process, Dokl, Akad. Nauk SSSR,1978, 19: 392－393.［6］Orey, S., Large deviations in ergodic theory, Seminar on Stochastic Processes, 1985, 12: 195－249.［7］Veretenikov, A. Y., On large deviations for ergodic process empirical measures, Adv. Sov. Math., 1992, 12: 125－133.［8］Deuschel, J. D., Stroock, D. W., Large Deviations, San Diego, CA: Academic Press, 1989.［9］Rosenblatt, M., Markov Processes, Structure and Asymptotic Behavior, Berlin: Springer-Verlag, 1971.［10］Liggett, T. M., Stochastic Interacting Systems: Contact, Voter, and Exclusion Processes, Berlin: Springer-Verlag, 1999.［11］Albevrio, S., Kondratiev, Y. G., Rockner, M., Ergodicity of L2-semigroups and extremality of Gibbs states, J. Funct.Anal. , 1997, 144: 293－423.［12］Liverani, C. , Olla, S. , Ergodicity in infinite Hamiltonian systems with conservative noise, Probab. Th. Rel. Fields, 1996,106: 401－445.［13］Varadhan, S. P. S., Large Deviations and Applications, Philadelphia: SIAM, 1984.［14］Chen, J. W. , A variational principle for Markov processes, J. Stat. Phys. , 1999, 96: 1359－1364.
Handbook of Markov chain Monte Carlo
Brooks, Steve
2011-01-01
""Handbook of Markov Chain Monte Carlo"" brings together the major advances that have occurred in recent years while incorporating enough introductory material for new users of MCMC. Along with thorough coverage of the theoretical foundations and algorithmic and computational methodology, this comprehensive handbook includes substantial realistic case studies from a variety of disciplines. These case studies demonstrate the application of MCMC methods and serve as a series of templates for the construction, implementation, and choice of MCMC methodology.
Modelling the Heterogeneous Markov Attrition Process .
Directory of Open Access Journals (Sweden)
Jau Yeu Menq
1993-01-01
Full Text Available A model for heterogeneous dynamics combat as a continuos-time Markov process has been studied, and on account of the special form of its infinitesimal generator, recursive algorithms are derived to compute the important characteristics of the combat, such as the combat time distribution, expected value and variance, and the probability of winning and expected survivors. Numerical results are also presented. This approach can also be used to consider initial contact forces of both sides as random variables.
Numerical methods in Markov chain modeling
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
Online Learning in Discrete Hidden Markov Models
Alamino, Roberto C.; Caticha, Nestor
2007-01-01
We present and analyse three online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare them with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalisation error we draw learning curves in simplified situations. The performance for learning drifting concepts of one of the presented algorithms is analysed and compared with the Baldi-Chauvin algorithm in the same situations. A brief discussion about learning and symmetry breaking b...
Image restoration using 2D autoregressive texture model and structure curve construction
Voronin, V. V.; Marchuk, V. I.; Petrosov, S. P.; Svirin, I.; Agaian, S.; Egiazarian, K.
2015-05-01
In this paper an image inpainting approach based on the construction of a composite curve for the restoration of the edges of objects in an image using the concepts of parametric and geometric continuity is presented. It is shown that this approach allows to restore the curved edges and provide more flexibility for curve design in damaged image by interpolating the boundaries of objects by cubic splines. After edge restoration stage, a texture restoration using 2D autoregressive texture model is carried out. The image intensity is locally modeled by a first spatial autoregressive model with support in a strongly causal prediction region on the plane. Model parameters are estimated by Yule-Walker method. Several examples considered in this paper show the effectiveness of the proposed approach for large objects removal as well as recovery of small regions on several test images.
Probing turbulence intermittency via Auto-Regressive Moving-Average models
Faranda, Davide; Dubrulle, Berengere; Daviaud, Francois
2014-01-01
We suggest a new approach to probing intermittency corrections to the Kolmogorov law in turbulent flows based on the Auto-Regressive Moving-Average modeling of turbulent time series. We introduce a new index $\\Upsilon$ that measures the distance from a Kolmogorov-Obukhov model in the Auto-Regressive Moving-Average models space. Applying our analysis to Particle Image Velocimetry and Laser Doppler Velocimetry measurements in a von K\\'arm\\'an swirling flow, we show that $\\Upsilon$ is proportional to the traditional intermittency correction computed from the structure function. Therefore it provides the same information, using much shorter time series. We conclude that $\\Upsilon$ is a suitable index to reconstruct the spatial intermittency of the dissipation in both numerical and experimental turbulent fields.
Very-short-term wind power probabilistic forecasts by sparse vector autoregression
DEFF Research Database (Denmark)
Dowell, Jethro; Pinson, Pierre
2016-01-01
A spatio-temporal method for producing very-shortterm parametric probabilistic wind power forecasts at a large number of locations is presented. Smart grids containing tens, or hundreds, of wind generators require skilled very-short-term forecasts to operate effectively, and spatial information....... The location parameter for multiple wind farms is modelled as a vector-valued spatiotemporal process, and the scale parameter is tracked by modified exponential smoothing. A state-of-the-art technique for fitting sparse vector autoregressive models is employed to model the location parameter and demonstrates...... numerical advantages over conventional vector autoregressive models. The proposed method is tested on a dataset of 5 minute mean wind power generation at 22 wind farms in Australia. 5-minute-ahead forecasts are produced and evaluated in terms of point and probabilistic forecast skill scores and calibration...
Chen, Gang; Glen, Daniel R; Saad, Ziad S; Paul Hamilton, J; Thomason, Moriah E; Gotlib, Ian H; Cox, Robert W
2011-12-01
Vector autoregression (VAR) and structural equation modeling (SEM) are two popular brain-network modeling tools. VAR, which is a data-driven approach, assumes that connected regions exert time-lagged influences on one another. In contrast, the hypothesis-driven SEM is used to validate an existing connectivity model where connected regions have contemporaneous interactions among them. We present the two models in detail and discuss their applicability to FMRI data, and their interpretational limits. We also propose a unified approach that models both lagged and contemporaneous effects. The unifying model, structural vector autoregression (SVAR), may improve statistical and explanatory power, and avoid some prevalent pitfalls that can occur when VAR and SEM are utilized separately.
Directory of Open Access Journals (Sweden)
Luis Gonzaga Baca Ruiz
2016-08-01
Full Text Available This paper addresses the problem of energy consumption prediction using neural networks over a set of public buildings. Since energy consumption in the public sector comprises a substantial share of overall consumption, the prediction of such consumption represents a decisive issue in the achievement of energy savings. In our experiments, we use the data provided by an energy consumption monitoring system in a compound of faculties and research centers at the University of Granada, and provide a methodology to predict future energy consumption using nonlinear autoregressive (NAR and the nonlinear autoregressive neural network with exogenous inputs (NARX, respectively. Results reveal that NAR and NARX neural networks are both suitable for performing energy consumption prediction, but also that exogenous data may help to improve the accuracy of predictions.
Application of Markov Chains to Stock Trends
Directory of Open Access Journals (Sweden)
Kevin J. Doubleday
2011-01-01
Full Text Available Problem statement: Modeling of the Dow Jones Industrial Average is frequently attempted in order to determine trading strategies with maximum payoff. Changes in the DJIA are important since movements may affect both individuals and corporations profoundly. Previous work showed that modeling a market as a random walk was valid and that a market may be viewed as having the Markov property. Approach: The aim of this research was to determine the relationship between a diverse portfolio of stocks and the market as a whole. To that end, the DJIA was analyzed using a discrete time stochastic model, namely a Markov Chain. Two models were highlighted, where the DJIA was considered as being in a state of (1 gain or loss and (2 small, moderate, or large gain or loss. A portfolio of five stocks was then considered and two models of the portfolio much the same as those for the DJIA. These models were used to obtain transitional probabilities and steady state probabilities. Results: Our results indicated that the portfolio behaved similarly to the entire DJIA, both in the simple model and the partitioned model. Conclusion: When treated as a Markov process, the entire market was useful in gauging how a diverse portfolio of stocks might behave. Future work may include different classifications of states to refine the transition matrices.
The semi-Markov model for the ‘technological module–storage device’ structure
Directory of Open Access Journals (Sweden)
Vadim Ya. Kopp
2016-03-01
Full Text Available The theory of semi-Markov processes has been used to design a model of a ‘technological module–storage device’ (TM–SD structure. Stationary characteristics based on the obtained equations were determined to find a stationary distribution of the Markov embedded chain. Relying upon the performed studies, the stationary distribution of a semi-Markov process was determined. This allowed calculating the availability ratio of the TM–SD structure, and the design formula was given. The Markov restoration equations for the TM–SD system with taking into account TM and SD failures were solved assuming the exponential behavior of these failures. The obtained expressions describe how such a system operates and allow substituting the TM–SD system with an equivalent element with two factor states. This result significantly simplifies the modeling problem for more complex systems. The legitimacy of using exponential distributions of random variables (error-free periods for TM and SD was analyzed. The performed simulation modeling revealed that the hypothesis for an exponential behavior of error-free periods for TM as a whole (and SD as well can be accepted even in the case when TM (or SD consists of six nodes.
Estimation and Forecasting in Vector Autoregressive Moving Average Models for Rich Datasets
DEFF Research Database (Denmark)
Dias, Gustavo Fruet; Kapetanios, George
We address the issue of modelling and forecasting macroeconomic variables using rich datasets, by adopting the class of Vector Autoregressive Moving Average (VARMA) models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares...... alternative scenarios. Our empirical application shows that VARMA models are feasible alternatives when forecasting with many predictors. We show that VARMA models outperform the AR(1), BVAR and factor models, considering different model dimensions....
Teräsvirta, Timo; Yang, Yukai
2014-01-01
We consider a nonlinear vector model called the logistic vector smooth transition autoregressive model. The bivariate single-transition vector smooth transition regression model of Camacho (2004) is generalised to a multivariate and multitransition one. A modelling strategy consisting of specification, including testing linearity, estimation and evaluation of these models is constructed. Nonlinear least squares estimation of the parameters of the model is discussed. Evaluation by misspecifica...
Time-varying parameter auto-regressive models for autocovariance nonstationary time series
Institute of Scientific and Technical Information of China (English)
FEI WanChun; BAI Lun
2009-01-01
In this paper,autocovariance nonstationary time series is clearly defined on a family of time series.We propose three types of TVPAR (time-varying parameter auto-regressive) models:the full order TVPAR model,the time-unvarying order TVPAR model and the time-varying order TVPAR model for autocovariance nonstationary time series.Related minimum AIC (Akaike information criterion) estimations are carried out.
Time-varying parameter auto-regressive models for autocovariance nonstationary time series
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the time-unvarying order TVPAR model and the time-varying order TV-PAR model for autocovariance nonstationary time series. Related minimum AIC (Akaike information criterion) estimations are carried out.
Markov invariants, plethysms, and phylogenetics (the long version)
Sumner, J G; Jermiin, L S; Jarvis, P D
2008-01-01
We explore model based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the Log-Det distance measure. We take as our primary tool group representation theory, and show that it provides a general framework for analysing Markov processes on trees. From this algebraic perspective, the inherent symmetries of these processes become apparent, and focusing on plethysms, we are able to define Markov invariants and give existence proofs. We give an explicit technique for constructing the invariants, valid for any number of character states and taxa. For phylogenetic trees with three and four leaves, we demonstrate that the corresponding Markov invariants can be fruitfully exploited in applied phylogenetic studies.
Markov chains and semi-Markov models in time-to-event analysis.
Abner, Erin L; Charnigo, Richard J; Kryscio, Richard J
2013-10-25
A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields.
Markov chain-based analysis of a modified Cooper-Frieze model
Institute of Scientific and Technical Information of China (English)
Jin-ying TONG; Zhen-ting HOU; Ding-hua SHI
2009-01-01
From the perspective of probability,the stability of a modified Cooper Frieze model is studied in the present paper.Based on the concept and technique of the first-passage probability in the Markov theory,we provide a rigorous proof for the existence of the steady-state degree distribution,and derive the explicit formula analytically.Moreover,we perform extensive numerical simulations of the model,including the degree distribution and the clustering.
Assistive system for people with Apraxia using a Markov decision process.
Jean-Baptiste, Emilie M D; Russell, Martin; Rothstein, Pia
2014-01-01
CogWatch is an assistive system to re-train stroke survivors suffering from Apraxia or Action Disorganization Syndrome (AADS) to complete activities of daily living (ADLs). This paper describes the approach to real-time planning based on a Markov Decision Process (MDP), and demonstrates its ability to improve task's performance via user simulation. The paper concludes with a discussion of the remaining challenges and future enhancements.
FEPI-MB: identifying SNPs-disease association using a Markov Blanket-based approach
Directory of Open Access Journals (Sweden)
Han Bing
2011-11-01
Full Text Available Abstract Background The interactions among genetic factors related to diseases are called epistasis. With the availability of genotyped data from genome-wide association studies, it is now possible to computationally unravel epistasis related to the susceptibility to common complex human diseases such as asthma, diabetes, and hypertension. However, the difficulties of detecting epistatic interaction arose from the large number of genetic factors and the enormous size of possible combinations of genetic factors. Most computational methods to detect epistatic interactions are predictor-based methods and can not find true causal factor elements. Moreover, they are both time-consuming and sample-consuming. Results We propose a new and fast Markov Blanket-based method, FEPI-MB (Fast EPistatic Interactions detection using Markov Blanket, for epistatic interactions detection. The Markov Blanket is a minimal set of variables that can completely shield the target variable from all other variables. Learning of Markov blankets can be used to detect epistatic interactions by a heuristic search for a minimal set of SNPs, which may cause the disease. Experimental results on both simulated data sets and a real data set demonstrate that FEPI-MB significantly outperforms other existing methods and is capable of finding SNPs that have a strong association with common diseases. Conclusions FEPI-MB algorithm outperforms other computational methods for detection of epistatic interactions in terms of both the power and sample-efficiency. Moreover, compared to other Markov Blanket learning methods, FEPI-MB is more time-efficient and achieves a better performance.
First and second order semi-Markov chains for wind speed modeling
Prattico, F.; Petroni, F.; D'Amico, G.
2012-04-01
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. Semi-Markov processes (SMP) are a wide class of stochastic processes which generalize at the same time both Markov chains and renewal processes. Their main advantage is that of using whatever type of waiting time distribution for modeling the time to have a transition from one state to another one. This major flexibility has a price to pay: availability of data to estimate the parameters of the model which are more numerous. Data availability is not an issue in wind speed studies, therefore, semi-Markov models can be used in a statistical efficient way. In this work we present three different semi-Markov chain models: the first one is a first-order SMP where the transition probabilities from two speed states (at time Tn and Tn-1) depend on the initial state (the state at Tn-1), final state (the state at Tn) and on the waiting time (given by t=Tn-Tn-1), the second model is a second order SMP where we consider the transition probabilities as depending also on the state the wind speed was before the initial state (which is the state at Tn-2) and the last one is still a second order SMP where the transition probabilities depends on the three states at Tn-2,Tn-1 and Tn and on the waiting times t_1=Tn-1-Tn-2 and t_2=Tn-Tn-1. The three models are used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling
Institute of Scientific and Technical Information of China (English)
Jiang Wei; Xiang Haige
2004-01-01
This paper addresses the issues of channel estimation in a Multiple-Input/Multiple-Output (MIMO) system. Markov Chain Monte Carlo (MCMC) method is employed to jointly estimate the Channel State Information (CSI) and the transmitted signals. The deduced algorithms can work well under circumstances of low Signal-to-Noise Ratio (SNR). Simulation results are presented to demonstrate their effectiveness.
Kieftenbeld, Vincent; Natesan, Prathiba
2012-01-01
Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…
Li, Xuesong; Northrop, William F.
2016-04-01
This paper describes a quantitative approach to approximate multiple scattering through an isotropic turbid slab based on Markov Chain theorem. There is an increasing need to utilize multiple scattering for optical diagnostic purposes; however, existing methods are either inaccurate or computationally expensive. Here, we develop a novel Markov Chain approximation approach to solve multiple scattering angular distribution (AD) that can accurately calculate AD while significantly reducing computational cost compared to Monte Carlo simulation. We expect this work to stimulate ongoing multiple scattering research and deterministic reconstruction algorithm development with AD measurements.
The Laplace Functional and Moments for Markov Branching Chains in Random Environments
Institute of Scientific and Technical Information of China (English)
HU Di-he; ZHANG Shu-lin
2005-01-01
The concepts of random Markov matrix, Markov branching chain in random environment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE) are introduced. The properties of LFMBCRE and the explicit formulas of moments of MBCRE are given.
平滑转换自回归模型的平稳性问题研究%Research on the Stationarity of Smooth Transition Autoregressive Model
Institute of Scientific and Technical Information of China (English)
赵春艳
2012-01-01
According to the definition of weakly stationary sequence, we consider that the sequence of smooth transition autoregressive model is not weakly stationary, and using the ADF statistic to test its stationarity makes no sense. Furthermore, based on Markov Chain ergodicity, we believe that the STAR model sequence is strictly stationary, and the joint limit of the model coefficients value ensures the stationarity of the model. Using the first order logarithmic STAR model as example, its stationary condition is｜β＋r｜〈1, whiteβ can be equal to 1 and the absolute value can also he less than 1.%根据时间序列宽平稳的定义，本文认为，平滑转换自回归模型的序列不是宽平稳序列，利用ADF统计量检验其平稳性是没有意义的；其次，依据马尔科夫链的遍历性，我们认为，STAR模型的序列是严平稳序列，且通过对模型系数的联合取值的限制保证了模型的平稳性。以一阶对数平滑转换自回归模型为例，其平稳的条件是，β与r符号相反，且｜β＋r｜〈1，β可以等于1，也可以绝对值小于1。
Continuity Properties of Distances for Markov Processes
DEFF Research Database (Denmark)
Jaeger, Manfred; Mao, Hua; Larsen, Kim Guldstrand
2014-01-01
In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable...... continuity properties for such distances are identified. We then establish a number of results that show that these two properties are in conflict, and not simultaneously fulfilled by any of our candidate natural distance functions. An impossibility result is derived that explains to some extent...
Evolving the structure of hidden Markov Models
DEFF Research Database (Denmark)
won, K. J.; Prugel-Bennett, A.; Krogh, A.
2006-01-01
A genetic algorithm (GA) is proposed for finding the structure of hidden Markov Models (HMMs) used for biological sequence analysis. The GA is designed to preserve biologically meaningful building blocks. The search through the space of HMM structures is combined with optimization of the emission...... and transition probabilities using the classic Baum-Welch algorithm. The system is tested on the problem of finding the promoter and coding region of C. jejuni. The resulting HMM has a superior discrimination ability to a handcrafted model that has been published in the literature....
Markov chains with quasitoeplitz transition matrix: applications
1990-01-01
Application problems are investigated for the Markov chains with quasitoeplitz transition matrix. Generating functions of transient and steady state probabilities, first zero hitting probabilities and mean times are found for various particular cases, corresponding to some known patterns of feedback ( warm-up, switch at threshold etc.), Level depending dams and queue-depending queueing systems of both M/G/1 and MI/G/1 types with arbitrary random sizes of arriving and departing groups are ...
Genetic Algorithms Principles Towards Hidden Markov Model
Directory of Open Access Journals (Sweden)
Nabil M. Hewahi
2011-10-01
Full Text Available In this paper we propose a general approach based on Genetic Algorithms (GAs to evolve Hidden Markov Models (HMM. The problem appears when experts assign probability values for HMM, they use only some limited inputs. The assigned probability values might not be accurate to serve in other cases related to the same domain. We introduce an approach based on GAs to find
out the suitable probability values for the HMM to be mostly correct in more cases than what have been used to assign the probability values.
Hybrid Discrete-Continuous Markov Decision Processes
Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich
2003-01-01
This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.
Dynamic system evolution and markov chain approximation
Directory of Open Access Journals (Sweden)
Roderick V. Nicholas Melnik
1998-01-01
Full Text Available In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of mathematical models is treated as a decision making process with limited available information.The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete space–time of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work.
Performance sensitivities for parameterized Markov systems
Institute of Scientific and Technical Information of China (English)
Xiren CAO; Junyu ZHANG
2004-01-01
It is known that the performance potentials (or equivalently, perturbation realization factors) can be used as building blocks for performance sensitivities of Markov systems. In parameterized systems, the changes in parameters may only affect some states, and the explicit transition probability matrix may not be known. In this paper, we use an example to show that we can use potentials to construct performance sensitivities in a more flexible way; only the potentials at the affected states need to be estimated, and the transition probability matrix need not be known. Policy iteration algorithms, which are simpler than the standard one, can be established.
Predicting Protein Secondary Structure with Markov Models
DEFF Research Database (Denmark)
Fischer, Paul; Larsen, Simon; Thomsen, Claus
2004-01-01
we are considering here, is to predict the secondary structure from the primary one. To this end we train a Markov model on training data and then use it to classify parts of unknown protein sequences as sheets, helices or coils. We show how to exploit the directional information contained......The primary structure of a protein is the sequence of its amino acids. The secondary structure describes structural properties of the molecule such as which parts of it form sheets, helices or coils. Spacial and other properties are described by the higher order structures. The classification task...
de Uña-Álvarez, Jacobo; Meira-Machado, Luís
2015-06-01
Multi-state models are often used for modeling complex event history data. In these models the estimation of the transition probabilities is of particular interest, since they allow for long-term predictions of the process. These quantities have been traditionally estimated by the Aalen-Johansen estimator, which is consistent if the process is Markov. Several non-Markov estimators have been proposed in the recent literature, and their superiority with respect to the Aalen-Johansen estimator has been proved in situations in which the Markov condition is strongly violated. However, the existing estimators have the drawback of requiring that the support of the censoring distribution contains the support of the lifetime distribution, which is not often the case. In this article, we propose two new methods for estimating the transition probabilities in the progressive illness-death model. Some asymptotic results are derived. The proposed estimators are consistent regardless the Markov condition and the referred assumption about the censoring support. We explore the finite sample behavior of the estimators through simulations. The main conclusion of this piece of research is that the proposed estimators are much more efficient than the existing non-Markov estimators in most cases. An application to a clinical trial on colon cancer is included. Extensions to progressive processes beyond the three-state illness-death model are discussed.
Performance evaluation:= (process algebra + model checking) x Markov chains
Hermanns, H.; Katoen, J.P.; Larsen, Kim G.; Nielsen, Mogens
2001-01-01
Markov chains are widely used in practice to determine system performance and reliability characteristics. The vast majority of applications considers continuous-time Markov chains (CTMCs). This tutorial paper shows how successful model specification and analysis techniques from concurrency theory c
On Equalities for BLUEs under Misspecified Gauss-Markov Models
Institute of Scientific and Technical Information of China (English)
Yong Ge TIAN
2009-01-01
This paper studies relationships between the best linear unbiased estimators (BLUEs) of an estimable parametric functions Kβ under the Gauss-Markov model {y, Xβ, σ~22∑} and its misspecified model {y, X_0β, σ~2∑_0}. In addition, relationships between BLUEs under a restricted Ganss-Markov model and its misspecified model are also investigated.
Testing the Adequacy of a Semi-Markov Process
2015-09-17
movements using Semi-Markov processes,” Tourism Management, Vol. 32, No. 4, 2011, pp. 844–851. [4] Titman, A. C. and Sharples, L. D., “Model...Reliability, No. 17, Siam, 1996. [13] Gorissen, M. and Vanderzande, C., “Semi-Markov models of mRNA- translation ,” arXiv preprint arXiv:1104.0131, 2011
Series Expansions for Finite-State Markov Chains
Heidergott, Bernd; Hordijk, Arie; Uitert, van Miranda
2005-01-01
This paper provides series expansions of the stationary distribution of a finite Markov chain. This leads to an efficient numerical algorithm for computing the stationary distribution of a finite Markov chain. Numerical examples are given to illustrate the performance of the algorithm.
Lifting—A nonreversible Markov chain Monte Carlo algorithm
Vucelja, Marija
2016-12-01
Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ reversible Markov chains. Reversible chains obey detailed balance and thus ensure that the system will eventually relax to equilibrium, though detailed balance is not necessary for convergence to equilibrium. We review nonreversible Markov chains, which violate detailed balance and yet still relax to a given target stationary distribution. In particular cases, nonreversible Markov chains are substantially better at sampling than the conventional reversible Markov chains with up to a square root improvement in the convergence time to the steady state. One kind of nonreversible Markov chain is constructed from the reversible ones by enlarging the state space and by modifying and adding extra transition rates to create non-reversible moves. Because of the augmentation of the state space, such chains are often referred to as lifted Markov Chains. We illustrate the use of lifted Markov chains for efficient sampling on several examples. The examples include sampling on a ring, sampling on a torus, the Ising model on a complete graph, and the one-dimensional Ising model. We also provide a pseudocode implementation, review related work, and discuss the applicability of such methods.
First hitting probabilities for semi markov chains and estimation
DEFF Research Database (Denmark)
Georgiadis, Stylianos
2017-01-01
We first consider a stochastic system described by an absorbing semi-Markov chain with finite state space and we introduce the absorption probability to a class of recurrent states. Afterwards, we study the first hitting probability to a subset of states for an irreducible semi-Markov chain...
Compositional Modeling and Minimization of Time-Inhomogeneous Markov Chains
Han, T.; Katoen, J.P.; Mereacre, A.
2008-01-01
This paper presents a compositional framework for the modeling of interactive continuous-time Markov chains with time-dependent rates, a subclass of communicating piecewise deterministic Markov processes. A poly-time algorithm is presented for computing the coarsest quotient under strong bisimulatio
On Chebyshev-Markov rational functions over several intervals
Lukashov, AL
1998-01-01
Chebyshev-Markov rational functions are the solutions of the following extremal problem [GRAPHICS] with K being a compact subset of R and omega(n)(x) being a fixed real polynomial of degree less than n, positive on K. A parametric representation of Chebyshev-Markov rational functions is found for K
Extending Markov Automata with State and Action Rewards
Guck, Dennis; Timmer, Mark; Blom, Stefan; Bertrand, N.; Bortolussi, L.
2014-01-01
This presentation introduces the Markov Reward Automaton (MRA), an extension of the Markov automaton that allows the modelling of systems incorporating rewards in addition to nondeterminism, discrete probabilistic choice and continuous stochastic timing. Our models support both rewards that are acqu
Efficient Incorporation of Markov Random Fields in Change Detection
DEFF Research Database (Denmark)
Aanæs, Henrik; Nielsen, Allan Aasbjerg; Carstensen, Jens Michael
2009-01-01
of noise, implying that the pixel-wise classifier is also noisy. There is thus a need for incorporating local homogeneity constraints into such a change detection framework. For this modelling task Markov Random Fields are suitable. Markov Random Fields have, however, previously been plagued by lack...
Markov transitions and the propagation of chaos
Energy Technology Data Exchange (ETDEWEB)
Gottlieb, Alexander David [Univ. of California, Berkeley, CA (United States)
1998-12-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also s how that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution.
A Markov model of the Indus script.
Rao, Rajesh P N; Yadav, Nisha; Vahia, Mayank N; Joglekar, Hrishikesh; Adhikari, R; Mahadevan, Iravatham
2009-08-18
Although no historical information exists about the Indus civilization (flourished ca. 2600-1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system.
Remarks on a monotone Markov chain
Directory of Open Access Journals (Sweden)
P. Todorovic
1987-01-01
Full Text Available In applications, considerations on stochastic models often involve a Markov chain {ζn}0∞ with state space in R+, and a transition probability Q. For each x R+ the support of Q(x,. is [0,x]. This implies that ζ0≥ζ1≥…. Under certain regularity assumptions on Q we show that Qn(x,Bu→1 as n→∞ for all u>0 and that 1−Qn(x,Bu≤[1−Q(x,Bu]n where Bu=[0,u. Set τ0=max{k;ζk=ζ0}, τn=max{k;ζk=ζτn−1+1} and write Xn=ζτn−1+1, Tn=τn−τn−1. We investigate some properties of the imbedded Markov chain {Xn}0∞ and of {Tn}0∞. We determine all the marginal distributions of {Tn}0∞ and show that it is asymptotically stationary and that it possesses a monotonicity property. We also prove that under some mild regularity assumptions on β(x=1−Q(x,Bx, ∑1n(Ti−a/bn→dZ∼N(0,1.
Monotone measures of ergodicity for Markov chains
Directory of Open Access Journals (Sweden)
J. Keilson
1998-01-01
Full Text Available The following paper, first written in 1974, was never published other than as part of an internal research series. Its lack of publication is unrelated to the merits of the paper and the paper is of current importance by virtue of its relation to the relaxation time. A systematic discussion is provided of the approach of a finite Markov chain to ergodicity by proving the monotonicity of an important set of norms, each measures of egodicity, whether or not time reversibility is present. The paper is of particular interest because the discussion of the relaxation time of a finite Markov chain [2] has only been clean for time reversible chains, a small subset of the chains of interest. This restriction is not present here. Indeed, a new relaxation time quoted quantifies the relaxation time for all finite ergodic chains (cf. the discussion of Q1(t below Equation (1.7]. This relaxation time was developed by Keilson with A. Roy in his thesis [6], yet to be published.
Epitope discovery with phylogenetic hidden Markov models.
LENUS (Irish Health Repository)
Lacerda, Miguel
2010-05-01
Existing methods for the prediction of immunologically active T-cell epitopes are based on the amino acid sequence or structure of pathogen proteins. Additional information regarding the locations of epitopes may be acquired by considering the evolution of viruses in hosts with different immune backgrounds. In particular, immune-dependent evolutionary patterns at sites within or near T-cell epitopes can be used to enhance epitope identification. We have developed a mutation-selection model of T-cell epitope evolution that allows the human leukocyte antigen (HLA) genotype of the host to influence the evolutionary process. This is one of the first examples of the incorporation of environmental parameters into a phylogenetic model and has many other potential applications where the selection pressures exerted on an organism can be related directly to environmental factors. We combine this novel evolutionary model with a hidden Markov model to identify contiguous amino acid positions that appear to evolve under immune pressure in the presence of specific host immune alleles and that therefore represent potential epitopes. This phylogenetic hidden Markov model provides a rigorous probabilistic framework that can be combined with sequence or structural information to improve epitope prediction. As a demonstration, we apply the model to a data set of HIV-1 protein-coding sequences and host HLA genotypes.
Directory of Open Access Journals (Sweden)
Shuntaro Okazaki
Full Text Available People's behaviors synchronize. It is difficult, however, to determine whether synchronized behaviors occur in a mutual direction--two individuals influencing one another--or in one direction--one individual leading the other, and what the underlying mechanism for synchronization is. To answer these questions, we hypothesized a non-leader-follower postural sway synchronization, caused by a reciprocal visuo-postural feedback system operating on pairs of individuals, and tested that hypothesis both experimentally and via simulation. In the behavioral experiment, 22 participant pairs stood face to face either 20 or 70 cm away from each other wearing glasses with or without vision blocking lenses. The existence and direction of visual information exchanged between pairs of participants were systematically manipulated. The time series data for the postural sway of these pairs were recorded and analyzed with cross correlation and causality. Results of cross correlation showed that postural sway of paired participants was synchronized, with a shorter time lag when participant pairs could see one another's head motion than when one of the participants was blindfolded. In addition, there was less of a time lag in the observed synchronization when the distance between participant pairs was smaller. As for the causality analysis, noise contribution ratio (NCR, the measure of influence using a multivariate autoregressive model, was also computed to identify the degree to which one's postural sway is explained by that of the other's and how visual information (sighted vs. blindfolded interacts with paired participants' postural sway. It was found that for synchronization to take place, it is crucial that paired participants be sighted and exert equal influence on one another by simultaneously exchanging visual information. Furthermore, a simulation for the proposed system with a wider range of visual input showed a pattern of results similar to the
Okazaki, Shuntaro; Hirotani, Masako; Koike, Takahiko; Bosch-Bayard, Jorge; Takahashi, Haruka K; Hashiguchi, Maho; Sadato, Norihiro
2015-01-01
People's behaviors synchronize. It is difficult, however, to determine whether synchronized behaviors occur in a mutual direction--two individuals influencing one another--or in one direction--one individual leading the other, and what the underlying mechanism for synchronization is. To answer these questions, we hypothesized a non-leader-follower postural sway synchronization, caused by a reciprocal visuo-postural feedback system operating on pairs of individuals, and tested that hypothesis both experimentally and via simulation. In the behavioral experiment, 22 participant pairs stood face to face either 20 or 70 cm away from each other wearing glasses with or without vision blocking lenses. The existence and direction of visual information exchanged between pairs of participants were systematically manipulated. The time series data for the postural sway of these pairs were recorded and analyzed with cross correlation and causality. Results of cross correlation showed that postural sway of paired participants was synchronized, with a shorter time lag when participant pairs could see one another's head motion than when one of the participants was blindfolded. In addition, there was less of a time lag in the observed synchronization when the distance between participant pairs was smaller. As for the causality analysis, noise contribution ratio (NCR), the measure of influence using a multivariate autoregressive model, was also computed to identify the degree to which one's postural sway is explained by that of the other's and how visual information (sighted vs. blindfolded) interacts with paired participants' postural sway. It was found that for synchronization to take place, it is crucial that paired participants be sighted and exert equal influence on one another by simultaneously exchanging visual information. Furthermore, a simulation for the proposed system with a wider range of visual input showed a pattern of results similar to the behavioral results.
Fitting timeseries by continuous-time Markov chains: A quadratic programming approach
Crommelin, D. T.; Vanden-Eijnden, E.
2006-09-01
Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows.
Directory of Open Access Journals (Sweden)
Rondeau Paul
2008-01-01
Full Text Available Speech coding techniques capable of generating encoded representations which are robust against channel losses play an important role in enabling reliable voice communication over packet networks and mobile wireless systems. In this paper, we investigate the use of multiple description index assignments (MDIAs for loss-tolerant transmission of line spectral frequency (LSF coefficients, typically generated by state-of-the-art speech coders. We propose a simulated annealing-based approach for optimizing MDIAs for Markov-model-based decoders which exploit inter- and intraframe correlations in LSF coefficients to reconstruct the quantized LSFs from coded bit streams corrupted by channel losses. Experimental results are presented which compare the performance of a number of novel LSF transmission schemes. These results clearly demonstrate that Markov-model-based decoders, when used in conjunction with optimized MDIA, can yield average spectral distortion much lower than that produced by methods such as interleaving/interpolation, commonly used to combat the packet losses.
Markov-Binary Visibility Graph: a new method for analyzing Complex Systems
Sadra, Yaser; Ahadpour, Sodief
2011-01-01
In this work, we introduce a new and simple transformation from time series to complex networks based on markov-binary visibility graph(MBVG). Due to the simple structure of this transformation in comparison with other transformations be obtained more precise results. Moreover, several topological aspects of the constructed graph, such as degree distribution, clustering coefficient, and mean visibility length have been thoroughly investigated. Numerical simulations confirm the reliability of markov-binary visibility graph for time series analysis. This algorithm have the capability of distinguishing between uncorrelated and correlated systems. Finaly, we illustrate this algorithm analyzing the human heartbeat dynamics. The results indicate that the human heartbeat (RR-interval) time series of normally, Congestive Heart Failure (CHF) and Atrial Fibrillation (AF) subjects are uncorrelated, chaotic and correlated stochastic systems, respectively.
An Improved Markov Model for IEEE 802.15.4 Slotted CSMA/CA Mechanism
Institute of Scientific and Technical Information of China (English)
Hao Wen; Chuang Lin; Zhi-Jia Chen; Hao Yin; Tao He; Eryk Dutkiewicz
2009-01-01
IEEE 802.15.4 protocol is proposed to meet the low latency and energy consumption needs in low-rate wireless applications, however, few analytical models are tractable enough for comprehensive evaluation of the protocol. To evaluate the IEEE 802.15.4 slotted CSMA/CA channel access mechanism in this paper, we propose a practical and accurate discrete Markov chain model, which can dynamically represent different network loads. By computing the steady-state distribution probability of the Markov chain, we obtain an evaluation formula for throughput, energy consumption, and access latency. Then we further analyze the parameters that influence performance including packet arrival rate, initial backoff exponent and maximum backoff number. Finally, NS2 simulator has been used to evaluate the performance of the 802.15.4 CSMA/CA mechanism under different scenarios and to validate the accuracy of the proposed model.
An extensive Markov system for ECG exact coding.
Tai, S C
1995-02-01
In this paper, an extensive Markov process, which considers both the coding redundancy and the intersample redundancy, is presented to measure the entropy value of an ECG signal more accurately. It utilizes the intersample correlations by predicting the incoming n samples based on the previous m samples which constitute an extensive Markov process state. Theories of the extensive Markov process and conventional n repeated applications of m-th order Markov process are studied first in this paper. After that, they are realized for ECG exact coding. Results show that a better performance can be achieved by our system. The average code length for the extensive Markov system on the second difference signals was 2.512 b/sample, while the average Huffman code length for the second difference signals was 3.326 b/sample.
Statistical early-warning indicators based on Auto-Regressive Moving-Average processes
Faranda, Davide; Dubrulle, Bérengère
2014-01-01
We address the problem of defining early warning indicators of critical transition. To this purpose, we fit the relevant time series through a class of linear models, known as Auto-Regressive Moving-Average (ARMA(p,q)) models. We define two indicators representing the total order and the total persistence of the process, linked, respectively, to the shape and to the characteristic decay time of the autocorrelation function of the process. We successfully test the method to detect transitions in a Langevin model and a 2D Ising model with nearest-neighbour interaction. We then apply the method to complex systems, namely for dynamo thresholds and financial crisis detection.
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
Kurganskiĭ, A V
2010-01-01
This review focuses on some practical issues of using vector autoregressive model (VAR) for multichannel EEG analysis. Those issues include: EEG preprocessing, checking if the necessary conditions of VAR model applicability are met, optimal order selection, and assessment of the validity of fitted VAR model. Both non-directed (ordinary coherence and imaginary part of the complex-valued coherency) and directed (directed coherence, directed transfer function and partial directed coherence) measures of the strength of inter-channel coupling are discussed. These measures are analyzed with respect to their properties (scale invariance) and known problems in using them (spurious interactions, volume conduction).
Institute of Scientific and Technical Information of China (English)
PAN; Jiazhu; WU; Guangxu
2005-01-01
We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.
DEFF Research Database (Denmark)
Thomsen, C E; Rosenfalck, A; Nørregaard Christensen, K
1991-01-01
The brain activity electroencephalogram (EEG) was recorded from 30 healthy women scheduled for hysterectomy. The patients were anaesthetized with isoflurane, halothane or etomidate/fentanyl. A multiparametric method was used for extraction of amplitude and frequency information from the EEG....... The method applied autoregressive modelling of the signal, segmented in 2 s fixed intervals. The features from the EEG segments were used for learning and for classification. The learning process was unsupervised and hierarchical clustering analysis was used to construct a learning set of EEG amplitude...
A representation theory for a class of vector autoregressive models for fractional processes
DEFF Research Database (Denmark)
Johansen, Søren
2008-01-01
Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a unit...... root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0...
A self-organizing power system stabilizer using Fuzzy Auto-Regressive Moving Average (FARMA) model
Energy Technology Data Exchange (ETDEWEB)
Park, Y.M.; Moon, U.C. [Seoul National Univ. (Korea, Republic of). Electrical Engineering Dept.; Lee, K.Y. [Pennsylvania State Univ., University Park, PA (United States). Electrical Engineering Dept.
1996-06-01
This paper presents a self-organizing power system stabilizer (SOPSS) which use the Fuzzy Auto-Regressive Moving Average (FARMA) model. The control rules and the membership functions of the proposed logic controller are generated automatically without using any plant model. The generated rules are stored in the fuzzy rule space and updated on-line by a self-organizing procedure. To show the effectiveness of the proposed controller, comparison with a conventional controller for one-machine infinite-bus system is presented.
Pal, Debdatta; Mitra, Subrata Kumar
2016-10-01
This study used a quantile autoregressive distributed lag (QARDL) model to capture asymmetric impact of rainfall on food production in India. It was found that the coefficient corresponding to the rainfall in the QARDL increased till the 75th quantile and started decreasing thereafter, though it remained in the positive territory. Another interesting finding is that at the 90th quantile and above the coefficients of rainfall though remained positive was not statistically significant and therefore, the benefit of high rainfall on crop production was not conclusive. However, the impact of other determinants, such as fertilizer and pesticide consumption, is quite uniform over the whole range of the distribution of food grain production.
A Pitfall in Using the Characterization of Granger Non-Causality in Vector Autoregressive Models
Directory of Open Access Journals (Sweden)
Umberto Triacca
2015-04-01
Full Text Available It is well known that in a vector autoregressive (VAR model Granger non-causality is characterized by a set of restrictions on the VAR coefficients. This characterization has been derived under the assumption of non-singularity of the covariance matrix of the innovations. This note shows that if this assumption is violated, then the characterization of Granger non-causality in a VAR model fails to hold. In these situations Granger non-causality test results must be interpreted with caution.
Deficit Financed Public Expenditure in Argentina: A Structural Vector Autoregression Analysis
2012-01-01
The goal of the paper is to analyze the importance of government debt in the propagation of fiscal shocks in the Argentine economy. For that reason we augment a standard fiscal policy vector Autoregression with the nominal debt to GDP ratio taken from a recently compiled IMF database. The main finding is that government debt has a crucial role for the implications of the model, and that the omission of the feedback of the debt (as a ratio of GDP) to the other variables in the system leads to ...
Searching for efficient Markov chain Monte Carlo proposal kernels.
Yang, Ziheng; Rodríguez, Carlos E
2013-11-26
Markov chain Monte Carlo (MCMC) or the Metropolis-Hastings algorithm is a simulation algorithm that has made modern Bayesian statistical inference possible. Nevertheless, the efficiency of different Metropolis-Hastings proposal kernels has rarely been studied except for the Gaussian proposal. Here we propose a unique class of Bactrian kernels, which avoid proposing values that are very close to the current value, and compare their efficiency with a number of proposals for simulating different target distributions, with efficiency measured by the asymptotic variance of a parameter estimate. The uniform kernel is found to be more efficient than the Gaussian kernel, whereas the Bactrian kernel is even better. When optimal scales are used for both, the Bactrian kernel is at least 50% more efficient than the Gaussian. Implementation in a Bayesian program for molecular clock dating confirms the general applicability of our results to generic MCMC algorithms. Our results refute a previous claim that all proposals had nearly identical performance and will prompt further research into efficient MCMC proposals.
Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit
Izvekov, Sergei
2017-01-01
We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013), 10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.