Reliability analysis of nuclear component cooling water system using semi-Markov process model

International Nuclear Information System (INIS)

Veeramany, Arun; Pandey, Mahesh D.

2011-01-01

Research highlights: → Semi-Markov process (SMP) model is used to evaluate system failure probability of the nuclear component cooling water (NCCW) system. → SMP is used because it can solve reliability block diagram with a mixture of redundant repairable and non-repairable components. → The primary objective is to demonstrate that SMP can consider Weibull failure time distribution for components while a Markov model cannot → Result: the variability in component failure time is directly proportional to the NCCW system failure probability. → The result can be utilized as an initiating event probability in probabilistic safety assessment projects. - Abstract: A reliability analysis of nuclear component cooling water (NCCW) system is carried out. Semi-Markov process model is used in the analysis because it has potential to solve a reliability block diagram with a mixture of repairable and non-repairable components. With Markov models it is only possible to assume an exponential profile for component failure times. An advantage of the proposed model is the ability to assume Weibull distribution for the failure time of components. In an attempt to reduce the number of states in the model, it is shown that usage of poly-Weibull distribution arises. The objective of the paper is to determine system failure probability under these assumptions. Monte Carlo simulation is used to validate the model result. This result can be utilized as an initiating event probability in probabilistic safety assessment projects.

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

Directory of Open Access Journals (Sweden)

Victor Kravets

2016-05-01

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

Finite Markov processes and their applications

CERN Document Server

Iosifescu, Marius

2007-01-01

A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch

Consistent Estimation of Partition Markov Models

Directory of Open Access Journals (Sweden)

Jesús E. García

2017-04-01

Full Text Available The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns.

Markov and mixed models with applications

DEFF Research Database (Denmark)

Mortensen, Stig Bousgaard

This thesis deals with mathematical and statistical models with focus on applications in pharmacokinetic and pharmacodynamic (PK/PD) modelling. These models are today an important aspect of the drug development in the pharmaceutical industry and continued research in statistical methodology within...... or uncontrollable factors in an individual. Modelling using SDEs also provides new tools for estimation of unknown inputs to a system and is illustrated with an application to estimation of insulin secretion rates in diabetic patients. Models for the eect of a drug is a broader area since drugs may affect...... 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...

Reviving Markov processes and applications

International Nuclear Information System (INIS)

Cai, H.

1988-01-01

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

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

Science.gov (United States)

Chen, Baojiang; Zhou, Xiao-Hua

2013-05-01

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

Pavement maintenance optimization model using Markov Decision Processes

Science.gov (United States)

Mandiartha, P.; Duffield, C. F.; Razelan, I. S. b. M.; Ismail, A. b. H.

2017-09-01

This paper presents an optimization model for selection of pavement maintenance intervention using a theory of Markov Decision Processes (MDP). There are some particular characteristics of the MDP developed in this paper which distinguish it from other similar studies or optimization models intended for pavement maintenance policy development. These unique characteristics include a direct inclusion of constraints into the formulation of MDP, the use of an average cost method of MDP, and the policy development process based on the dual linear programming solution. The limited information or discussions that are available on these matters in terms of stochastic based optimization model in road network management motivates this study. This paper uses a data set acquired from road authorities of state of Victoria, Australia, to test the model and recommends steps in the computation of MDP based stochastic optimization model, leading to the development of optimum pavement maintenance policy.

Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

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A. Valor

2013-01-01

Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.

Availability Control for Means of Transport in Decisive Semi-Markov Models of Exploitation Process

Science.gov (United States)

Migawa, Klaudiusz

2012-12-01

The issues presented in this research paper refer to problems connected with the control process for exploitation implemented in the complex systems of exploitation for technical objects. The article presents the description of the method concerning the control availability for technical objects (means of transport) on the basis of the mathematical model of the exploitation process with the implementation of the decisive processes by semi-Markov. The presented method means focused on the preparing the decisive for the exploitation process for technical objects (semi-Markov model) and after that specifying the best control strategy (optimal strategy) from among possible decisive variants in accordance with the approved criterion (criteria) of the activity evaluation of the system of exploitation for technical objects. In the presented method specifying the optimal strategy for control availability in the technical objects means a choice of a sequence of control decisions made in individual states of modelled exploitation process for which the function being a criterion of evaluation reaches the extreme value. In order to choose the optimal control strategy the implementation of the genetic algorithm was chosen. The opinions were presented on the example of the exploitation process of the means of transport implemented in the real system of the bus municipal transport. The model of the exploitation process for the means of transports was prepared on the basis of the results implemented in the real transport system. The mathematical model of the exploitation process was built taking into consideration the fact that the model of the process constitutes the homogenous semi-Markov process.

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

DEFF Research Database (Denmark)

Kristensen, Anders Ringgaard; Søllested, Thomas Algot

2004-01-01

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

Bearing Degradation Process Prediction Based on the Support Vector Machine and Markov Model

Directory of Open Access Journals (Sweden)

Shaojiang Dong

2014-01-01

Full Text Available Predicting the degradation process of bearings before they reach the failure threshold is extremely important in industry. This paper proposed a novel method based on the support vector machine (SVM and the Markov model to achieve this goal. Firstly, the features are extracted by time and time-frequency domain methods. However, the extracted original features are still with high dimensional and include superfluous information, and the nonlinear multifeatures fusion technique LTSA is used to merge the features and reduces the dimension. Then, based on the extracted features, the SVM model is used to predict the bearings degradation process, and the CAO method is used to determine the embedding dimension of the SVM model. After the bearing degradation process is predicted by SVM model, the Markov model is used to improve the prediction accuracy. The proposed method was validated by two bearing run-to-failure experiments, and the results proved the effectiveness of the methodology.

Markov chain aggregation for agent-based models

CERN Document Server

Banisch, Sven

2016-01-01

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

Markov decision processes: a tool for sequential decision making under uncertainty.

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Zhang Xueqing; Gao Hui

2012-01-01

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

Nonlinearly perturbed semi-Markov processes

CERN Document Server

Silvestrov, Dmitrii

2017-01-01

The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will cont...

An integrated Markov decision process and nested logit consumer response model of air ticket pricing

NARCIS (Netherlands)

Lu, J.; Feng, T.; Timmermans, H.P.J.; Yang, Z.

2017-01-01

The paper attempts to propose an optimal air ticket pricing model during the booking horizon by taking into account passengers' purchasing behavior of air tickets. A Markov decision process incorporating a nested logit consumer response model is established to modeling the dynamic pricing process.

Asymptotics for Estimating Equations in Hidden Markov Models

DEFF Research Database (Denmark)

Hansen, Jørgen Vinsløv; Jensen, Jens Ledet

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...

Rate estimation in partially observed Markov jump processes with measurement errors

OpenAIRE

Amrein, Michael; Kuensch, Hans R.

2010-01-01

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

Markov decision processes in artificial intelligence

CERN Document Server

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 modulated Poisson process models incorporating covariates for rainfall intensity.

Science.gov (United States)

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.

Generalized Boolean logic Driven Markov Processes: A powerful modeling framework for Model-Based Safety Analysis of dynamic repairable and reconfigurable systems

International Nuclear Information System (INIS)

Piriou, Pierre-Yves; Faure, Jean-Marc; Lesage, Jean-Jacques

2017-01-01

This paper presents a modeling framework that permits to describe in an integrated manner the structure of the critical system to analyze, by using an enriched fault tree, the dysfunctional behavior of its components, by means of Markov processes, and the reconfiguration strategies that have been planned to ensure safety and availability, with Moore machines. This framework has been developed from BDMP (Boolean logic Driven Markov Processes), a previous framework for dynamic repairable systems. First, the contribution is motivated by pinpointing the limitations of BDMP to model complex reconfiguration strategies and the failures of the control of these strategies. The syntax and semantics of GBDMP (Generalized Boolean logic Driven Markov Processes) are then formally defined; in particular, an algorithm to analyze the dynamic behavior of a GBDMP model is developed. The modeling capabilities of this framework are illustrated on three representative examples. Last, qualitative and quantitative analysis of GDBMP models highlight the benefits of the approach.

Markov Chains and Markov Processes

OpenAIRE

Ogunbayo, Segun

2016-01-01

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

Markov Chain Modelling for Short-Term NDVI Time Series Forecasting

Directory of Open Access Journals (Sweden)

Stepčenko Artūrs

2016-12-01

Full Text Available In this paper, the NDVI time series forecasting model has been developed based on the use of discrete time, continuous state Markov chain of suitable order. The normalised difference vegetation index (NDVI is an indicator that describes the amount of chlorophyll (the green mass and shows the relative density and health of vegetation; therefore, it is an important variable for vegetation forecasting. A Markov chain is a stochastic process that consists of a state space. This stochastic process undergoes transitions from one state to another in the state space with some probabilities. A Markov chain forecast model is flexible in accommodating various forecast assumptions and structures. The present paper discusses the considerations and techniques in building a Markov chain forecast model at each step. Continuous state Markov chain model is analytically described. Finally, the application of the proposed Markov chain model is illustrated with reference to a set of NDVI time series data.

Segmenting Continuous Motions with Hidden Semi-markov Models and Gaussian Processes

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Tomoaki Nakamura

2017-12-01

Full Text Available Humans divide perceived continuous information into segments to facilitate recognition. For example, humans can segment speech waves into recognizable morphemes. Analogously, continuous motions are segmented into recognizable unit actions. People can divide continuous information into segments without using explicit segment points. This capacity for unsupervised segmentation is also useful for robots, because it enables them to flexibly learn languages, gestures, and actions. In this paper, we propose a Gaussian process-hidden semi-Markov model (GP-HSMM that can divide continuous time series data into segments in an unsupervised manner. Our proposed method consists of a generative model based on the hidden semi-Markov model (HSMM, the emission distributions of which are Gaussian processes (GPs. Continuous time series data is generated by connecting segments generated by the GP. Segmentation can be achieved by using forward filtering-backward sampling to estimate the model's parameters, including the lengths and classes of the segments. In an experiment using the CMU motion capture dataset, we tested GP-HSMM with motion capture data containing simple exercise motions; the results of this experiment showed that the proposed GP-HSMM was comparable with other methods. We also conducted an experiment using karate motion capture data, which is more complex than exercise motion capture data; in this experiment, the segmentation accuracy of GP-HSMM was 0.92, which outperformed other methods.

Timed Comparisons of Semi-Markov Processes

DEFF Research Database (Denmark)

Pedersen, Mathias Ruggaard; Larsen, Kim Guldstrand; Bacci, Giorgio

2018-01-01

-Markov processes, and investigate the question of how to compare two semi-Markov processes with respect to their time-dependent behaviour. To this end, we introduce the relation of being “faster than” between processes and study its algorithmic complexity. Through a connection to probabilistic automata we obtain...

On the entropy of a hidden Markov process.

Science.gov (United States)

Jacquet, Philippe; Seroussi, Gadiel; Szpankowski, Wojciech

2008-05-01

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

Neyman, Markov processes and survival analysis.

Science.gov (United States)

Yang, Grace

2013-07-01

J. Neyman used stochastic processes extensively in his applied work. One example is the Fix and Neyman (F-N) competing risks model (1951) that uses finite homogeneous Markov processes to analyse clinical trials with breast cancer patients. We revisit the F-N model, and compare it with the Kaplan-Meier (K-M) formulation for right censored data. The comparison offers a way to generalize the K-M formulation to include risks of recovery and relapses in the calculation of a patient's survival probability. The generalization is to extend the F-N model to a nonhomogeneous Markov process. Closed-form solutions of the survival probability are available in special cases of the nonhomogeneous processes, like the popular multiple decrement model (including the K-M model) and Chiang's staging model, but these models do not consider recovery and relapses while the F-N model does. An analysis of sero-epidemiology current status data with recurrent events is illustrated. Fix and Neyman used Neyman's RBAN (regular best asymptotic normal) estimates for the risks, and provided a numerical example showing the importance of considering both the survival probability and the length of time of a patient living a normal life in the evaluation of clinical trials. The said extension would result in a complicated model and it is unlikely to find analytical closed-form solutions for survival analysis. With ever increasing computing power, numerical methods offer a viable way of investigating the problem.

Prediction and generation of binary Markov processes: Can a finite-state fox catch a Markov mouse?

Science.gov (United States)

Ruebeck, Joshua B.; James, Ryan G.; Mahoney, John R.; Crutchfield, James P.

2018-01-01

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for different regions of parameter space. We show that a previously proposed generator for a particular set of binary Markov processes is, in fact, not minimal. Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation. We find, for instance, that the difference between prediction and generation is maximized when the process is approximately independently, identically distributed.

Criterion of Semi-Markov Dependent Risk Model

Institute of Scientific and Technical Information of China (English)

Xiao Yun MO; Xiang Qun YANG

2014-01-01

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

Generated dynamics of Markov and quantum processes

CERN Document Server

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...

Projected metastable Markov processes and their estimation with observable operator models

International Nuclear Information System (INIS)

Wu, Hao; Prinz, Jan-Hendrik; Noé, Frank

2015-01-01

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

Nonlinear Markov processes: Deterministic case

International Nuclear Information System (INIS)

Frank, T.D.

2008-01-01

Deterministic Markov processes that exhibit nonlinear transition mechanisms for probability densities are studied. In this context, the following issues are addressed: Markov property, conditional probability densities, propagation of probability densities, multistability in terms of multiple stationary distributions, stability analysis of stationary distributions, and basin of attraction of stationary distribution

Active Learning of Markov Decision Processes for System Verification

DEFF Research Database (Denmark)

Chen, Yingke; Nielsen, Thomas Dyhre

2012-01-01

deterministic Markov decision processes from data by actively guiding the selection of input actions. The algorithm is empirically analyzed by learning system models of slot machines, and it is demonstrated that the proposed active learning procedure can significantly reduce the amount of data required...... demanding process, and this shortcoming has motivated the development of algorithms for automatically learning system models from observed system behaviors. Recently, algorithms have been proposed for learning Markov decision process representations of reactive systems based on alternating sequences...... of input/output observations. While alleviating the problem of manually constructing a system model, the collection/generation of observed system behaviors can also prove demanding. Consequently we seek to minimize the amount of data required. In this paper we propose an algorithm for learning...

Constructing Dynamic Event Trees from Markov Models

International Nuclear Information System (INIS)

Paolo Bucci; Jason Kirschenbaum; Tunc Aldemir; Curtis Smith; Ted Wood

2006-01-01

In the probabilistic risk assessment (PRA) of process plants, Markov models can be used to model accurately the complex dynamic interactions between plant physical process variables (e.g., temperature, pressure, etc.) and the instrumentation and control system that monitors and manages the process. One limitation of this approach that has prevented its use in nuclear power plant PRAs is the difficulty of integrating the results of a Markov analysis into an existing PRA. In this paper, we explore a new approach to the generation of failure scenarios and their compilation into dynamic event trees from a Markov model of the system. These event trees can be integrated into an existing PRA using software tools such as SAPHIRE. To implement our approach, we first construct a discrete-time Markov chain modeling the system of interest by: (a) partitioning the process variable state space into magnitude intervals (cells), (b) using analytical equations or a system simulator to determine the transition probabilities between the cells through the cell-to-cell mapping technique, and, (c) using given failure/repair data for all the components of interest. The Markov transition matrix thus generated can be thought of as a process model describing the stochastic dynamic behavior of the finite-state system. We can therefore search the state space starting from a set of initial states to explore all possible paths to failure (scenarios) with associated probabilities. We can also construct event trees of arbitrary depth by tracing paths from a chosen initiating event and recording the following events while keeping track of the probabilities associated with each branch in the tree. As an example of our approach, we use the simple level control system often used as benchmark in the literature with one process variable (liquid level in a tank), and three control units: a drain unit and two supply units. Each unit includes a separate level sensor to observe the liquid level in the tank

Benchmarking of a Markov multizone model of contaminant transport.

Science.gov (United States)

Jones, Rachael M; Nicas, Mark

2014-10-01

A Markov chain model previously applied to the simulation of advection and diffusion process of gaseous contaminants is extended to three-dimensional transport of particulates in indoor environments. The model framework and assumptions are described. The performance of the Markov model is benchmarked against simple conventional models of contaminant transport. The Markov model is able to replicate elutriation predictions of particle deposition with distance from a point source, and the stirred settling of respirable particles. Comparisons with turbulent eddy diffusion models indicate that the Markov model exhibits numerical diffusion in the first seconds after release, but over time accurately predicts mean lateral dispersion. The Markov model exhibits some instability with grid length aspect when turbulence is incorporated by way of the turbulent diffusion coefficient, and advection is present. However, the magnitude of prediction error may be tolerable for some applications and can be avoided by incorporating turbulence by way of fluctuating velocity (e.g. turbulence intensity). © The Author 2014. Published by Oxford University Press on behalf of the British Occupational Hygiene Society.

Context Tree Estimation in Variable Length Hidden Markov Models

OpenAIRE

Dumont, Thierry

2011-01-01

We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove that the estimator is strongly consistent. This uses information-theoretic mixture inequalities in the spirit of Finesso and Lorenzo(Consistent estimation of the order for Markov and hidden Markov chains(1990)) and E.Gassiat and S.Boucheron (Optimal error exp...

Monte Carlo Simulation of Markov, Semi-Markov, and Generalized Semi- Markov Processes in Probabilistic Risk Assessment

Science.gov (United States)

English, Thomas

2005-01-01

A standard tool of reliability analysis used at NASA-JSC is the event tree. An event tree is simply a probability tree, with the probabilities determining the next step through the tree specified at each node. The nodal probabilities are determined by a reliability study of the physical system at work for a particular node. The reliability study performed at a node is typically referred to as a fault tree analysis, with the potential of a fault tree existing.for each node on the event tree. When examining an event tree it is obvious why the event tree/fault tree approach has been adopted. Typical event trees are quite complex in nature, and the event tree/fault tree approach provides a systematic and organized approach to reliability analysis. The purpose of this study was two fold. Firstly, we wanted to explore the possibility that a semi-Markov process can create dependencies between sojourn times (the times it takes to transition from one state to the next) that can decrease the uncertainty when estimating time to failures. Using a generalized semi-Markov model, we studied a four element reliability model and were able to demonstrate such sojourn time dependencies. Secondly, we wanted to study the use of semi-Markov processes to introduce a time variable into the event tree diagrams that are commonly developed in PRA (Probabilistic Risk Assessment) analyses. Event tree end states which change with time are more representative of failure scenarios than are the usual static probability-derived end states.

Non-homogeneous Markov process models with informative observations with an application to Alzheimer's disease.

Science.gov (United States)

Chen, Baojiang; Zhou, Xiao-Hua

2011-05-01

Identifying risk factors for transition rates among normal cognition, mildly cognitive impairment, dementia and death in an Alzheimer's disease study is very important. It is known that transition rates among these states are strongly time dependent. While Markov process models are often used to describe these disease progressions, the literature mainly focuses on time homogeneous processes, and limited tools are available for dealing with non-homogeneity. Further, patients may choose when they want to visit the clinics, which creates informative observations. In this paper, we develop methods to deal with non-homogeneous Markov processes through time scale transformation when observation times are pre-planned with some observations missing. Maximum likelihood estimation via the EM algorithm is derived for parameter estimation. Simulation studies demonstrate that the proposed method works well under a variety of situations. An application to the Alzheimer's disease study identifies that there is a significant increase in transition rates as a function of time. Furthermore, our models reveal that the non-ignorable missing mechanism is perhaps reasonable. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bayesian analysis of Markov point processes

DEFF Research Database (Denmark)

Berthelsen, Kasper Klitgaard; Møller, Jesper

2006-01-01

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

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.

NonMarkov Ito Processes with 1- state memory

Science.gov (United States)

McCauley, Joseph L.

2010-08-01

A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.

Quantum Markov processes and applications in many-body systems

International Nuclear Information System (INIS)

Temme, P. K.

2010-01-01

also gives access to the computation of their static properties. After this, we turn to an investigation of classical non-equilibrium steady states with methods derived from quantum information theory. We construct a special class of matrix product states that exhibit correlations which can best be understood in terms of classical Markov processes. Finally, we investigate the transport properties of non-equilibrium steady states. The dynamical equations are constructed in such a manner that they allow for both stochastic as well as coherent transport in the same formal framework. It is therefore possible to compare different forms of transport within the same model. (author) [de

Modeling dyadic processes using Hidden Markov Models: A time series approach to mother-infant interactions during infant immunization.

Science.gov (United States)

Stifter, Cynthia A; Rovine, Michael

2015-01-01

The focus of the present longitudinal study, to examine mother-infant interaction during the administration of immunizations at two and six months of age, used hidden Markov modeling, a time series approach that produces latent states to describe how mothers and infants work together to bring the infant to a soothed state. Results revealed a 4-state model for the dyadic responses to a two-month inoculation whereas a 6-state model best described the dyadic process at six months. Two of the states at two months and three of the states at six months suggested a progression from high intensity crying to no crying with parents using vestibular and auditory soothing methods. The use of feeding and/or pacifying to soothe the infant characterized one two-month state and two six-month states. These data indicate that with maturation and experience, the mother-infant dyad is becoming more organized around the soothing interaction. Using hidden Markov modeling to describe individual differences, as well as normative processes, is also presented and discussed.

Modeling treatment of ischemic heart disease with partially observable Markov decision processes.

Science.gov (United States)

Hauskrecht, M; Fraser, H

1998-01-01

Diagnosis of a disease and its treatment are not separate, one-shot activities. Instead they are very often dependent and interleaved over time, mostly due to uncertainty about the underlying disease, uncertainty associated with the response of a patient to the treatment and varying cost of different diagnostic (investigative) and treatment procedures. The framework of Partially observable Markov decision processes (POMDPs) developed and used in operations research, control theory and artificial intelligence communities is particularly suitable for modeling such a complex decision process. In the paper, we show how the POMDP framework could be used to model and solve the problem of the management of patients with ischemic heart disease, and point out modeling advantages of the framework over standard decision formalisms.

A Novel Analytical Model for Network-on-Chip using Semi-Markov Process

Directory of Open Access Journals (Sweden)

WANG, J.

2011-02-01

Full Text Available Network-on-Chip (NoC communication architecture is proposed to resolve the bottleneck of Multi-processor communication in a single chip. In this paper, a performance analytical model using Semi-Markov Process (SMP is presented to obtain the NoC performance. More precisely, given the related parameters, SMP is used to describe the behavior of each channel and the header flit routing time on each channel can be calculated by analyzing the SMP. Then, the average packet latency in NoC can be calculated. The accuracy of our model is illustrated through simulation. Indeed, the experimental results show that the proposed model can be used to obtain NoC performance and it performs better than the state-of-art models. Therefore, our model can be used as a useful tool to guide the NoC design process.

Detecting Faults By Use Of Hidden Markov Models

Science.gov (United States)

Smyth, Padhraic J.

1995-01-01

Frequency of false alarms reduced. Faults in complicated dynamic system (e.g., antenna-aiming system, telecommunication network, or human heart) detected automatically by method of automated, continuous monitoring. Obtains time-series data by sampling multiple sensor outputs at discrete intervals of t and processes data via algorithm determining whether system in normal or faulty state. Algorithm implements, among other things, hidden first-order temporal Markov model of states of system. Mathematical model of dynamics of system not needed. Present method is "prior" method mentioned in "Improved Hidden-Markov-Model Method of Detecting Faults" (NPO-18982).

Markov processes characterization and convergence

CERN Document Server

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...

Performance Modeling of Communication Networks with Markov Chains

CERN Document Server

Mo, Jeonghoon

2010-01-01

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

Prediction of pipeline corrosion rate based on grey Markov models

International Nuclear Information System (INIS)

Chen Yonghong; Zhang Dafa; Peng Guichu; Wang Yuemin

2009-01-01

Based on the model that combined by grey model and Markov model, the prediction of corrosion rate of nuclear power pipeline was studied. Works were done to improve the grey model, and the optimization unbiased grey model was obtained. This new model was used to predict the tendency of corrosion rate, and the Markov model was used to predict the residual errors. In order to improve the prediction precision, rolling operation method was used in these prediction processes. The results indicate that the improvement to the grey model is effective and the prediction precision of the new model combined by the optimization unbiased grey model and Markov model is better, and the use of rolling operation method may improve the prediction precision further. (authors)

Operations and support cost modeling using Markov chains

Science.gov (United States)

Unal, Resit

1989-01-01

Systems for future missions will be selected with life cycle costs (LCC) as a primary evaluation criterion. This reflects the current realization that only systems which are considered affordable will be built in the future due to the national budget constaints. Such an environment calls for innovative cost modeling techniques which address all of the phases a space system goes through during its life cycle, namely: design and development, fabrication, operations and support; and retirement. A significant portion of the LCC for reusable systems are generated during the operations and support phase (OS). Typically, OS costs can account for 60 to 80 percent of the total LCC. Clearly, OS costs are wholly determined or at least strongly influenced by decisions made during the design and development phases of the project. As a result OS costs need to be considered and estimated early in the conceptual phase. To be effective, an OS cost estimating model needs to account for actual instead of ideal processes by associating cost elements with probabilities. One approach that may be suitable for OS cost modeling is the use of the Markov Chain Process. Markov chains are an important method of probabilistic analysis for operations research analysts but they are rarely used for life cycle cost analysis. This research effort evaluates the use of Markov Chains in LCC analysis by developing OS cost model for a hypothetical reusable space transportation vehicle (HSTV) and suggests further uses of the Markov Chain process as a design-aid tool.

Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

OpenAIRE

Valor, A.; Caleyo, F.; Alfonso, L.; Velázquez, J. C.; Hallen, J. M.

2013-01-01

The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure ...

Tornadoes and related damage costs: statistical modeling with a semi-Markov approach

OpenAIRE

Corini, Chiara; D'Amico, Guglielmo; Petroni, Filippo; Prattico, Flavio; Manca, Raimondo

2015-01-01

We propose a statistical approach to tornadoes modeling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modeling the tornadoes intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornadoes intensity into six states, it is possible to model the tornadoes intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reprod...

Markov processes from K. Ito's perspective (AM-155)

CERN Document Server

Stroock, Daniel W

2003-01-01

Kiyosi Itô''s greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô''s program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov''s approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed incremen

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

CERN Document Server

Barbu, Vlad

2008-01-01

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

A study on the stochastic model for nuclide transport in the fractured porous rock using continuous time Markov process

International Nuclear Information System (INIS)

Lee, Youn Myoung

1995-02-01

As a newly approaching model, a stochastic model using continuous time Markov process for nuclide decay chain transport of arbitrary length in the fractured porous rock medium has been proposed, by which the need for solving a set of partial differential equations corresponding to various sets of side conditions can be avoided. Once the single planar fracture in the rock matrix is represented by a series of finite number of compartments having region wise constant parameter values in them, the medium is continuous in view of various processes associated with nuclide transport but discrete in medium space and such geologic system is assumed to have Markov property, since the Markov process requires that only the present value of the time dependent random variable be known to determine the future value of random variable, nuclide transport in the medium can then be modeled as a continuous time Markov process. Processes that are involved in nuclide transport are advective transport due to groundwater flow, diffusion into the rock matrix, adsorption onto the wall of the fracture and within the pores in the rock matrix, and radioactive decay chain. The transition probabilities for nuclide from the transition intensities between and out of the compartments are represented utilizing Chapman-Kolmogorov equation, through which the expectation and the variance of nuclide distribution for each compartment or the fractured rock medium can be obtained. Some comparisons between Markov process model developed in this work and available analytical solutions for one-dimensional layered porous medium, fractured medium with rock matrix diffusion, and porous medium considering three member nuclide decay chain without rock matrix diffusion have been made showing comparatively good agreement for all cases. To verify the model developed in this work another comparative study was also made by fitting the experimental data obtained with NaLS and uranine running in the artificial fractured

Efficient Modelling and Generation of Markov Automata

NARCIS (Netherlands)

Koutny, M.; Timmer, Mark; Ulidowski, I.; Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette

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

Markov chain modelling of pitting corrosion in underground pipelines

Energy Technology Data Exchange (ETDEWEB)

Caleyo, F. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)], E-mail: fcaleyo@gmail.com; Velazquez, J.C. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico); Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 La Habana (Cuba); Hallen, J.M. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)

2009-09-15

A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.

Markov chain modelling of pitting corrosion in underground pipelines

International Nuclear Information System (INIS)

Caleyo, F.; Velazquez, J.C.; Valor, A.; Hallen, J.M.

2009-01-01

A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.

Nuclide transport of decay chain in the fractured rock medium: a model using continuous time Markov process

International Nuclear Information System (INIS)

Younmyoung Lee; Kunjai Lee

1995-01-01

A model using continuous time Markov process for nuclide transport of decay chain of arbitrary length in the fractured rock medium has been developed. Considering the fracture in the rock matrix as a finite number of compartments, the transition probability for nuclide from the transition intensity between and out of the compartments is represented utilizing Chapman-Kolmogorov equation, with which the expectation and the variance of nuclide distribution for the fractured rock medium could be obtained. A comparison between continuous time Markov process model and available analytical solutions for the nuclide transport of three decay chains without rock matrix diffusion has been made showing comparatively good agreement. Fittings with experimental breakthrough curves obtained with nonsorbing materials such as NaLS and uranine in the artificial fractured rock are also made. (author)

Exact solution of the hidden Markov processes

Science.gov (United States)

Saakian, David B.

2017-11-01

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

Application of Hidden Markov Models in Biomolecular Simulations.

Science.gov (United States)

Shukla, Saurabh; Shamsi, Zahra; Moffett, Alexander S; Selvam, Balaji; Shukla, Diwakar

2017-01-01

Hidden Markov models (HMMs) provide a framework to analyze large trajectories of biomolecular simulation datasets. HMMs decompose the conformational space of a biological molecule into finite number of states that interconvert among each other with certain rates. HMMs simplify long timescale trajectories for human comprehension, and allow comparison of simulations with experimental data. In this chapter, we provide an overview of building HMMs for analyzing bimolecular simulation datasets. We demonstrate the procedure for building a Hidden Markov model for Met-enkephalin peptide simulation dataset and compare the timescales of the process.

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.

Hidden Markov models: the best models for forager movements?

Science.gov (United States)

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

2013-01-01

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

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.

Testing the Adequacy of a Semi-Markov Process

Science.gov (United States)

2015-09-17

classical Brownian motion are two common examples of martingales. Submartingales and supermartingales are two extended classes of martingales. They... movements using Semi-Markov processes,” Tourism Management, Vol. 32, No. 4, 2011, pp. 844–851. [4] Titman, A. C. and Sharples, L. D., “Model

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

Science.gov (United States)

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

2010-08-01

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

Tornadoes and related damage costs: statistical modelling with a semi-Markov approach

Directory of Open Access Journals (Sweden)

Guglielmo D’Amico

2016-09-01

Full Text Available We propose a statistical approach to modelling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modelling the tornado intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornado intensity into six states, it is possible to model the tornado intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reproduce the duration effect that is detected in tornado occurrence. The superiority of the semi-Markov model as compared to the Markov chain model is also affirmed by means of a statistical test of hypothesis. As an application, we compute the expected value and the variance of the costs generated by the tornadoes over a given time interval in a given area. The paper contributes to the literature by demonstrating that semi-Markov models represent an effective tool for physical analysis of tornadoes as well as for the estimation of the economic damages to human things.

An Approach of Diagnosis Based On The Hidden Markov Chains Model

Directory of Open Access Journals (Sweden)

Karim Bouamrane

2008-07-01

Full Text Available Diagnosis is a key element in industrial system maintenance process performance. A diagnosis tool is proposed allowing the maintenance operators capitalizing on the knowledge of their trade and subdividing it for better performance improvement and intervention effectiveness within the maintenance process service. The Tool is based on the Markov Chain Model and more precisely the Hidden Markov Chains (HMC which has the system failures determination advantage, taking into account the causal relations, stochastic context modeling of their dynamics and providing a relevant diagnosis help by their ability of dubious information use. Since the FMEA method is a well adapted artificial intelligence field, the modeling with Markov Chains is carried out with its assistance. Recently, a dynamic programming recursive algorithm, called 'Viterbi Algorithm', is being used in the Hidden Markov Chains field. This algorithm provides as input to the HMC a set of system observed effects and generates at exit the various causes having caused the loss from one or several system functions.

Hierarchical Multiple Markov Chain Model for Unsupervised Texture Segmentation

Czech Academy of Sciences Publication Activity Database

Scarpa, G.; Gaetano, R.; Haindl, Michal; Zerubia, J.

2009-01-01

Roč. 18, č. 8 (2009), s. 1830-1843 ISSN 1057-7149 R&D Projects: GA ČR GA102/08/0593 EU Projects: European Commission(XE) 507752 - MUSCLE Institutional research plan: CEZ:AV0Z10750506 Keywords : Classification * texture analysis * segmentation * hierarchical image models * Markov process Subject RIV: BD - Theory of Information Impact factor: 2.848, year: 2009 http://library.utia.cas.cz/separaty/2009/RO/haindl-hierarchical multiple markov chain model for unsupervised texture segmentation.pdf

An integral equation approach to the interval reliability of systems modelled by finite semi-Markov processes

International Nuclear Information System (INIS)

Csenki, A.

1995-01-01

The interval reliability for a repairable system which alternates between working and repair periods is defined as the probability of the system being functional throughout a given time interval. In this paper, a set of integral equations is derived for this dependability measure, under the assumption that the system is modelled by an irreducible finite semi-Markov process. The result is applied to the semi-Markov model of a two-unit system with sequential preventive maintenance. The method used for the numerical solution of the resulting system of integral equations is a two-point trapezoidal rule. The system of implementation is the matrix computation package MATLAB on the Apple Macintosh SE/30. The numerical results are discussed and compared with those from simulation

Markov chains models, algorithms and applications

CERN Document Server

Ching, Wai-Ki; Ng, Michael K; Siu, Tak-Kuen

2013-01-01

This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters.  Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods

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

Directory of Open Access Journals (Sweden)

Robert Adam Sobolewski

2015-09-01

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

Fracture Mechanical Markov Chain Crack Growth Model

DEFF Research Database (Denmark)

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

1991-01-01

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

An open Markov chain scheme model for a credit consumption portfolio fed by ARIMA and SARMA processes

Science.gov (United States)

Esquível, Manuel L.; Fernandes, José Moniz; Guerreiro, Gracinda R.

2016-06-01

We introduce a schematic formalism for the time evolution of a random population entering some set of classes and such that each member of the population evolves among these classes according to a scheme based on a Markov chain model. We consider that the flow of incoming members is modeled by a time series and we detail the time series structure of the elements in each of the classes. We present a practical application to data from a credit portfolio of a Cape Verdian bank; after modeling the entering population in two different ways - namely as an ARIMA process and as a deterministic sigmoid type trend plus a SARMA process for the residues - we simulate the behavior of the population and compare the results. We get that the second method is more accurate in describing the behavior of the populations when compared to the observed values in a direct simulation of the Markov chain.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models.

Science.gov (United States)

Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I

2018-01-01

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

Combining experimental and simulation data of molecular processes via augmented Markov models.

Science.gov (United States)

Olsson, Simon; Wu, Hao; Paul, Fabian; Clementi, Cecilia; Noé, Frank

2017-08-01

Accurate mechanistic description of structural changes in biomolecules is an increasingly important topic in structural and chemical biology. Markov models have emerged as a powerful way to approximate the molecular kinetics of large biomolecules while keeping full structural resolution in a divide-and-conquer fashion. However, the accuracy of these models is limited by that of the force fields used to generate the underlying molecular dynamics (MD) simulation data. Whereas the quality of classical MD force fields has improved significantly in recent years, remaining errors in the Boltzmann weights are still on the order of a few [Formula: see text], which may lead to significant discrepancies when comparing to experimentally measured rates or state populations. Here we take the view that simulations using a sufficiently good force-field sample conformations that are valid but have inaccurate weights, yet these weights may be made accurate by incorporating experimental data a posteriori. To do so, we propose augmented Markov models (AMMs), an approach that combines concepts from probability theory and information theory to consistently treat systematic force-field error and statistical errors in simulation and experiment. Our results demonstrate that AMMs can reconcile conflicting results for protein mechanisms obtained by different force fields and correct for a wide range of stationary and dynamical observables even when only equilibrium measurements are incorporated into the estimation process. This approach constitutes a unique avenue to combine experiment and computation into integrative models of biomolecular structure and dynamics.

The Candy model revisited: Markov properties and inference

NARCIS (Netherlands)

M.N.M. van Lieshout (Marie-Colette); R.S. Stoica

2001-01-01

textabstractThis paper studies the Candy model, a marked point process introduced by Stoica et al. (2000). We prove Ruelle and local stability, investigate its Markov properties, and discuss how the model may be sampled. Finally, we consider estimation of the model parameters and present some

A hierarchical Markov decision process modeling feeding and marketing decisions of growing pigs

DEFF Research Database (Denmark)

Pourmoayed, Reza; Nielsen, Lars Relund; Kristensen, Anders Ringgaard

2016-01-01

Feeding is the most important cost in the production of growing pigs and has a direct impact on the marketing decisions, growth and the final quality of the meat. In this paper, we address the sequential decision problem of when to change the feed-mix within a finisher pig pen and when to pick pigs...... for marketing. We formulate a hierarchical Markov decision process with three levels representing the decision process. The model considers decisions related to feeding and marketing and finds the optimal decision given the current state of the pen. The state of the system is based on information from on...

Prognostics for Steam Generator Tube Rupture using Markov Chain model

International Nuclear Information System (INIS)

Kim, Gibeom; Heo, Gyunyoung; Kim, Hyeonmin

2016-01-01

This paper will describe the prognostics method for evaluating and forecasting the ageing effect and demonstrate the procedure of prognostics for the Steam Generator Tube Rupture (SGTR) accident. Authors will propose the data-driven method so called MCMC (Markov Chain Monte Carlo) which is preferred to the physical-model method in terms of flexibility and availability. Degradation data is represented as growth of burst probability over time. Markov chain model is performed based on transition probability of state. And the state must be discrete variable. Therefore, burst probability that is continuous variable have to be changed into discrete variable to apply Markov chain model to the degradation data. The Markov chain model which is one of prognostics methods was described and the pilot demonstration for a SGTR accident was performed as a case study. The Markov chain model is strong since it is possible to be performed without physical models as long as enough data are available. However, in the case of the discrete Markov chain used in this study, there must be loss of information while the given data is discretized and assigned to the finite number of states. In this process, original information might not be reflected on prediction sufficiently. This should be noted as the limitation of discrete models. Now we will be studying on other prognostics methods such as GPM (General Path Model) which is also data-driven method as well as the particle filer which belongs to physical-model method and conducting comparison analysis

Pathwise duals of monotone and additive Markov processes

Czech Academy of Sciences Publication Activity Database

Sturm, A.; Swart, Jan M.

-, - (2018) ISSN 0894-9840 R&D Projects: GA ČR GAP201/12/2613 Institutional support: RVO:67985556 Keywords : pathwise duality * monotone Markov process * additive Markov process * interacting particle system Subject RIV: BA - General Mathematics Impact factor: 0.854, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/swart-0465436.pdf

Markov Models for Handwriting Recognition

CERN Document Server

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

Model Checking Markov Reward Models with Impulse Rewards

NARCIS (Netherlands)

Cloth, Lucia; Katoen, Joost-Pieter; Khattri, Maneesh; Pulungan, Reza; Bondavalli, Andrea; Haverkort, Boudewijn; Tang, Dong

This paper considers model checking of Markov reward models (MRMs), continuous-time Markov chains with state rewards as well as impulse rewards. The reward extension of the logic CSL (Continuous Stochastic Logic) is interpreted over such MRMs, and two numerical algorithms are provided to check the

A Novel Method for Decoding Any High-Order Hidden Markov Model

Directory of Open Access Journals (Sweden)

Fei Ye

2014-01-01

Full Text Available This paper proposes a novel method for decoding any high-order hidden Markov model. First, the high-order hidden Markov model is transformed into an equivalent first-order hidden Markov model by Hadar’s transformation. Next, the optimal state sequence of the equivalent first-order hidden Markov model is recognized by the existing Viterbi algorithm of the first-order hidden Markov model. Finally, the optimal state sequence of the high-order hidden Markov model is inferred from the optimal state sequence of the equivalent first-order hidden Markov model. This method provides a unified algorithm framework for decoding hidden Markov models including the first-order hidden Markov model and any high-order hidden Markov model.

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...... 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...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code....

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...... 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...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code. © 2014 Elsevier...

Comparison of Langevin and Markov channel noise models for neuronal signal generation.

Science.gov (United States)

Sengupta, B; Laughlin, S B; Niven, J E

2010-01-01

The stochastic opening and closing of voltage-gated ion channels produce noise in neurons. The effect of this noise on the neuronal performance has been modeled using either an approximate or Langevin model based on stochastic differential equations or an exact model based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produced by the Markov model remains unclear. Here we present a comparison between Langevin and Markov models of channel noise in neurons using single compartment Hodgkin-Huxley models containing either Na+ and K+, or only K+ voltage-gated ion channels. The performance of the Langevin and Markov models was quantified over a range of stimulus statistics, membrane areas, and channel numbers. We find that in comparison to the Markov model, the Langevin model underestimates the noise contributed by voltage-gated ion channels, overestimating information rates for both spiking and nonspiking membranes. Even with increasing numbers of channels, the difference between the two models persists. This suggests that the Langevin model may not be suitable for accurately simulating channel noise in neurons, even in simulations with large numbers of ion channels.

The Markov process admits a consistent steady-state thermodynamic formalism

Science.gov (United States)

Peng, Liangrong; Zhu, Yi; Hong, Liu

2018-01-01

The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.

A Markov Chain Model for Contagion

Directory of Open Access Journals (Sweden)

Angelos Dassios

2014-11-01

Full Text Available We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the clustering arrival of events, such as jumps, bankruptcies, crises and catastrophes in finance, insurance and economics with both internal contagion risk and external common risk. Key distributional properties, such as the moments and probability generating functions, for this process are derived. Some special cases with explicit results and numerical examples and the motivation for further actuarial applications are also discussed. The model can be considered a generalisation of the dynamic contagion process introduced by Dassios and Zhao (2011.

Nuclear security assessment with Markov model approach

International Nuclear Information System (INIS)

Suzuki, Mitsutoshi; Terao, Norichika

2013-01-01

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

Markov processes an introduction for physical scientists

CERN Document Server

Gillespie, Daniel T

1991-01-01

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

Markov LIMID processes for representing and solving renewal problems

DEFF Research Database (Denmark)

Jørgensen, Erik; Kristensen, Anders Ringgaard; Nilsson, Dennis

2014-01-01

to model a Markov Limid Process, where each TemLimid represents a macro action. Algorithms are presented to find optimal plans for a sequence of such macro actions. Use of algorithms is illustrated based on an extended version of an example from pig production originally used to introduce the Limid concept...

Stochastic modeling of pitting corrosion in underground pipelines using Markov chains

Energy Technology Data Exchange (ETDEWEB)

Velazquez, J.C.; Caleyo, F.; Hallen, J.M.; Araujo, J.E. [Instituto Politecnico Nacional (IPN), Mexico D.F. (Mexico). Escuela Superior de Ingenieria Quimica e Industrias Extractivas (ESIQIE); Valor, A. [Universidad de La Habana, La Habana (Cuba)

2009-07-01

A non-homogenous, linear growth (pure birth) Markov process, with discrete states in continuous time, has been used to model external pitting corrosion in underground pipelines. The transition probability function for the pit depth is obtained from the analytical solution of the forward Kolmogorov equations for this process. The parameters of the transition probability function between depth states can be identified from the observed time evolution of the mean of the pit depth distribution. Monte Carlo simulations were used to predict the time evolution of the mean value of the pit depth distribution in soils with different physicochemical characteristics. The simulated distributions have been used to create an empirical Markov-chain-based stochastic model for predicting the evolution of pitting corrosion from the observed properties of the soil in contact with the pipeline. Real- life case studies, involving simulated and measured pit depth distributions are presented to illustrate the application of the proposed Markov chains model. (author)

Segmentation of laser range radar images using hidden Markov field models

International Nuclear Information System (INIS)

Pucar, P.

1993-01-01

Segmentation of images in the context of model based stochastic techniques is connected with high, very often unpracticle computational complexity. The objective with this thesis is to take the models used in model based image processing, simplify and use them in suboptimal, but not computationally demanding algorithms. Algorithms that are essentially one-dimensional, and their extensions to two dimensions are given. The model used in this thesis is the well known hidden Markov model. Estimation of the number of hidden states from observed data is a problem that is addressed. The state order estimation problem is of general interest and is not specifically connected to image processing. An investigation of three state order estimation techniques for hidden Markov models is given. 76 refs

Zipf exponent of trajectory distribution in the hidden Markov model

Science.gov (United States)

Bochkarev, V. V.; Lerner, E. Yu

2014-03-01

This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.

Zipf exponent of trajectory distribution in the hidden Markov model

International Nuclear Information System (INIS)

Bochkarev, V V; Lerner, E Yu

2014-01-01

This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different

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...

Efficient Modelling and Generation of Markov Automata (extended version)

NARCIS (Netherlands)

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

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

Neuroevolution Mechanism for Hidden Markov Model

Directory of Open Access Journals (Sweden)

Nabil M. Hewahi

2011-12-01

Full Text Available Hidden Markov Model (HMM is a statistical model based on probabilities. HMM is becoming one of the major models involved in many applications such as natural language
processing, handwritten recognition, image processing, prediction systems and many more. In this research we are concerned with finding out the best HMM for a certain application domain. We propose a neuroevolution process that is based first on converting the HMM to a neural network, then generating many neural networks at random where each represents a HMM. We proceed by
applying genetic operators to obtain new set of neural networks where each represents HMMs, and updating the population. Finally select the best neural network based on a fitness function.

A Multi-stage Representation of Cell Proliferation as a Markov Process.

Science.gov (United States)

Yates, Christian A; Ford, Matthew J; Mort, Richard L

2017-12-01

The stochastic simulation algorithm commonly known as Gillespie's algorithm (originally derived for modelling well-mixed systems of chemical reactions) is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular level it is often reasonable to assume that times between successive reaction/interaction events are exponentially distributed and can be appropriately modelled as a Markov process and hence simulated by the Gillespie algorithm. However, Gillespie's algorithm is routinely applied to model biological systems for which it was never intended. In particular, processes in which cell proliferation is important (e.g. embryonic development, cancer formation) should not be simulated naively using the Gillespie algorithm since the history-dependent nature of the cell cycle breaks the Markov process. The variance in experimentally measured cell cycle times is far less than in an exponential cell cycle time distribution with the same mean.Here we suggest a method of modelling the cell cycle that restores the memoryless property to the system and is therefore consistent with simulation via the Gillespie algorithm. By breaking the cell cycle into a number of independent exponentially distributed stages, we can restore the Markov property at the same time as more accurately approximating the appropriate cell cycle time distributions. The consequences of our revised mathematical model are explored analytically as far as possible. We demonstrate the importance of employing the correct cell cycle time distribution by recapitulating the results from two models incorporating cellular proliferation (one spatial and one non-spatial) and demonstrating that changing the cell cycle time distribution makes quantitative and qualitative differences to the outcome of the models. Our adaptation will allow modellers and experimentalists alike to appropriately represent cellular

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...

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

Science.gov (United States)

Nickelsen, Daniel

2017-07-01

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

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

DEFF Research Database (Denmark)

Kristensen, Anders Ringgaard; Søllested, Thomas Algot

2004-01-01

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

Discrete-time semi-Markov modeling of human papillomavirus persistence

Science.gov (United States)

Mitchell, C. E.; Hudgens, M. G.; King, C. C.; Cu-Uvin, S.; Lo, Y.; Rompalo, A.; Sobel, J.; Smith, J. S.

2011-01-01

Multi-state modeling is often employed to describe the progression of a disease process. In epidemiological studies of certain diseases, the disease state is typically only observed at periodic clinical visits, producing incomplete longitudinal data. In this paper we consider fitting semi-Markov models to estimate the persistence of human papillomavirus (HPV) type-specific infection in studies where the status of HPV type(s) is assessed periodically. Simulation study results are presented indicating the semi-Markov estimator is more accurate than an estimator currently used in the HPV literature. The methods are illustrated using data from the HIV Epidemiology Research Study (HERS). PMID:21538985

A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.

Science.gov (United States)

van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F

2013-08-01

Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

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...

Phasic Triplet Markov Chains.

Science.gov (United States)

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

2014-11-01

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

Extracting Markov Models of Peptide Conformational Dynamics from Simulation Data.

Science.gov (United States)

Schultheis, Verena; Hirschberger, Thomas; Carstens, Heiko; Tavan, Paul

2005-07-01

A high-dimensional time series obtained by simulating a complex and stochastic dynamical system (like a peptide in solution) may code an underlying multiple-state Markov process. We present a computational approach to most plausibly identify and reconstruct this process from the simulated trajectory. Using a mixture of normal distributions we first construct a maximum likelihood estimate of the point density associated with this time series and thus obtain a density-oriented partition of the data space. This discretization allows us to estimate the transfer operator as a matrix of moderate dimension at sufficient statistics. A nonlinear dynamics involving that matrix and, alternatively, a deterministic coarse-graining procedure are employed to construct respective hierarchies of Markov models, from which the model most plausibly mapping the generating stochastic process is selected by consideration of certain observables. Within both procedures the data are classified in terms of prototypical points, the conformations, marking the various Markov states. As a typical example, the approach is applied to analyze the conformational dynamics of a tripeptide in solution. The corresponding high-dimensional time series has been obtained from an extended molecular dynamics simulation.

Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy

CERN Document Server

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 ...

Hidden-Markov-Model Analysis Of Telemanipulator Data

Science.gov (United States)

Hannaford, Blake; Lee, Paul

1991-01-01

Mathematical model and procedure based on hidden-Markov-model concept undergoing development for use in analysis and prediction of outputs of force and torque sensors of telerobotic manipulators. In model, overall task broken down into subgoals, and transition probabilities encode ease with which operator completes each subgoal. Process portion of model encodes task-sequence/subgoal structure, and probability-density functions for forces and torques associated with each state of manipulation encode sensor signals that one expects to observe at subgoal. Parameters of model constructed from engineering knowledge of task.

Markov Decision Processes in Practice

NARCIS (Netherlands)

Boucherie, Richardus J.; van Dijk, N.M.

2017-01-01

It is over 30 years ago since D.J. White started his series of surveys on practical applications of Markov decision processes (MDP), over 20 years after the phenomenal book by Martin Puterman on the theory of MDP, and over 10 years since Eugene A. Feinberg and Adam Shwartz published their Handbook

Bisimulation on Markov Processes over Arbitrary Measurable Spaces

DEFF Research Database (Denmark)

Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand

2014-01-01

We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates with a mea......We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates...

Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study.

Science.gov (United States)

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. © 2015, The International Biometric Society.

On mean reward variance in semi-Markov processes

Czech Academy of Sciences Publication Activity Database

Sladký, Karel

2005-01-01

Roč. 62, č. 3 (2005), s. 387-397 ISSN 1432-2994 R&D Projects: GA ČR(CZ) GA402/05/0115; GA ČR(CZ) GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : Markov and semi-Markov processes with rewards * variance of cumulative reward * asymptotic behaviour Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.259, year: 2005

Perturbation approach to scaled type Markov renewal processes with infinite mean

OpenAIRE

Pajor-Gyulai, Zsolt; Szász, Domokos

2010-01-01

Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary interest here is the asymptotic distribution of the Markovian parameter at time t \\to \\infty. The limit, of course, depends on the stationary distribution of the Markov chain. The results, however, are essentially different depending on whether the expectation...

Continuous-Time Semi-Markov Models in Health Economic Decision Making: An Illustrative Example in Heart Failure Disease Management.

Science.gov (United States)

Cao, Qi; Buskens, Erik; Feenstra, Talitha; Jaarsma, Tiny; Hillege, Hans; Postmus, Douwe

2016-01-01

Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease progression can often be obtained by assuming that the future state transitions do not depend only on the present state (Markov assumption) but also on the past through time since entry in the present state. Despite that these so-called semi-Markov models are still relatively straightforward to specify and implement, they are not yet routinely applied in health economic evaluation to assess the cost-effectiveness of alternative interventions. To facilitate a better understanding of this type of model among applied health economic analysts, the first part of this article provides a detailed discussion of what the semi-Markov model entails and how such models can be specified in an intuitive way by adopting an approach called vertical modeling. In the second part of the article, we use this approach to construct a semi-Markov model for assessing the long-term cost-effectiveness of 3 disease management programs for heart failure. Compared with a standard Markov model with the same disease states, our proposed semi-Markov model fitted the observed data much better. When subsequently extrapolating beyond the clinical trial period, these relatively large differences in goodness-of-fit translated into almost a doubling in mean total cost and a 60-d decrease in mean survival time when using the Markov model instead of the semi-Markov model. For the disease process considered in our case study, the semi-Markov model thus provided a sensible balance between model parsimoniousness and computational complexity. © The Author(s) 2015.

Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media

Science.gov (United States)

Delgoshaie, A. H.; Jenny, P.; Tchelepi, H.

2017-12-01

The transport of fluids in porous media is dominated by flow­-field heterogeneity resulting from the underlying permeability field. Due to the high uncertainty in the permeability field, many realizations of the reference geological model are used to describe the statistics of the transport phenomena in a Monte Carlo (MC) framework. There has been strong interest in working with stochastic formulations of the transport that are different from the standard MC approach. Several stochastic models based on a velocity process for tracer particle trajectories have been proposed. Previous studies have shown that for high variances of the log-conductivity, the stochastic models need to account for correlations between consecutive velocity transitions to predict dispersion accurately. The correlated velocity models proposed in the literature can be divided into two general classes of temporal and spatial Markov models. Temporal Markov models have been applied successfully to tracer transport in both the longitudinal and transverse directions. These temporal models are Stochastic Differential Equations (SDEs) with very specific drift and diffusion terms tailored for a specific permeability correlation structure. The drift and diffusion functions devised for a certain setup would not necessarily be suitable for a different scenario, (e.g., a different permeability correlation structure). The spatial Markov models are simple discrete Markov chains that do not require case specific assumptions. However, transverse spreading of contaminant plumes has not been successfully modeled with the available correlated spatial models. Here, we propose a temporal discrete Markov chain to model both the longitudinal and transverse dispersion in a two-dimensional domain. We demonstrate that these temporal Markov models are valid for different correlation structures without modification. Similar to the temporal SDEs, the proposed model respects the limited asymptotic transverse spreading of

Markov chains and semi-Markov models in time-to-event analysis.

Science.gov (United States)

Abner, Erin L; Charnigo, Richard J; Kryscio, Richard J

2013-10-25

A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields.

Inhomogeneous Markov Models for Describing Driving Patterns

DEFF Research Database (Denmark)

Iversen, Emil Banning; Møller, Jan K.; Morales, Juan Miguel

2017-01-01

. Specifically, an inhomogeneous Markov model that captures the diurnal variation in the use of a vehicle is presented. The model is defined by the time-varying probabilities of starting and ending a trip, and is justified due to the uncertainty associated with the use of the vehicle. The model is fitted to data...... collected from the actual utilization of a vehicle. Inhomogeneous Markov models imply a large number of parameters. The number of parameters in the proposed model is reduced using B-splines....

Inhomogeneous Markov Models for Describing Driving Patterns

DEFF Research Database (Denmark)

Iversen, Jan Emil Banning; Møller, Jan Kloppenborg; Morales González, Juan Miguel

. Specically, an inhomogeneous Markov model that captures the diurnal variation in the use of a vehicle is presented. The model is dened by the time-varying probabilities of starting and ending a trip and is justied due to the uncertainty associated with the use of the vehicle. The model is tted to data...... collected from the actual utilization of a vehicle. Inhomogeneous Markov models imply a large number of parameters. The number of parameters in the proposed model is reduced using B-splines....

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...

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

Science.gov (United States)

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

2010-09-01

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

Effects of stochastic interest rates in decision making under risk: A Markov decision process model for forest management

Science.gov (United States)

Mo Zhou; Joseph Buongiorno

2011-01-01

Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...

Prediction of Annual Rainfall Pattern Using Hidden Markov Model ...

African Journals Online (AJOL)

ADOWIE PERE

Hidden Markov model is very influential in stochastic world because of its ... the earth from the clouds. The usual ... Rainfall modelling and ... Markov Models have become popular tools ... environment sciences, University of Jos, plateau state,.

Switching Markov chains for a holistic modeling of SIS unavailability

International Nuclear Information System (INIS)

Mechri, Walid; Simon, Christophe; BenOthman, Kamel

2015-01-01

This paper proposes a holistic approach to model the Safety Instrumented Systems (SIS). The model is based on Switching Markov Chain and integrates several parameters like Common Cause Failure, Imperfect Proof testing, partial proof testing, etc. The basic concepts of Switching Markov Chain applied to reliability analysis are introduced and a model to compute the unavailability for a case study is presented. The proposed Switching Markov Chain allows us to assess the effect of each parameter on the SIS performance. The proposed method ensures the relevance of the results. - Highlights: • A holistic approach to model the unavailability safety systems using Switching Markov chains. • The model integrates several parameters like probability of failure due to the test, the probability of not detecting a failure in a test. • The basic concepts of the Switching Markov Chains are introduced and applied to compute the unavailability for safety systems. • The proposed Switching Markov Chain allows assessing the effect of each parameter on the chemical reactor performance

Classification of customer lifetime value models using Markov chain

Science.gov (United States)

Permana, Dony; Pasaribu, Udjianna S.; Indratno, Sapto W.; Suprayogi

2017-10-01

A firm’s potential reward in future time from a customer can be determined by customer lifetime value (CLV). There are some mathematic methods to calculate it. One method is using Markov chain stochastic model. Here, a customer is assumed through some states. Transition inter the states follow Markovian properties. If we are given some states for a customer and the relationships inter states, then we can make some Markov models to describe the properties of the customer. As Markov models, CLV is defined as a vector contains CLV for a customer in the first state. In this paper we make a classification of Markov Models to calculate CLV. Start from two states of customer model, we make develop in many states models. The development a model is based on weaknesses in previous model. Some last models can be expected to describe how real characters of customers in a firm.

Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy

International Nuclear Information System (INIS)

Abler, Daniel; Kanellopoulos, Vassiliki; Dosanjh, Manjit; Davies, Jim; Peach, Ken; Jena, Raj; Kirkby, Norman

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 and argue that the proposed method can automate the creation of Markov models from existing data. The approach has the potential to support the radiotherapy community in conducting systematic analyses involving predictive modelling of existing and upcoming radiotherapy data. We expect it to facilitate the application of modelling techniques in medical decision problems beyond the field of radiotherapy, and to improve the comparability of their results. (author)

The semi-Markov process. Generalizations and calculation rules for application in the analysis of systems

International Nuclear Information System (INIS)

Hirschmann, H.

1983-06-01

The consequences of the basic assumptions of the semi-Markov process as defined from a homogeneous renewal process with a stationary Markov condition are reviewed. The notion of the semi-Markov process is generalized by its redefinition from a nonstationary Markov renewal process. For both the nongeneralized and the generalized case a representation of the first order conditional state probabilities is derived in terms of the transition probabilities of the Markov renewal process. Some useful calculation rules (regeneration rules) are derived for the conditional state probabilities of the semi-Markov process. Compared to the semi-Markov process in its usual definition the generalized process allows the analysis of a larger class of systems. For instance systems with arbitrarily distributed lifetimes of their components can be described. There is also a chance to describe systems which are modified during time by forces or manipulations from outside. (Auth.)

Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy

Science.gov (United States)

Abler, Daniel; Kanellopoulos, Vassiliki; 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 and argue that the proposed method can automate the creation of Markov models from existing data. The approach has the potential to support the radiotherapy community in conducting systematic analyses involving predictive modelling of existing and upcoming radiotherapy data. We expect it to facilitate the application of modelling techniques in medical decision problems beyond the field of radiotherapy, and to improve the comparability of their results. PMID:23824126

Identification of Optimal Policies in Markov Decision Processes

Czech Academy of Sciences Publication Activity Database

Sladký, Karel

46 2010, č. 3 (2010), s. 558-570 ISSN 0023-5954. [International Conference on Mathematical Methods in Economy and Industry. České Budějovice, 15.06.2009-18.06.2009] R&D Projects: GA ČR(CZ) GA402/08/0107; GA ČR GA402/07/1113 Institutional research plan: CEZ:AV0Z10750506 Keywords : finite state Markov decision processes * discounted and average costs * elimination of suboptimal policies Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/E/sladky-identification of optimal policies in markov decision processes.pdf

2nd International Symposium on Semi-Markov Models : Theory and Applications

CERN Document Server

Limnios, Nikolaos

1999-01-01

This book presents a selection of papers presented to the Second Inter­ national Symposium on Semi-Markov Models: Theory and Applications held in Compiegne (France) in December 1998. This international meeting had the same aim as the first one held in Brussels in 1984 : to make, fourteen years later, the state of the art in the field of semi-Markov processes and their applications, bring together researchers in this field and also to stimulate fruitful discussions. The set of the subjects of the papers presented in Compiegne has a lot of similarities with the preceding Symposium; this shows that the main fields of semi-Markov processes are now well established particularly for basic applications in Reliability and Maintenance, Biomedicine, Queue­ ing, Control processes and production. A growing field is the one of insurance and finance but this is not really a surprising fact as the problem of pricing derivative products represents now a crucial problem in economics and finance. For example, stochastic mode...

Automatic creation of Markov models for reliability assessment of safety instrumented systems

International Nuclear Information System (INIS)

Guo Haitao; Yang Xianhui

2008-01-01

After the release of new international functional safety standards like IEC 61508, people care more for the safety and availability of safety instrumented systems. Markov analysis is a powerful and flexible technique to assess the reliability measurements of safety instrumented systems, but it is fallible and time-consuming to create Markov models manually. This paper presents a new technique to automatically create Markov models for reliability assessment of safety instrumented systems. Many safety related factors, such as failure modes, self-diagnostic, restorations, common cause and voting, are included in Markov models. A framework is generated first based on voting, failure modes and self-diagnostic. Then, repairs and common-cause failures are incorporated into the framework to build a complete Markov model. Eventual simplification of Markov models can be done by state merging. Examples given in this paper show how explosively the size of Markov model increases as the system becomes a little more complicated as well as the advancement of automatic creation of Markov models

Discounted semi-Markov decision processes : linear programming and policy iteration

NARCIS (Netherlands)

Wessels, J.; van Nunen, J.A.E.E.

1975-01-01

For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal

Discounted semi-Markov decision processes : linear programming and policy iteration

NARCIS (Netherlands)

Wessels, J.; van Nunen, J.A.E.E.

1974-01-01

For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal

Markov Processes in Image Processing

Science.gov (United States)

Petrov, E. P.; Kharina, N. L.

2018-05-01

Digital images are used as an information carrier in different sciences and technologies. The aspiration to increase the number of bits in the image pixels for the purpose of obtaining more information is observed. In the paper, some methods of compression and contour detection on the basis of two-dimensional Markov chain are offered. Increasing the number of bits on the image pixels will allow one to allocate fine object details more precisely, but it significantly complicates image processing. The methods of image processing do not concede by the efficiency to well-known analogues, but surpass them in processing speed. An image is separated into binary images, and processing is carried out in parallel with each without an increase in speed, when increasing the number of bits on the image pixels. One more advantage of methods is the low consumption of energy resources. Only logical procedures are used and there are no computing operations. The methods can be useful in processing images of any class and assignment in processing systems with a limited time and energy resources.

Elements of the theory of Markov processes and their applications

CERN Document Server

Bharucha-Reid, A T

2010-01-01

This graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition.

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

Science.gov (United States)

Rains, Emily K; Andersen, Hans C

2010-10-14

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

Grey-Markov prediction model based on background value optimization and central-point triangular whitenization weight function

Science.gov (United States)

Ye, Jing; Dang, Yaoguo; Li, Bingjun

2018-01-01

Grey-Markov forecasting model is a combination of grey prediction model and Markov chain which show obvious optimization effects for data sequences with characteristics of non-stationary and volatility. However, the state division process in traditional Grey-Markov forecasting model is mostly based on subjective real numbers that immediately affects the accuracy of forecasting values. To seek the solution, this paper introduces the central-point triangular whitenization weight function in state division to calculate possibilities of research values in each state which reflect preference degrees in different states in an objective way. On the other hand, background value optimization is applied in the traditional grey model to generate better fitting data. By this means, the improved Grey-Markov forecasting model is built. Finally, taking the grain production in Henan Province as an example, it verifies this model's validity by comparing with GM(1,1) based on background value optimization and the traditional Grey-Markov forecasting model.

a multi-period markov model for monthly rainfall in lagos, nigeria

African Journals Online (AJOL)

PUBLICATIONS1

A twelve-period. Markov model has been developed for the monthly rainfall data for Lagos, along the coast of .... autoregressive process to model river flow; Deo et al. (2015) utilized an ...... quences for the analysis of river basins by simulation.

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.

Hidden Markov models applied to a subsequence of the Xylella fastidiosa genome

Directory of Open Access Journals (Sweden)

Silva Cibele Q. da

2003-01-01

Full Text Available Dependencies in DNA sequences are frequently modeled using Markov models. However, Markov chains cannot account for heterogeneity that may be present in different regions of the same DNA sequence. Hidden Markov models are more realistic than Markov models since they allow for the identification of heterogeneous regions of a DNA sequence. In this study we present an application of hidden Markov models to a subsequence of the Xylella fastidiosa DNA data. We found that a three-state model provides a good description for the data considered.

Weighted-indexed semi-Markov models for modeling financial returns

International Nuclear Information System (INIS)

D’Amico, Guglielmo; Petroni, Filippo

2012-01-01

In this paper we propose a new stochastic model based on a generalization of semi-Markov chains for studying the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted-indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series such as the first-passage-time distributions and the persistence of volatility. The model is applied to data from the Italian and German stock markets from 1 January 2007 until the end of December 2010. (paper)

Deteksi Fraud Menggunakan Metode Model Markov Tersembunyi Pada Proses Bisnis

Directory of Open Access Journals (Sweden)

Andrean Hutama Koosasi

2017-03-01

Full Text Available Model Markov Tersembunyi merupakan sebuah metode statistik berdasarkan Model Markov sederhana yang memodelkan sistem serta membaginya dalam 2 (dua state, state tersembunyi dan state observasi. Dalam pengerjaan tugas akhir ini, penulis mengusulkan penggunaan metode Model Markov Tersembunyi untuk menemukan fraud didalam sebuah pelaksanaan proses bisnis. Dengan penggunaan metode Model Markov Tersembunyi ini, maka pengamatan terhadap elemen penyusun sebuah kasus/kejadian, yakni beberapa aktivitas, akan diperoleh sebuah nilai peluang, yang sekaligus memberikan prediksi terhadap kasus/kejadian tersebut, sebuah fraud atau tidak. Hasil ekpserimen ini menunjukkan bahwa metode yang diusulkan mampu memberikan prediksi akhir dengan evaluasi TPR sebesar 87,5% dan TNR sebesar 99,4%.

A Metrized Duality Theorem for Markov Processes

DEFF Research Database (Denmark)

Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash

2014-01-01

We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...

[Compared Markov with fractal models by using single-channel experimental and simulation data].

Science.gov (United States)

Lan, Tonghan; Wu, Hongxiu; Lin, Jiarui

2006-10-01

The gating mechanical kinetical of ion channels has been modeled as a Markov process. In these models it is assumed that the channel protein has a small number of discrete conformational states and kinetic rate constants connecting these states are constant, the transition rate constants among the states is independent both of time and of the previous channel activity. It is assumed in Liebovitch's fractal model that the channel exists in an infinite number of energy states, consequently, transitions from one conductance state to another would be governed by a continuum of rate constants. In this paper, a statistical comparison is presented of Markov and fractal models of ion channel gating, the analysis is based on single-channel data from ion channel voltage-dependence K+ single channel of neuron cell and simulation data from three-states Markov model.

Partially Hidden Markov Models

DEFF Research Database (Denmark)

Forchhammer, Søren Otto; Rissanen, Jorma

1996-01-01

Partially Hidden Markov Models (PHMM) are introduced. They differ from the ordinary HMM's in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations. As an illustration they are applied to black and white image compression where...

Markov-CA model using analytical hierarchy process and multiregression technique

International Nuclear Information System (INIS)

Omar, N Q; Sanusi, S A M; Hussin, W M W; Samat, N; Mohammed, K S

2014-01-01

The unprecedented increase in population and rapid rate of urbanisation has led to extensive land use changes. Cellular automata (CA) are increasingly used to simulate a variety of urban dynamics. This paper introduces a new CA based on an integration model built-in multi regression and multi-criteria evaluation to improve the representation of CA transition rule. This multi-criteria evaluation is implemented by utilising data relating to the environmental and socioeconomic factors in the study area in order to produce suitability maps (SMs) using an analytical hierarchical process, which is a well-known method. Before being integrated to generate suitability maps for the periods from 1984 to 2010 based on the different decision makings, which have become conditioned for the next step of CA generation. The suitability maps are compared in order to find the best maps based on the values of the root equation (R 2 ). This comparison can help the stakeholders make better decisions. Thus, the resultant suitability map derives a predefined transition rule for the last step for CA model. The approach used in this study highlights a mechanism for monitoring and evaluating land-use and land-cover changes in Kirkuk city, Iraq owing changes in the structures of governments, wars, and an economic blockade over the past decades. The present study asserts the high applicability and flexibility of Markov-CA model. The results have shown that the model and its interrelated concepts are performing rather well

Logics and Models for Stochastic Analysis Beyond Markov Chains

DEFF Research Database (Denmark)

Zeng, Kebin

, because of the generality of ME distributions, we have to leave the world of Markov chains. To support ME distributions with multiple exits, we introduce a multi-exits ME distribution together with a process algebra MEME to express the systems having the semantics as Markov renewal processes with ME...

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...... in the Markov model for this task. Classifications that are purely based on statistical models might not always be biologically meaningful. We present combinatorial methods to incorporate biological background knowledge to enhance the prediction performance....

Operational Markov Condition for Quantum Processes

Science.gov (United States)

Pollock, Felix A.; Rodríguez-Rosario, César; Frauenheim, Thomas; Paternostro, Mauro; Modi, Kavan

2018-01-01

We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process or the experimental falsifiability of a Markovian hypothesis.

Spectral analysis of multi-dimensional self-similar Markov processes

International Nuclear Information System (INIS)

Modarresi, N; Rezakhah, S

2010-01-01

In this paper we consider a discrete scale invariant (DSI) process {X(t), t in R + } with scale l > 1. We consider a fixed number of observations in every scale, say T, and acquire our samples at discrete points α k , k in W, where α is obtained by the equality l = α T and W = {0, 1, ...}. We thus provide a discrete time scale invariant (DT-SI) process X(.) with the parameter space {α k , k in W}. We find the spectral representation of the covariance function of such a DT-SI process. By providing the harmonic-like representation of multi-dimensional self-similar processes, spectral density functions of them are presented. We assume that the process {X(t), t in R + } is also Markov in the wide sense and provide a discrete time scale invariant Markov (DT-SIM) process with the above scheme of sampling. We present an example of the DT-SIM process, simple Brownian motion, by the above sampling scheme and verify our results. Finally, we find the spectral density matrix of such a DT-SIM process and show that its associated T-dimensional self-similar Markov process is fully specified by {R H j (1), R j H (0), j = 0, 1, ..., T - 1}, where R H j (τ) is the covariance function of jth and (j + τ)th observations of the process.

Modeling Uncertainty of Directed Movement via Markov Chains

Directory of Open Access Journals (Sweden)

YIN Zhangcai

2015-10-01

Full Text Available Probabilistic time geography (PTG is suggested as an extension of (classical time geography, in order to present the uncertainty of an agent located at the accessible position by probability. This may provide a quantitative basis for most likely finding an agent at a location. In recent years, PTG based on normal distribution or Brown bridge has been proposed, its variance, however, is irrelevant with the agent's speed or divergent with the increase of the speed; so they are difficult to take into account application pertinence and stability. In this paper, a new method is proposed to model PTG based on Markov chain. Firstly, a bidirectional conditions Markov chain is modeled, the limit of which, when the moving speed is large enough, can be regarded as the Brown bridge, thus has the characteristics of digital stability. Then, the directed movement is mapped to Markov chains. The essential part is to build step length, the state space and transfer matrix of Markov chain according to the space and time position of directional movement, movement speed information, to make sure the Markov chain related to the movement speed. Finally, calculating continuously the probability distribution of the directed movement at any time by the Markov chains, it can be get the possibility of an agent located at the accessible position. Experimental results show that, the variance based on Markov chains not only is related to speed, but also is tending towards stability with increasing the agent's maximum speed.

A Markov reward model checker

NARCIS (Netherlands)

Katoen, Joost P.; Maneesh Khattri, M.; Zapreev, I.S.; Zapreev, I.S.

2005-01-01

This short tool paper introduces MRMC, a model checker for discrete-time and continuous-time Markov reward models. It supports reward extensions of PCTL and CSL, and allows for the automated verification of properties concerning long-run and instantaneous rewards as well as cumulative rewards. In

An introduction to hidden Markov models for biological sequences

DEFF Research Database (Denmark)

Krogh, Anders Stærmose

1998-01-01

A non-matematical tutorial on hidden Markov models (HMMs) plus a description of one of the applications of HMMs: gene finding.......A non-matematical tutorial on hidden Markov models (HMMs) plus a description of one of the applications of HMMs: gene finding....

Generalization of the Wide-Sense Markov Concept to a Widely Linear Processing

International Nuclear Information System (INIS)

Espinosa-Pulido, Juan Antonio; Navarro-Moreno, Jesús; Fernández-Alcalá, Rosa María; Ruiz-Molina, Juan Carlos; Oya-Lechuga, Antonia; Ruiz-Fuentes, Nuria

2014-01-01

In this paper we show that the classical definition and the associated characterizations of wide-sense Markov (WSM) signals are not valid for improper complex signals. For that, we propose an extension of the concept of WSM to a widely linear (WL) setting and the study of new characterizations. Specifically, we introduce a new class of signals, called widely linear Markov (WLM) signals, and we analyze some of their properties based either on second-order properties or on state-space models from a WL processing standpoint. The study is performed in both the forwards and backwards directions of time. Thus, we provide two forwards and backwards Markovian representations for WLM signals. Finally, different estimation recursive algorithms are obtained for these models

Hidden Markov models and other machine learning approaches in computational molecular biology

Energy Technology Data Exchange (ETDEWEB)

Baldi, P. [California Inst. of Tech., Pasadena, CA (United States)

1995-12-31

This tutorial was one of eight tutorials selected to be presented at the Third International Conference on Intelligent Systems for Molecular Biology which was held in the United Kingdom from July 16 to 19, 1995. Computational tools are increasingly needed to process the massive amounts of data, to organize and classify sequences, to detect weak similarities, to separate coding from non-coding regions, and reconstruct the underlying evolutionary history. The fundamental problem in machine learning is the same as in scientific reasoning in general, as well as statistical modeling: to come up with a good model for the data. In this tutorial four classes of models are reviewed. They are: Hidden Markov models; artificial Neural Networks; Belief Networks; and Stochastic Grammars. When dealing with DNA and protein primary sequences, Hidden Markov models are one of the most flexible and powerful alignments and data base searches. In this tutorial, attention is focused on the theory of Hidden Markov Models, and how to apply them to problems in molecular biology.

Multivariate longitudinal data analysis with mixed effects hidden Markov models.

Science.gov (United States)

Raffa, Jesse D; Dubin, Joel A

2015-09-01

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

Dynamic neutron scattering from conformational dynamics. I. Theory and Markov models.

Science.gov (United States)

Lindner, Benjamin; Yi, Zheng; Prinz, Jan-Hendrik; Smith, Jeremy C; Noé, Frank

2013-11-07

The dynamics of complex molecules can be directly probed by inelastic neutron scattering experiments. However, many of the underlying dynamical processes may exist on similar timescales, which makes it difficult to assign processes seen experimentally to specific structural rearrangements. Here, we show how Markov models can be used to connect structural changes observed in molecular dynamics simulation directly to the relaxation processes probed by scattering experiments. For this, a conformational dynamics theory of dynamical neutron and X-ray scattering is developed, following our previous approach for computing dynamical fingerprints of time-correlation functions [F. Noé, S. Doose, I. Daidone, M. Löllmann, J. Chodera, M. Sauer, and J. Smith, Proc. Natl. Acad. Sci. U.S.A. 108, 4822 (2011)]. Markov modeling is used to approximate the relaxation processes and timescales of the molecule via the eigenvectors and eigenvalues of a transition matrix between conformational substates. This procedure allows the establishment of a complete set of exponential decay functions and a full decomposition into the individual contributions, i.e., the contribution of every atom and dynamical process to each experimental relaxation process.

Simulation-based algorithms for Markov decision processes

CERN Document Server

Chang, Hyeong Soo; Fu, Michael C; Marcus, Steven I

2013-01-01

Markov decision process (MDP) models are widely used for modeling sequential decision-making problems that arise in engineering, economics, computer science, and the social sciences.  Many real-world problems modeled by MDPs have huge state and/or action spaces, giving an opening to the curse of dimensionality and so making practical solution of the resulting models intractable.  In other cases, the system of interest is too complex to allow explicit specification of some of the MDP model parameters, but simulation samples are readily available (e.g., for random transitions and costs). For these settings, various sampling and population-based algorithms have been developed to overcome the difficulties of computing an optimal solution in terms of a policy and/or value function.  Specific approaches include adaptive sampling, evolutionary policy iteration, evolutionary random policy search, and model reference adaptive search. This substantially enlarged new edition reflects the latest developments in novel ...

Model Checking Structured Infinite Markov Chains

NARCIS (Netherlands)

Remke, Anne Katharina Ingrid

2008-01-01

In the past probabilistic model checking hast mostly been restricted to finite state models. This thesis explores the possibilities of model checking with continuous stochastic logic (CSL) on infinite-state Markov chains. We present an in-depth treatment of model checking algorithms for two special

Assessing type I error and power of multistate Markov models for panel data-A simulation study.

Science.gov (United States)

Cassarly, Christy; Martin, Renee' H; Chimowitz, Marc; Peña, Edsel A; Ramakrishnan, Viswanathan; Palesch, Yuko Y

2017-01-01

Ordinal outcomes collected at multiple follow-up visits are common in clinical trials. Sometimes, one visit is chosen for the primary analysis and the scale is dichotomized amounting to loss of information. Multistate Markov models describe how a process moves between states over time. Here, simulation studies are performed to investigate the type I error and power characteristics of multistate Markov models for panel data with limited non-adjacent state transitions. The results suggest that the multistate Markov models preserve the type I error and adequate power is achieved with modest sample sizes for panel data with limited non-adjacent state transitions.

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.

Using multi-state markov models to identify credit card risk

Directory of Open Access Journals (Sweden)

Daniel Evangelista Régis

2016-06-01

Full Text Available Abstract The main interest of this work is to analyze the application of multi-state Markov models to evaluate credit card risk by investigating the characteristics of different state transitions in client-institution relationships over time, thereby generating score models for various purposes. We also used logistic regression models to compare the results with those obtained using multi-state Markov models. The models were applied to an actual database of a Brazilian financial institution. In this application, multi-state Markov models performed better than logistic regression models in predicting default risk, and logistic regression models performed better in predicting cancellation risk.

Hidden Markov processes theory and applications to biology

CERN Document Server

Vidyasagar, M

2014-01-01

This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. The book starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are t

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

Science.gov (United States)

Sughiyama, Yuki; Kobayashi, Testuya J.

2018-03-01

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

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...

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model

Science.gov (United States)

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-01

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.

Observation uncertainty in reversible Markov chains.

Science.gov (United States)

Metzner, Philipp; Weber, Marcus; Schütte, Christof

2010-09-01

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

Estimation with Right-Censored Observations Under A Semi-Markov Model.

Science.gov (United States)

Zhao, Lihui; Hu, X Joan

2013-06-01

The semi-Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end-point of the support of the censoring time is strictly less than the right end-point of the support of the semi-Markov kernel, the transition probability of the semi-Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi-Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study.

Critical Age-Dependent Branching Markov Processes and their ...

Indian Academy of Sciences (India)

This paper studies: (i) the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence of age-dependent critical branching Brownian motions.

Limits of performance for the model reduction problem of hidden Markov models

KAUST Repository

Kotsalis, Georgios

2015-12-15

We introduce system theoretic notions of a Hankel operator, and Hankel norm for hidden Markov models. We show how the related Hankel singular values provide lower bounds on the norm of the difference between a hidden Markov model of order n and any lower order approximant of order n̂ < n.

Limits of performance for the model reduction problem of hidden Markov models

KAUST Repository

Kotsalis, Georgios; Shamma, Jeff S.

2015-01-01

We introduce system theoretic notions of a Hankel operator, and Hankel norm for hidden Markov models. We show how the related Hankel singular values provide lower bounds on the norm of the difference between a hidden Markov model of order n and any lower order approximant of order n̂ < n.

A Partially Observed Markov Decision Process for Dynamic Pricing

OpenAIRE

Yossi Aviv; Amit Pazgal

2005-01-01

In this paper, we develop a stylized partially observed Markov decision process (POMDP) framework to study a dynamic pricing problem faced by sellers of fashion-like goods. We consider a retailer that plans to sell a given stock of items during a finite sales season. The objective of the retailer is to dynamically price the product in a way that maximizes expected revenues. Our model brings together various types of uncertainties about the demand, some of which are resolvable through sales ob...

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...

Post processing of optically recognized text via second order hidden Markov model

Science.gov (United States)

Poudel, Srijana

In this thesis, we describe a postprocessing system on Optical Character Recognition(OCR) generated text. Second Order Hidden Markov Model (HMM) approach is used to detect and correct the OCR related errors. The reason for choosing the 2nd order HMM is to keep track of the bigrams so that the model can represent the system more accurately. Based on experiments with training data of 159,733 characters and testing of 5,688 characters, the model was able to correct 43.38 % of the errors with a precision of 75.34 %. However, the precision value indicates that the model introduced some new errors, decreasing the correction percentage to 26.4%.

Mathematical model of the loan portfolio dynamics in the form of Markov chain considering the process of new customers attraction

Science.gov (United States)

Bozhalkina, Yana

2017-12-01

Mathematical model of the loan portfolio structure change in the form of Markov chain is explored. This model considers in one scheme both the process of customers attraction, their selection based on the credit score, and loans repayment. The model describes the structure and volume of the loan portfolio dynamics, which allows to make medium-term forecasts of profitability and risk. Within the model corrective actions of bank management in order to increase lending volumes or to reduce the risk are formalized.

Learning Markov models for stationary system behaviors

DEFF Research Database (Denmark)

Chen, Yingke; Mao, Hua; Jaeger, Manfred

2012-01-01

to a single long observation sequence, and in these situations existing automatic learning methods cannot be applied. In this paper, we adapt algorithms for learning variable order Markov chains from a single observation sequence of a target system, so that stationary system properties can be verified using......Establishing an accurate model for formal verification of an existing hardware or software system is often a manual process that is both time consuming and resource demanding. In order to ease the model construction phase, methods have recently been proposed for automatically learning accurate...... the learned model. Experiments demonstrate that system properties (formulated as stationary probabilities of LTL formulas) can be reliably identified using the learned model....

Dynamical fluctuations for semi-Markov processes

Czech Academy of Sciences Publication Activity Database

Maes, C.; Netočný, Karel; Wynants, B.

2009-01-01

Roč. 42, č. 36 (2009), 365002/1-365002/21 ISSN 1751-8113 R&D Projects: GA ČR GC202/07/J051 Institutional research plan: CEZ:AV0Z10100520 Keywords : nonequilibrium fluctuations * semi-Markov processes Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.577, year: 2009 http://www.iop.org/EJ/abstract/1751-8121/42/36/365002

The algebra of the general Markov model on phylogenetic trees and networks.

Science.gov (United States)

Sumner, J G; Holland, B R; Jarvis, P D

2012-04-01

It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the “splitting” operator that generates the branching process on phylogenetic trees. For simplicity, we proceed by discussing the two state case and then show that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the Hadamard approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give an argument that our extension to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications.

A Bayesian model for binary Markov chains

Directory of Open Access Journals (Sweden)

Belkheir Essebbar

2004-02-01

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

Simulation based sequential Monte Carlo methods for discretely observed Markov processes

OpenAIRE

Neal, Peter

2014-01-01

Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective sequential Monte Carlo (SMC) algorithm for obtaining samples from the posterior distribution of the parameters. In particular, we introduce two key innovations, coupled simulations, which allow us to study multiple parameter values on the basis of a single sim...

Markov decision processes and the belief-desire-intention model bridging the gap for autonomous agents

CERN Document Server

Simari, Gerardo I

2011-01-01

In this work, we provide a treatment of the relationship between two models that have been widely used in the implementation of autonomous agents: the Belief DesireIntention (BDI) model and Markov Decision Processes (MDPs). We start with an informal description of the relationship, identifying the common features of the two approaches and the differences between them. Then we hone our understanding of these differences through an empirical analysis of the performance of both models on the TileWorld testbed. This allows us to show that even though the MDP model displays consistently better behavior than the BDI model for small worlds, this is not the case when the world becomes large and the MDP model cannot be solved exactly. Finally we present a theoretical analysis of the relationship between the two approaches, identifying mappings that allow us to extract a set of intentions from a policy (a solution to an MDP), and to extract a policy from a set of intentions.

Hidden Markov models for labeled sequences

DEFF Research Database (Denmark)

Krogh, Anders Stærmose

1994-01-01

A hidden Markov model for labeled observations, called a class HMM, is introduced and a maximum likelihood method is developed for estimating the parameters of the model. Instead of training it to model the statistics of the training sequences it is trained to optimize recognition. It resembles MMI...

«Concurrency» in M-L-Parallel Semi-Markov Process

Directory of Open Access Journals (Sweden)

Larkin Eugene

2017-01-01

Full Text Available This article investigates the functioning of a swarm of robots, each of which receives instructions from the external human operator and autonomously executes them. An abstract model of functioning of a robot, a group of robots and multiple groups of robots was obtained using the notion of semi-Markov process. The concepts of aggregated initial and aggregated absorbing states were introduced. Correspondences for calculation of time parameters of concurrency were obtained.

Adaptive Partially Hidden Markov Models

DEFF Research Database (Denmark)

Forchhammer, Søren Otto; Rasmussen, Tage

1996-01-01

Partially Hidden Markov Models (PHMM) have recently been introduced. The transition and emission probabilities are conditioned on the past. In this report, the PHMM is extended with a multiple token version. The different versions of the PHMM are applied to bi-level image coding....

A Constraint Model for Constrained Hidden Markov Models

DEFF Research Database (Denmark)

Christiansen, Henning; Have, Christian Theil; Lassen, Ole Torp

2009-01-01

A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we extend HMMs with constraints and show how the familiar Viterbi algorithm can be generalized, based on constraint solving ...

Continuous-time Markov decision processes theory and applications

CERN Document Server

Guo, Xianping

2009-01-01

This volume provides the first book entirely devoted to recent developments on the theory and applications of continuous-time Markov decision processes (MDPs). The MDPs presented here include most of the cases that arise in applications.

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

Energy Technology Data Exchange (ETDEWEB)

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

2011-05-09

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

Analyzing the profit-loss sharing contracts with Markov model

Directory of Open Access Journals (Sweden)

Imam Wahyudi

2016-12-01

Full Text Available The purpose of this paper is to examine how to use first order Markov chain to build a reliable monitoring system for the profit-loss sharing based contracts (PLS as the mode of financing contracts in Islamic bank with censored continuous-time observations. The paper adopts the longitudinal analysis with the first order Markov chain framework. Laplace transform was used with homogenous continuous time assumption, from discretized generator matrix, to generate the transition matrix. Various metrics, i.e.: eigenvalue and eigenvector were used to test the first order Markov chain assumption. Cox semi parametric model was used also to analyze the momentum and waiting time effect as non-Markov behavior. The result shows that first order Markov chain is powerful as a monitoring tool for Islamic banks. We find that waiting time negatively affected present rating downgrade (upgrade significantly. Likewise, momentum covariate showed negative effect. Finally, the result confirms that different origin rating have different movement behavior. The paper explores the potential of Markov chain framework as a risk management tool for Islamic banks. It provides valuable insight and integrative model for banks to manage their borrower accounts. This model can be developed to be a powerful early warning system to identify which borrower needs to be monitored intensively. Ultimately, this model could potentially increase the efficiency, productivity and competitiveness of Islamic banks in Indonesia. The analysis used only rating data. Further study should be able to give additional information about the determinant factors of rating movement of the borrowers by incorporating various factors such as contract-related factors, bank-related factors, borrower-related factors and macroeconomic factors.

Generalized Markov branching models

OpenAIRE

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...

The Consensus String Problem and the Complexity of Comparing Hidden Markov Models

DEFF Research Database (Denmark)

Lyngsø, Rune Bang; Pedersen, Christian Nørgaard Storm

2002-01-01

The basic theory of hidden Markov models was developed and applied to problems in speech recognition in the late 1960s, and has since then been applied to numerous problems, e.g. biological sequence analysis. Most applications of hidden Markov models are based on efficient algorithms for computing...... the probability of generating a given string, or computing the most likely path generating a given string. In this paper we consider the problem of computing the most likely string, or consensus string, generated by a given model, and its implications on the complexity of comparing hidden Markov models. We show...... that computing the consensus string, and approximating its probability within any constant factor, is NP-hard, and that the same holds for the closely related labeling problem for class hidden Markov models. Furthermore, we establish the NP-hardness of comparing two hidden Markov models under the L∞- and L1...

Model Checking Markov Chains: Techniques and Tools

NARCIS (Netherlands)

Zapreev, I.S.

2008-01-01

This dissertation deals with four important aspects of model checking Markov chains: the development of efficient model-checking tools, the improvement of model-checking algorithms, the efficiency of the state-space reduction techniques, and the development of simulation-based model-checking

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

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. The fi...

Simulation on a computer the cascade probabilistic functions and theirs relation with Markov's processes

International Nuclear Information System (INIS)

Kupchishin, A.A.; Kupchishin, A.I.; Shmygaleva, T.A.

2002-01-01

Within framework of the cascade-probabilistic (CP) method the radiation and physical processes are studied, theirs relation with Markov's processes are found. The conclusion that CP-function for electrons, protons, alpha-particles and ions are describing by unhomogeneous Markov's chain is drawn. The algorithms are developed, the CP-functions calculations for charged particles, concentration of radiation defects in solids at ion irradiation are carried out as well. Tables for CPF different parameters and radiation defects concentration at charged particle interaction with solids are given. The book consists of the introduction and two chapters: (1) Cascade probabilistic function and the Markov's processes; (2) Radiation defects formation in solids as a part of the Markov's processes. The book is intended for specialists on the radiation defects mathematical stimulation, solid state physics, elementary particles physics and applied mathematics

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.

Multi-state Markov models for disease progression in the presence of informative examination times: an application to hepatitis C.

Science.gov (United States)

Sweeting, M J; Farewell, V T; De Angelis, D

2010-05-20

In many chronic diseases it is important to understand the rate at which patients progress from infection through a series of defined disease states to a clinical outcome, e.g. cirrhosis in hepatitis C virus (HCV)-infected individuals or AIDS in HIV-infected individuals. Typically data are obtained from longitudinal studies, which often are observational in nature, and where disease state is observed only at selected examinations throughout follow-up. Transition times between disease states are therefore interval censored. Multi-state Markov models are commonly used to analyze such data, but rely on the assumption that the examination times are non-informative, and hence the examination process is ignorable in a likelihood-based analysis. In this paper we develop a Markov model that relaxes this assumption through the premise that the examination process is ignorable only after conditioning on a more regularly observed auxiliary variable. This situation arises in a study of HCV disease progression, where liver biopsies (the examinations) are sparse, irregular, and potentially informative with respect to the transition times. We use additional information on liver function tests (LFTs), commonly collected throughout follow-up, to inform current disease state and to assume an ignorable examination process. The model developed has a similar structure to a hidden Markov model and accommodates both the series of LFT measurements and the partially latent series of disease states. We show through simulation how this model compares with the commonly used ignorable Markov model, and a Markov model that assumes the examination process is non-ignorable. Copyright 2010 John Wiley & Sons, Ltd.

Model Checking Infinite-State Markov Chains

NARCIS (Netherlands)

Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Cloth, L.

2004-01-01

In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state

DISEÑO Y MANIPULACIÓN DE MODELOS OCULTOS DE MARKOV, UTILIZANDO HERRAMIENTAS HTK: UNA TUTORÍA DESIGN AND MANIPULATION OF HIDDEN MARKOV MODELS USING HTK TOOLS: A TUTORIAL

Directory of Open Access Journals (Sweden)

Roberto Carrillo Aguilar

2007-04-01

Full Text Available Este trabajo da a conocer el sistema de desarrollo de software para el diseño y manipulación de modelos ocultos de Markov, denominado HTK. Actualmente, la técnica de modelos ocultos de Markov es la herramienta más efectiva para implementar sistemas reconocedores del habla. HTK está orientado principalmente a ese aspecto. Su arquitectura es robusta y autosuficiente. Permite: la entrada lógica y natural desde un micrófono, dispone de módulos para la conversión A/D, preprocesado y parametrización de la información, posee herramientas para definir y manipular modelos ocultos de Markov, tiene librerías para entrenamiento y manipulación de los modelos ocultos de Markov ya definidos, considera funciones para definir la gramática, y además: Una serie de herramientas adicionales permiten lograr el objetivo final de obtener una hipotética transcripción del habla (conversión voz - texto.This paper presents HTK, a software development platform for the design and management of Hidden Markov Models. Nowadays, the Hidden Markov Models technique is the more effective one to implement voice recognition systems. HTK is mainly oriented to this application. Its architecture is robust and self-sufficient. It allows a natural input from a microphone, it has modules for A/D conversion, it allows pre-processing and parameterization of information, it possesses tools to define and manage the Hidden Markov Models, libraries for training and use the already defined Hidden Markov Models. It has functions to define the grammar and it has additional tools to reach the final objective, to obtain an hypothetical transcription of the talking (voice to text translation.

Markov-modulated infinite-server queues driven by a common background process

OpenAIRE

Mandjes , Michel; De Turck , Koen

2016-01-01

International audience; This paper studies a system with multiple infinite-server queues which are modulated by a common background process. If this background process, being modeled as a finite-state continuous-time Markov chain, is in state j, then the arrival rate into the i-th queue is λi,j, whereas the service times of customers present in this queue are exponentially distributed with mean µ −1 i,j ; at each of the individual queues all customers present are served in parallel (thus refl...

Inference with constrained hidden Markov models in PRISM

DEFF Research Database (Denmark)

Christiansen, Henning; Have, Christian Theil; Lassen, Ole Torp

2010-01-01

A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we show how HMMs can be extended with side-constraints and present constraint solving techniques for efficient inference. De......_different are integrated. We experimentally validate our approach on the biologically motivated problem of global pairwise alignment.......A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we show how HMMs can be extended with side-constraints and present constraint solving techniques for efficient inference...

A Bayesian Markov geostatistical model for estimation of hydrogeological properties

International Nuclear Information System (INIS)

Rosen, L.; Gustafson, G.

1996-01-01

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

On the record process of time-reversible spectrally-negative Markov additive processes

NARCIS (Netherlands)

J. Ivanovs; M.R.H. Mandjes (Michel)

2009-01-01

htmlabstractWe study the record process of a spectrally-negative Markov additive process (MAP). Assuming time-reversibility, a number of key quantities can be given explicitly. It is shown how these key quantities can be used when analyzing the distribution of the all-time maximum attained by MAPs

Performability assessment by model checking of Markov reward models

NARCIS (Netherlands)

Baier, Christel; Cloth, L.; Haverkort, Boudewijn R.H.M.; Hermanns, H.; Katoen, Joost P.

2010-01-01

This paper describes efficient procedures for model checking Markov reward models, that allow us to evaluate, among others, the performability of computer-communication systems. We present the logic CSRL (Continuous Stochastic Reward Logic) to specify performability measures. It provides flexibility

Strategic level proton therapy patient admission planning: a Markov decision process modeling approach.

Science.gov (United States)

Gedik, Ridvan; Zhang, Shengfan; Rainwater, Chase

2017-06-01

A relatively new consideration in proton therapy planning is the requirement that the mix of patients treated from different categories satisfy desired mix percentages. Deviations from these percentages and their impacts on operational capabilities are of particular interest to healthcare planners. In this study, we investigate intelligent ways of admitting patients to a proton therapy facility that maximize the total expected number of treatment sessions (fractions) delivered to patients in a planning period with stochastic patient arrivals and penalize the deviation from the patient mix restrictions. We propose a Markov Decision Process (MDP) model that provides very useful insights in determining the best patient admission policies in the case of an unexpected opening in the facility (i.e., no-shows, appointment cancellations, etc.). In order to overcome the curse of dimensionality for larger and more realistic instances, we propose an aggregate MDP model that is able to approximate optimal patient admission policies using the worded weight aggregation technique. Our models are applicable to healthcare treatment facilities throughout the United States, but are motivated by collaboration with the University of Florida Proton Therapy Institute (UFPTI).

Recursive smoothers for hidden discrete-time Markov chains

Directory of Open Access Journals (Sweden)

Lakhdar Aggoun

2005-01-01

Full Text Available We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995. We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM algorithm.

Study on the systematic approach of Markov modeling for dependability analysis of complex fault-tolerant features with voting logics

International Nuclear Information System (INIS)

Son, Kwang Seop; Kim, Dong Hoon; Kim, Chang Hwoi; Kang, Hyun Gook

2016-01-01

The Markov analysis is a technique for modeling system state transitions and calculating the probability of reaching various system states. While it is a proper tool for modeling complex system designs involving timing, sequencing, repair, redundancy, and fault tolerance, as the complexity or size of the system increases, so does the number of states of interest, leading to difficulty in constructing and solving the Markov model. This paper introduces a systematic approach of Markov modeling to analyze the dependability of a complex fault-tolerant system. This method is based on the decomposition of the system into independent subsystem sets, and the system-level failure rate and the unavailability rate for the decomposed subsystems. A Markov model for the target system is easily constructed using the system-level failure and unavailability rates for the subsystems, which can be treated separately. This approach can decrease the number of states to consider simultaneously in the target system by building Markov models of the independent subsystems stage by stage, and results in an exact solution for the Markov model of the whole target system. To apply this method we construct a Markov model for the reactor protection system found in nuclear power plants, a system configured with four identical channels and various fault-tolerant architectures. The results show that the proposed method in this study treats the complex architecture of the system in an efficient manner using the merits of the Markov model, such as a time dependent analysis and a sequential process analysis. - Highlights: • Systematic approach of Markov modeling for system dependability analysis is proposed based on the independent subsystem set, its failure rate and unavailability rate. • As an application example, we construct the Markov model for the digital reactor protection system configured with four identical and independent channels, and various fault-tolerant architectures. • The

Assessing type I error and power of multistate Markov models for panel data-A simulation study

OpenAIRE

Cassarly, Christy; Martin, Renee’ H.; Chimowitz, Marc; Peña, Edsel A.; Ramakrishnan, Viswanathan; Palesch, Yuko Y.

2016-01-01

Ordinal outcomes collected at multiple follow-up visits are common in clinical trials. Sometimes, one visit is chosen for the primary analysis and the scale is dichotomized amounting to loss of information. Multistate Markov models describe how a process moves between states over time. Here, simulation studies are performed to investigate the type I error and power characteristics of multistate Markov models for panel data with limited non-adjacent state transitions. The results suggest that ...

Continuous strong Markov processes in dimension one a stochastic calculus approach

CERN Document Server

Assing, Sigurd

1998-01-01

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Nonparametric model validations for hidden Markov models with applications in financial econometrics.

Science.gov (United States)

Zhao, Zhibiao

2011-06-01

We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise.

A high-fidelity weather time series generator using the Markov Chain process on a piecewise level

Science.gov (United States)

Hersvik, K.; Endrerud, O.-E. V.

2017-12-01

A method is developed for generating a set of unique weather time-series based on an existing weather series. The method allows statistically valid weather variations to take place within repeated simulations of offshore operations. The numerous generated time series need to share the same statistical qualities as the original time series. Statistical qualities here refer mainly to the distribution of weather windows available for work, including durations and frequencies of such weather windows, and seasonal characteristics. The method is based on the Markov chain process. The core new development lies in how the Markov Process is used, specifically by joining small pieces of random length time series together rather than joining individual weather states, each from a single time step, which is a common solution found in the literature. This new Markov model shows favorable characteristics with respect to the requirements set forth and all aspects of the validation performed.

Markov Chain-Based Stochastic Modeling of Chloride Ion Transport in Concrete Bridges

Directory of Open Access Journals (Sweden)

Yan Zhang

2018-03-01

Full Text Available Over the last decade, there has been an increasing interest in models for the evaluation and prediction of the condition of bridges in Canada due to their large number in an advanced state of deterioration. The models are used to develop optimal maintenance and replacement strategies to extend service life and optimally allocate financial and technical resources. The main process of deterioration of concrete bridges in Canada is corrosion of the reinforcing steel due to the widespread use of de-icing salts. In this article, numerical models of the diffusion process and chemical reactions of chloride ions in concrete are used to estimate the time to initiation of corrosion and for the progression of corrosion. The analyses are performed for a range of typical concrete properties, exposure and climatic conditions. The results from these simulations are used to develop parametric surrogate Markov chain models of increasing states of deterioration. The surrogate models are more efficient than physical models for the portfolio analysis of a large number of structures. The procedure provides an alternative to Markov models derived from condition ratings when historical inspection data is limited.

Transient Properties of Probability Distribution for a Markov Process with Size-dependent Additive Noise

Science.gov (United States)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

This study considered a stochastic model for cluster growth in a Markov process with a cluster size dependent additive noise. According to this model, the probability distribution of the cluster size transiently becomes an exponential or a log-normal distribution depending on the initial condition of the growth. In this letter, a master equation is obtained for this model, and derivation of the distributions is discussed.

Composable Markov Building Blocks

NARCIS (Netherlands)

Evers, S.; Fokkinga, M.M.; Apers, Peter M.G.; Prade, H.; Subrahmanian, V.S.

2007-01-01

In situations where disjunct parts of the same process are described by their own first-order Markov models and only one model applies at a time (activity in one model coincides with non-activity in the other models), these models can be joined together into one. Under certain conditions, nearly all

Fitting and interpreting continuous-time latent Markov models for panel data.

Science.gov (United States)

Lange, Jane M; Minin, Vladimir N

2013-11-20

Multistate models characterize disease processes within an individual. Clinical studies often observe the disease status of individuals at discrete time points, making exact times of transitions between disease states unknown. Such panel data pose considerable modeling challenges. Assuming the disease process progresses accordingly, a standard continuous-time Markov chain (CTMC) yields tractable likelihoods, but the assumption of exponential sojourn time distributions is typically unrealistic. More flexible semi-Markov models permit generic sojourn distributions yet yield intractable likelihoods for panel data in the presence of reversible transitions. One attractive alternative is to assume that the disease process is characterized by an underlying latent CTMC, with multiple latent states mapping to each disease state. These models retain analytic tractability due to the CTMC framework but allow for flexible, duration-dependent disease state sojourn distributions. We have developed a robust and efficient expectation-maximization algorithm in this context. Our complete data state space consists of the observed data and the underlying latent trajectory, yielding computationally efficient expectation and maximization steps. Our algorithm outperforms alternative methods measured in terms of time to convergence and robustness. We also examine the frequentist performance of latent CTMC point and interval estimates of disease process functionals based on simulated data. The performance of estimates depends on time, functional, and data-generating scenario. Finally, we illustrate the interpretive power of latent CTMC models for describing disease processes on a dataset of lung transplant patients. We hope our work will encourage wider use of these models in the biomedical setting. Copyright © 2013 John Wiley & Sons, Ltd.

Data-Driven Markov Decision Process Approximations for Personalized Hypertension Treatment Planning

Directory of Open Access Journals (Sweden)

Greggory J. Schell PhD

2016-10-01

Full Text Available Background: Markov decision process (MDP models are powerful tools. They enable the derivation of optimal treatment policies but may incur long computational times and generate decision rules that are challenging to interpret by physicians. Methods: In an effort to improve usability and interpretability, we examined whether Poisson regression can approximate optimal hypertension treatment policies derived by an MDP for maximizing a patient’s expected discounted quality-adjusted life years. Results: We found that our Poisson approximation to the optimal treatment policy matched the optimal policy in 99% of cases. This high accuracy translates to nearly identical health outcomes for patients. Furthermore, the Poisson approximation results in 104 additional quality-adjusted life years per 1000 patients compared to the Seventh Joint National Committee’s treatment guidelines for hypertension. The comparative health performance of the Poisson approximation was robust to the cardiovascular disease risk calculator used and calculator calibration error. Limitations: Our results are based on Markov chain modeling. Conclusions: Poisson model approximation for blood pressure treatment planning has high fidelity to optimal MDP treatment policies, which can improve usability and enhance transparency of more personalized treatment policies.

Hidden Markov latent variable models with multivariate longitudinal data.

Science.gov (United States)

Song, Xinyuan; Xia, Yemao; Zhu, Hongtu

2017-03-01

Cocaine addiction is chronic and persistent, and has become a major social and health problem in many countries. Existing studies have shown that cocaine addicts often undergo episodic periods of addiction to, moderate dependence on, or swearing off cocaine. Given its reversible feature, cocaine use can be formulated as a stochastic process that transits from one state to another, while the impacts of various factors, such as treatment received and individuals' psychological problems on cocaine use, may vary across states. This article develops a hidden Markov latent variable model to study multivariate longitudinal data concerning cocaine use from a California Civil Addict Program. The proposed model generalizes conventional latent variable models to allow bidirectional transition between cocaine-addiction states and conventional hidden Markov models to allow latent variables and their dynamic interrelationship. We develop a maximum-likelihood approach, along with a Monte Carlo expectation conditional maximization (MCECM) algorithm, to conduct parameter estimation. The asymptotic properties of the parameter estimates and statistics for testing the heterogeneity of model parameters are investigated. The finite sample performance of the proposed methodology is demonstrated by simulation studies. The application to cocaine use study provides insights into the prevention of cocaine use. © 2016, The International Biometric Society.

PELACAKAN DAN PENGENALAN WAJAH MENGGUNAKAN METODE EMBEDDED HIDDEN MARKOV MODELS

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Arie Wirawan Margono

2004-01-01

Full Text Available Tracking and recognizing human face becomes one of the important research subjects nowadays, where it is applicable in security system like room access, surveillance, as well as searching for person identity in police database. Because of applying in security case, it is necessary to have robust system for certain conditions such as: background influence, non-frontal face pose of male or female in different age and race. The aim of this research is to develop software which combines human face tracking using CamShift algorithm and face recognition system using Embedded Hidden Markov Models. The software uses video camera (webcam for real-time input, video AVI for dynamic input, and image file for static input. The software uses Object Oriented Programming (OOP coding style with C++ programming language, Microsoft Visual C++ 6.0® compiler, and assisted by some libraries of Intel Image Processing Library (IPL and Intel Open Source Computer Vision (OpenCV. System testing shows that object tracking based on skin complexion using CamShift algorithm comes out well, for tracking of single or even two face objects at once. Human face recognition system using Embedded Hidden Markov Models method has reach accuracy percentage of 82.76%, using 341 human faces in database that consists of 31 individuals with 11 poses and 29 human face testers. Abstract in Bahasa Indonesia : Pelacakan dan pengenalan wajah manusia merupakan salah satu bidang yang cukup berkembang dewasa ini, dimana aplikasi dapat diterapkan dalam bidang keamanan (security system seperti ijin akses masuk ruangan, pengawasan lokasi (surveillance, maupun pencarian identitas individu pada database kepolisian. Karena diterapkan dalam kasus keamanan, dibutuhkan sistem yang handal terhadap beberapa kondisi, seperti: pengaruh latar belakang, pose wajah non-frontal terhadap pria maupun wanita dalam perbedaan usia dan ras. Tujuan penelitiam ini adalah untuk membuat perangkat lunak yang menggabungkan

On the representability of complete genomes by multiple competing finite-context (Markov models.

Directory of Open Access Journals (Sweden)

Armando J Pinho

Full Text Available A finite-context (Markov model of order k yields the probability distribution of the next symbol in a sequence of symbols, given the recent past up to depth k. Markov modeling has long been applied to DNA sequences, for example to find gene-coding regions. With the first studies came the discovery that DNA sequences are non-stationary: distinct regions require distinct model orders. Since then, Markov and hidden Markov models have been extensively used to describe the gene structure of prokaryotes and eukaryotes. However, to our knowledge, a comprehensive study about the potential of Markov models to describe complete genomes is still lacking. We address this gap in this paper. Our approach relies on (i multiple competing Markov models of different orders (ii careful programming techniques that allow orders as large as sixteen (iii adequate inverted repeat handling (iv probability estimates suited to the wide range of context depths used. To measure how well a model fits the data at a particular position in the sequence we use the negative logarithm of the probability estimate at that position. The measure yields information profiles of the sequence, which are of independent interest. The average over the entire sequence, which amounts to the average number of bits per base needed to describe the sequence, is used as a global performance measure. Our main conclusion is that, from the probabilistic or information theoretic point of view and according to this performance measure, multiple competing Markov models explain entire genomes almost as well or even better than state-of-the-art DNA compression methods, such as XM, which rely on very different statistical models. This is surprising, because Markov models are local (short-range, contrasting with the statistical models underlying other methods, where the extensive data repetitions in DNA sequences is explored, and therefore have a non-local character.

A Markov decision model for optimising economic production lot size ...

African Journals Online (AJOL)

Adopting such a Markov decision process approach, the states of a Markov chain represent possible states of demand. The decision of whether or not to produce additional inventory units is made using dynamic programming. This approach demonstrates the existence of an optimal state-dependent EPL size, and produces ...

A Probabilistic Short-Term Water Demand Forecasting Model Based on the Markov Chain

Directory of Open Access Journals (Sweden)

Francesca Gagliardi

2017-07-01

Full Text Available This paper proposes a short-term water demand forecasting method based on the use of the Markov chain. This method provides estimates of future demands by calculating probabilities that the future demand value will fall within pre-assigned intervals covering the expected total variability. More specifically, two models based on homogeneous and non-homogeneous Markov chains were developed and presented. These models, together with two benchmark models (based on artificial neural network and naïve methods, were applied to three real-life case studies for the purpose of forecasting the respective water demands from 1 to 24 h ahead. The results obtained show that the model based on a homogeneous Markov chain provides more accurate short-term forecasts than the one based on a non-homogeneous Markov chain, which is in line with the artificial neural network model. Both Markov chain models enable probabilistic information regarding the stochastic demand forecast to be easily obtained.

Computing characterizations of drugs for ion channels and receptors using Markov models

CERN Document Server

Tveito, Aslak

2016-01-01

Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.

Berman-Konsowa principle for reversible Markov jump processes

NARCIS (Netherlands)

Hollander, den W.Th.F.; Jansen, S.

2013-01-01

In this paper we prove a version of the Berman-Konsowa principle for reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle provides a variational formula for the capacity of a pair of disjoint measurable sets. There are two versions, one involving a class of probability

Filtering of a Markov Jump Process with Counting Observations

International Nuclear Information System (INIS)

Ceci, C.; Gerardi, A.

2000-01-01

This paper concerns the filtering of an R d -valued Markov pure jump process when only the total number of jumps are observed. Strong and weak uniqueness for the solutions of the filtering equations are discussed

Composable Markov Building Blocks

NARCIS (Netherlands)

Evers, S.; Fokkinga, M.M.; Apers, Peter M.G.

2007-01-01

In situations where disjunct parts of the same process are described by their own first-order Markov models, these models can be joined together under the constraint that there can only be one activity at a time, i.e. the activities of one model coincide with non-activity in the other models. Under

Markov chain model for demersal fish catch analysis in Indonesia

Science.gov (United States)

Firdaniza; Gusriani, N.

2018-03-01

As an archipelagic country, Indonesia has considerable potential fishery resources. One of the fish resources that has high economic value is demersal fish. Demersal fish is a fish with a habitat in the muddy seabed. Demersal fish scattered throughout the Indonesian seas. Demersal fish production in each Indonesia’s Fisheries Management Area (FMA) varies each year. In this paper we have discussed the Markov chain model for demersal fish yield analysis throughout all Indonesia’s Fisheries Management Area. Data of demersal fish catch in every FMA in 2005-2014 was obtained from Directorate of Capture Fisheries. From this data a transition probability matrix is determined by the number of transitions from the catch that lie below the median or above the median. The Markov chain model of demersal fish catch data was an ergodic Markov chain model, so that the limiting probability of the Markov chain model can be determined. The predictive value of demersal fishing yields was obtained by calculating the combination of limiting probability with average catch results below the median and above the median. The results showed that for 2018 and long-term demersal fishing results in most of FMA were below the median value.

A Markov Model for Commen-Cause Failures

DEFF Research Database (Denmark)

Platz, Ole

1984-01-01

A continuous time four-state Markov chain is shown to cover several of the models that have been used for describing dependencies between failures of components in redundant systems. Among these are the models derived by Marshall and Olkin and by Freund and models for one-out-of-three and two...

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution

Directory of Open Access Journals (Sweden)

Ivan B. Djordjevic

2015-08-01

Full Text Available Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i Markovian classical model, (ii Markovian-like quantum model, and (iii hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage Markov chain-like models of aging, which

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

Science.gov (United States)

Wang, Xinlei; Zang, Miao; Xiao, Guanghua

2013-06-15

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

Detecting critical state before phase transition of complex biological systems by hidden Markov model.

Science.gov (United States)

Chen, Pei; Liu, Rui; Li, Yongjun; Chen, Luonan

2016-07-15

Identifying the critical state or pre-transition state just before the occurrence of a phase transition is a challenging task, because the state of the system may show little apparent change before this critical transition during the gradual parameter variations. Such dynamics of phase transition is generally composed of three stages, i.e. before-transition state, pre-transition state and after-transition state, which can be considered as three different Markov processes. By exploring the rich dynamical information provided by high-throughput data, we present a novel computational method, i.e. hidden Markov model (HMM) based approach, to detect the switching point of the two Markov processes from the before-transition state (a stationary Markov process) to the pre-transition state (a time-varying Markov process), thereby identifying the pre-transition state or early-warning signals of the phase transition. To validate the effectiveness, we apply this method to detect the signals of the imminent phase transitions of complex systems based on the simulated datasets, and further identify the pre-transition states as well as their critical modules for three real datasets, i.e. the acute lung injury triggered by phosgene inhalation, MCF-7 human breast cancer caused by heregulin and HCV-induced dysplasia and hepatocellular carcinoma. Both functional and pathway enrichment analyses validate the computational results. The source code and some supporting files are available at https://github.com/rabbitpei/HMM_based-method lnchen@sibs.ac.cn or liyj@scut.edu.cn Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

The application of Markov decision process with penalty function in restaurant delivery robot

Science.gov (United States)

Wang, Yong; Hu, Zhen; Wang, Ying

2017-05-01

As the restaurant delivery robot is often in a dynamic and complex environment, including the chairs inadvertently moved to the channel and customers coming and going. The traditional Markov decision process path planning algorithm is not save, the robot is very close to the table and chairs. To solve this problem, this paper proposes the Markov Decision Process with a penalty term called MDPPT path planning algorithm according to the traditional Markov decision process (MDP). For MDP, if the restaurant delivery robot bumps into an obstacle, the reward it receives is part of the current status reward. For the MDPPT, the reward it receives not only the part of the current status but also a negative constant term. Simulation results show that the MDPPT algorithm can plan a more secure path.

Semi-Markov models control of restorable systems with latent failures

CERN Document Server

Obzherin, Yuriy E

2015-01-01

Featuring previously unpublished results, Semi-Markov Models: Control of Restorable Systems with Latent Failures describes valuable methodology which can be used by readers to build mathematical models of a wide class of systems for various applications. In particular, this information can be applied to build models of reliability, queuing systems, and technical control. Beginning with a brief introduction to the area, the book covers semi-Markov models for different control strategies in one-component systems, defining their stationary characteristics of reliability and efficiency, and uti

Modeling Dyadic Processes Using Hidden Markov Models: A Time Series Approach to Mother-Infant Interactions during Infant Immunization

Science.gov (United States)

Stifter, Cynthia A.; Rovine, Michael

2015-01-01

The focus of the present longitudinal study, to examine mother-infant interaction during the administration of immunizations at 2 and 6?months of age, used hidden Markov modelling, a time series approach that produces latent states to describe how mothers and infants work together to bring the infant to a soothed state. Results revealed a…

Markov process of muscle motors

International Nuclear Information System (INIS)

Kondratiev, Yu; Pechersky, E; Pirogov, S

2008-01-01

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

Markov chain modeling of evolution of strains in reinforced concrete flexural beams

Directory of Open Access Journals (Sweden)

Anoop, M. B.

2012-09-01

Full Text Available From the analysis of experimentally observed variations in surface strains with loading in reinforced concrete beams, it is noted that there is a need to consider the evolution of strains (with loading as a stochastic process. Use of Markov Chains for modeling stochastic evolution of strains with loading in reinforced concrete flexural beams is studied in this paper. A simple, yet practically useful, bi-level homogeneous Gaussian Markov Chain (BLHGMC model is proposed for determining the state of strain in reinforced concrete beams. The BLHGMC model will be useful for predicting behavior/response of reinforced concrete beams leading to more rational design.A través del análisis de la evolución de la deformación superficial observada experimentalmente en vigas de hormigón armado al entrar en carga, se constata que dicho proceso debe considerarse estocástico. En este trabajo se estudia la utilización de cadenas de Markov para modelizar la evolución estocástica de la deformación de vigas flexotraccionadas. Se propone, para establecer el estado de deformación de estas, un modelo con distribución gaussiana tipo cadena de Markov homogénea de dos niveles (BLHGMC por sus siglas en inglés, cuyo empleo resulta sencillo y práctico. Se comprueba la utilidad del modelo BLHGMC para prever el comportamiento de estos elementos, lo que determina a su vez una mayor racionalidad a la hora de su cálculo y diseño

Dual Sticky Hierarchical Dirichlet Process Hidden Markov Model and Its Application to Natural Language Description of Motions.

Science.gov (United States)

Hu, Weiming; Tian, Guodong; Kang, Yongxin; Yuan, Chunfeng; Maybank, Stephen

2017-09-25

In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. On combining the learnt sources and sinks, semantic motion regions, and the learnt sequence of atomic activities, the action represented by the trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.

A Method for Speeding Up Value Iteration in Partially Observable Markov Decision Processes

OpenAIRE

Zhang, Nevin Lianwen; Lee, Stephen S.; Zhang, Weihong

2013-01-01

We present a technique for speeding up the convergence of value iteration for partially observable Markov decisions processes (POMDPs). The underlying idea is similar to that behind modified policy iteration for fully observable Markov decision processes (MDPs). The technique can be easily incorporated into any existing POMDP value iteration algorithms. Experiments have been conducted on several test problems with one POMDP value iteration algorithm called incremental pruning. We find that th...

K­MEANS CLUSTERING FOR HIDDEN MARKOV MODEL

NARCIS (Netherlands)

Perrone, M.P.; Connell, S.D.

2004-01-01

An unsupervised k­means clustering algorithm for hidden Markov models is described and applied to the task of generating subclass models for individual handwritten character classes. The algorithm is compared to a related clustering method and shown to give a relative change in the error rate of as

The exit-time problem for a Markov jump process

Science.gov (United States)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Markov model of fatigue of a composite material with the poisson process of defect initiation

Science.gov (United States)

Paramonov, Yu.; Chatys, R.; Andersons, J.; Kleinhofs, M.

2012-05-01

As a development of the model where only one weak microvolume (WMV) and only a pulsating cyclic loading are considered, in the current version of the model, we take into account the presence of several weak sites where fatigue damage can accumulate and a loading with an arbitrary (but positive) stress ratio. The Poisson process of initiation of WMVs is considered, whose rate depends on the size of a specimen. The cumulative distribution function (cdf) of the fatigue life of every individual WMV is calculated using the Markov model of fatigue. For the case where this function is approximated by a lognormal distribution, a formula for calculating the cdf of fatigue life of the specimen (modeled as a chain of WMVs) is obtained. Only a pulsating cyclic loading was considered in the previous version of the model. Now, using the modified energy method, a loading cycle with an arbitrary stress ratio is "transformed" into an equivalent cycle with some other stress ratio. In such a way, the entire probabilistic fatigue diagram for any stress ratio with a positive cycle stress can be obtained. Numerical examples are presented.

On Characterisation of Markov Processes Via Martingale Problems

Indian Academy of Sciences (India)

This extension is used to improve on a criterion for a probability measure to be invariant for the semigroup associated with the Markov process. We also give examples of martingale problems that are well-posed in the class of solutions which are continuous in probability but for which no r.c.l.l. solution exists.

Input modeling with phase-type distributions and Markov models theory and applications

CERN Document Server

Buchholz, Peter; Felko, Iryna

2014-01-01

Containing a summary of several recent results on Markov-based input modeling in a coherent notation, this book introduces and compares algorithms for parameter fitting and gives an overview of available software tools in the area. Due to progress made in recent years with respect to new algorithms to generate PH distributions and Markovian arrival processes from measured data, the models outlined are useful alternatives to other distributions or stochastic processes used for input modeling. Graduate students and researchers in applied probability, operations research and computer science along with practitioners using simulation or analytical models for performance analysis and capacity planning will find the unified notation and up-to-date results presented useful. Input modeling is the key step in model based system analysis to adequately describe the load of a system using stochastic models. The goal of input modeling is to find a stochastic model to describe a sequence of measurements from a real system...

Double-observer line transect surveys with Markov-modulated Poisson process models for animal availability.

Science.gov (United States)

Borchers, D L; Langrock, R

2015-12-01

We develop maximum likelihood methods for line transect surveys in which animals go undetected at distance zero, either because they are stochastically unavailable while within view or because they are missed when they are available. These incorporate a Markov-modulated Poisson process model for animal availability, allowing more clustered availability events than is possible with Poisson availability models. They include a mark-recapture component arising from the independent-observer survey, leading to more accurate estimation of detection probability given availability. We develop models for situations in which (a) multiple detections of the same individual are possible and (b) some or all of the availability process parameters are estimated from the line transect survey itself, rather than from independent data. We investigate estimator performance by simulation, and compare the multiple-detection estimators with estimators that use only initial detections of individuals, and with a single-observer estimator. Simultaneous estimation of detection function parameters and availability model parameters is shown to be feasible from the line transect survey alone with multiple detections and double-observer data but not with single-observer data. Recording multiple detections of individuals improves estimator precision substantially when estimating the availability model parameters from survey data, and we recommend that these data be gathered. We apply the methods to estimate detection probability from a double-observer survey of North Atlantic minke whales, and find that double-observer data greatly improve estimator precision here too. © 2015 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.

Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant

Science.gov (United States)

Aggarwal, Anil Kr.; Kumar, Sanjeev; Singh, Vikram; Garg, Tarun Kr.

2015-12-01

This paper deals with the Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant. This system was modeled using Markov birth-death process with the assumption that the failure and repair rates of each subsystem follow exponential distribution. The first-order Chapman-Kolmogorov differential equations are developed with the use of mnemonic rule and these equations are solved with Runga-Kutta fourth-order method. The long-run availability, reliability and mean time between failures are computed for various choices of failure and repair rates of subsystems of the system. The findings of the paper are discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the performance of the urea synthesis system of the fertilizer plant.

Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium

Science.gov (United States)

Kapfer, Sebastian C.; Krauth, Werner

2017-12-01

We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.

Confluence reduction for Markov automata

NARCIS (Netherlands)

Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette

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

Confluence Reduction for Markov Automata

NARCIS (Netherlands)

Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Braberman, Victor; Fribourg, Laurent

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

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

Science.gov (United States)

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

2014-02-01

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

The Consensus String Problem and the Complexity of Comparing Hidden Markov Models

DEFF Research Database (Denmark)

Lyngsø, Rune Bang; Pedersen, Christian Nørgaard Storm

2002-01-01

The basic theory of hidden Markov models was developed and applied to problems in speech recognition in the late 1960s, and has since then been applied to numerous problems, e.g. biological sequence analysis. Most applications of hidden Markov models are based on efficient algorithms for computing......-norms. We discuss the applicability of the technique used for proving the hardness of comparing two hidden Markov models under the L1-norm to other measures of distance between probability distributions. In particular, we show that it cannot be used for proving NP-hardness of determining the Kullback...

Planning treatment of ischemic heart disease with partially observable Markov decision processes.

Science.gov (United States)

Hauskrecht, M; Fraser, H

2000-03-01

Diagnosis of a disease and its treatment are not separate, one-shot activities. Instead, they are very often dependent and interleaved over time. This is mostly due to uncertainty about the underlying disease, uncertainty associated with the response of a patient to the treatment and varying cost of different diagnostic (investigative) and treatment procedures. The framework of partially observable Markov decision processes (POMDPs) developed and used in the operations research, control theory and artificial intelligence communities is particularly suitable for modeling such a complex decision process. In this paper, we show how the POMDP framework can be used to model and solve the problem of the management of patients with ischemic heart disease (IHD), and demonstrate the modeling advantages of the framework over standard decision formalisms.

Development of Markov model of emergency diesel generator for dynamic reliability analysis

Energy Technology Data Exchange (ETDEWEB)

Jin, Young Ho; Choi, Sun Yeong; Yang, Joon Eon [Korea Atomic Energy Research Institute, Taejon (Korea)

1999-02-01

The EDG (Emergency Diesal Generator) of nuclear power plant is one of the most important equipments in mitigating accidents. The FT (Fault Tree) method is widely used to assess the reliability of safety systems like an EDG in nuclear power plant. This method, however, has limitations in modeling dynamic features of safety systems exactly. We, hence, have developed a Markov model to represent the stochastic process of dynamic systems whose states change as time moves on. The Markov model enables us to develop a dynamic reliability model of EDG. This model can represent all possible states of EDG comparing to the FRANTIC code developed by U.S. NRC for the reliability analysis of standby systems. to access the regulation policy for test interval, we performed two simulations based on the generic data and plant specific data of YGN 3, respectively by using the developed model. We also estimate the effects of various repair rates and the fractions of starting failures by demand shock to the reliability of EDG. And finally, Aging effect is analyzed. (author). 23 refs., 19 figs., 9 tabs.

Risk aversion and risk seeking in multicriteria forest management: a Markov decision process approach

Science.gov (United States)

Joseph Buongiorno; Mo Zhou; Craig Johnston

2017-01-01

Markov decision process models were extended to reflect some consequences of the risk attitude of forestry decision makers. One approach consisted of maximizing the expected value of a criterion subject to an upper bound on the variance or, symmetrically, minimizing the variance subject to a lower bound on the expected value.  The other method used the certainty...

Mean-Variance Optimization in Markov Decision Processes

OpenAIRE

Mannor, Shie; Tsitsiklis, John N.

2011-01-01

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

Dynamic neutron scattering from conformational dynamics. II. Application using molecular dynamics simulation and Markov modeling.

Science.gov (United States)

Yi, Zheng; Lindner, Benjamin; Prinz, Jan-Hendrik; Noé, Frank; Smith, Jeremy C

2013-11-07

Neutron scattering experiments directly probe the dynamics of complex molecules on the sub pico- to microsecond time scales. However, the assignment of the relaxations seen experimentally to specific structural rearrangements is difficult, since many of the underlying dynamical processes may exist on similar timescales. In an accompanying article, we present a theoretical approach to the analysis of molecular dynamics simulations with a Markov State Model (MSM) that permits the direct identification of structural transitions leading to each contributing relaxation process. Here, we demonstrate the use of the method by applying it to the configurational dynamics of the well-characterized alanine dipeptide. A practical procedure for deriving the MSM from an MD is introduced. The result is a 9-state MSM in the space of the backbone dihedral angles and the side-chain methyl group. The agreement between the quasielastic spectrum calculated directly from the atomic trajectories and that derived from the Markov state model is excellent. The dependence on the wavevector of the individual Markov processes is described. The procedure means that it is now practicable to interpret quasielastic scattering spectra in terms of well-defined intramolecular transitions with minimal a priori assumptions as to the nature of the dynamics taking place.

Markov stochasticity coordinates

International Nuclear Information System (INIS)

Eliazar, Iddo

2017-01-01

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

Markov stochasticity coordinates

Energy Technology Data Exchange (ETDEWEB)

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

2017-01-15

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

Cascade probabilistic function and the Markov's processes. Chapter 1

International Nuclear Information System (INIS)

2002-01-01

In the Chapter 1 the physical and mathematical descriptions of radiation processes are carried out. The relation of the cascade probabilistic functions (CPF) for electrons, protons, alpha-particles and ions with Markov's chain is shown. The algorithms for CPF calculation with accounting energy losses are given

Evaluation of Usability Utilizing Markov Models

Science.gov (United States)

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…

MARKOV Model Application to Proliferation Risk Reduction of an Advanced Nuclear System

International Nuclear Information System (INIS)

Bari, R.A.

2008-01-01

The Generation IV International Forum (GIF) emphasizes proliferation resistance and physical protection (PR and PP) as a main goal for future nuclear energy systems. The GIF PR and PP Working Group has developed a methodology for the evaluation of these systems. As an application of the methodology, Markov model has been developed for the evaluation of proliferation resistance and is demonstrated for a hypothetical Example Sodium Fast Reactor (ESFR) system. This paper presents the case of diversion by the facility owner/operator to obtain material that could be used in a nuclear weapon. The Markov model is applied to evaluate material diversion strategies. The following features of the Markov model are presented here: (1) An effective detection rate has been introduced to account for the implementation of multiple safeguards approaches at a given strategic point; (2) Technical failure to divert material is modeled as intrinsic barriers related to the design of the facility or the properties of the material in the facility; and (3) Concealment to defeat or degrade the performance of safeguards is recognized in the Markov model. Three proliferation risk measures are calculated directly by the Markov model: the detection probability, technical failure probability, and proliferation time. The material type is indicated by an index that is based on the quality of material diverted. Sensitivity cases have been done to demonstrate the effects of different modeling features on the measures of proliferation resistance

Enhanced Map-Matching Algorithm with a Hidden Markov Model for Mobile Phone Positioning

Directory of Open Access Journals (Sweden)

An Luo

2017-10-01

Full Text Available Numerous map-matching techniques have been developed to improve positioning, using Global Positioning System (GPS data and other sensors. However, most existing map-matching algorithms process GPS data with high sampling rates, to achieve a higher correct rate and strong universality. This paper introduces a novel map-matching algorithm based on a hidden Markov model (HMM for GPS positioning and mobile phone positioning with a low sampling rate. The HMM is a statistical model well known for providing solutions to temporal recognition applications such as text and speech recognition. In this work, the hidden Markov chain model was built to establish a map-matching process, using the geometric data, the topologies matrix of road links in road network and refined quad-tree data structure. HMM-based map-matching exploits the Viterbi algorithm to find the optimized road link sequence. The sequence consists of hidden states in the HMM model. The HMM-based map-matching algorithm is validated on a vehicle trajectory using GPS and mobile phone data. The results show a significant improvement in mobile phone positioning and high and low sampling of GPS data.

On Markov processes in the hadron-nuclear and nuclear-nuclear collisions at superhigh energies

International Nuclear Information System (INIS)

Lebedeva, A.A.; Rus'kin, V.I.

2001-01-01

In the article the possibility of the Markov processes use as simulation method for mean characteristics of hadron-nuclear and nucleus-nuclear collisions at superhigh energies is discussed. The simple (hadron-nuclear collisions) and non-simple (nucleus-nuclear collisions) non-uniform Markov process of output constant spectrum and absorption in a nucleon's nucleus-target with rapidity y are considered. The expression allowing to simulate the different collision modes were obtained

Reliability analysis and prediction of mixed mode load using Markov Chain Model

International Nuclear Information System (INIS)

Nikabdullah, N.; Singh, S. S. K.; Alebrahim, R.; Azizi, M. A.; K, Elwaleed A.; Noorani, M. S. M.

2014-01-01

The aim of this paper is to present the reliability analysis and prediction of mixed mode loading by using a simple two state Markov Chain Model for an automotive crankshaft. The reliability analysis and prediction for any automotive component or structure is important for analyzing and measuring the failure to increase the design life, eliminate or reduce the likelihood of failures and safety risk. The mechanical failures of the crankshaft are due of high bending and torsion stress concentration from high cycle and low rotating bending and torsional stress. The Markov Chain was used to model the two states based on the probability of failure due to bending and torsion stress. In most investigations it revealed that bending stress is much serve than torsional stress, therefore the probability criteria for the bending state would be higher compared to the torsion state. A statistical comparison between the developed Markov Chain Model and field data was done to observe the percentage of error. The reliability analysis and prediction was derived and illustrated from the Markov Chain Model were shown in the Weibull probability and cumulative distribution function, hazard rate and reliability curve and the bathtub curve. It can be concluded that Markov Chain Model has the ability to generate near similar data with minimal percentage of error and for a practical application; the proposed model provides a good accuracy in determining the reliability for the crankshaft under mixed mode loading

Markov chain model helps predict pitting corrosion depth and rate in underground pipelines

Energy Technology Data Exchange (ETDEWEB)

Caleyo, F.; Velazquez, J.C.; Hallen, J. M. [ESIQIE, Instituto Politecnico Nacional, Mexico D. F. (Mexico); Esquivel-Amezcua, A. [PEMEX PEP Region Sur, Villahermosa, Tabasco (Mexico); Valor, A. [Universidad de la Habana, Vedado, La Habana (Cuba)

2010-07-01

Recent reports place pipeline corrosion costs in North America at seven billion dollars per year. Pitting corrosion causes the higher percentage of failures among other corrosion mechanisms. This has motivated multiple modelling studies to be focused on corrosion pitting of underground pipelines. In this study, a continuous-time, non-homogenous pure birth Markov chain serves to model external pitting corrosion in buried pipelines. The analytical solution of Kolmogorov's forward equations for this type of Markov process gives the transition probability function in a discrete space of pit depths. The transition probability function can be completely identified by making a correlation between the stochastic pit depth mean and the deterministic mean obtained experimentally. The model proposed in this study can be applied to pitting corrosion data from repeated in-line pipeline inspections. Case studies presented in this work show how pipeline inspection and maintenance planning can be improved by using the proposed Markovian model for pitting corrosion.

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...

Fast-slow asymptotics for a Markov chain model of fast sodium current

Science.gov (United States)

Starý, Tomáš; Biktashev, Vadim N.

2017-09-01

We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.

Description of quantum-mechanical motion by using the formalism of non-Markov stochastic process

International Nuclear Information System (INIS)

Skorobogatov, G.A.; Svertilov, S.I.

1999-01-01

The principle possibilities of mathematical modeling of quantum mechanical motion by the theory of a real stochastic processes is considered. The set of equations corresponding to the simplest case of a two-level system undergoing transitions under the influence of electromagnetic field are obtained. It is shown that quantum-mechanical processes are purely discrete processes of non-Markovian type. They are continuous processes in the space of probability amplitudes and posses the properties of quantum Markovity. The formulation of quantum mechanics in terms of the theory of stochastic processes is necessary for its generalization on small space-time intervals [ru

Two-boundary first exit time of Gauss-Markov processes for stochastic modeling of acto-myosin dynamics.

Science.gov (United States)

D'Onofrio, Giuseppe; Pirozzi, Enrica

2017-05-01

We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.

Estimation and uncertainty of reversible Markov models.

Science.gov (United States)

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

2015-11-07

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

[Application of Markov model in post-marketing pharmacoeconomic evaluation of traditional Chinese medicine].

Science.gov (United States)

Wang, Xin; Su, Xia; Sun, Wentao; Xie, Yanming; Wang, Yongyan

2011-10-01

In post-marketing study of traditional Chinese medicine (TCM), pharmacoeconomic evaluation has an important applied significance. However, the economic literatures of TCM have been unable to fully and accurately reflect the unique overall outcomes of treatment with TCM. For the special nature of TCM itself, we recommend that Markov model could be introduced into post-marketing pharmacoeconomic evaluation of TCM, and also explore the feasibility of model application. Markov model can extrapolate the study time horizon, suit with effectiveness indicators of TCM, and provide measurable comprehensive outcome. In addition, Markov model can promote the development of TCM quality of life scale and the methodology of post-marketing pharmacoeconomic evaluation.

Markov Chain model for the stochastic behaviors of wind-direction data

International Nuclear Information System (INIS)

Masseran, Nurulkamal

2015-01-01

Highlights: • I develop a Markov chain model to describe about the stochastic and probabilistic behaviors of wind direction data. • I describe some of the theoretical arguments regarding the Markov chain model in term of wind direction data. • I suggest a limiting probabilities approach to determine a dominant directions of wind blow. - Abstract: Analyzing the behaviors of wind direction can complement knowledge concerning wind speed and help researchers draw conclusions regarding wind energy potential. Knowledge of the wind’s direction enables the wind turbine to be positioned in such a way as to maximize the total amount of captured energy and optimize the wind farm’s performance. In this paper, first-order and higher-order Markov chain models are proposed to describe the probabilistic behaviors of wind-direction data. A case study is conducted using data from Mersing, Malaysia. The wind-direction data are classified according to an eight-state Markov chain based on natural geographical directions. The model’s parameters are estimated using the maximum likelihood method and the linear programming formulation. Several theoretical arguments regarding the model are also discussed. Finally, limiting probabilities are used to determine a long-run proportion of the wind directions generated. The results explain the dominant direction for Mersing’s wind in terms of probability metrics

Discrete time Markov chains (DTMC) susceptible infected susceptible (SIS) epidemic model with two pathogens in two patches

Science.gov (United States)

Lismawati, Eka; Respatiwulan; Widyaningsih, Purnami

2017-06-01

The SIS epidemic model describes the pattern of disease spread with characteristics that recovered individuals can be infected more than once. The number of susceptible and infected individuals every time follows the discrete time Markov process. It can be represented by the discrete time Markov chains (DTMC) SIS. The DTMC SIS epidemic model can be developed for two pathogens in two patches. The aims of this paper are to reconstruct and to apply the DTMC SIS epidemic model with two pathogens in two patches. The model was presented as transition probabilities. The application of the model obtain that the number of susceptible individuals decreases while the number of infected individuals increases for each pathogen in each patch.

Markov state models of protein misfolding

Science.gov (United States)

Sirur, Anshul; De Sancho, David; Best, Robert B.

2016-02-01

Markov state models (MSMs) are an extremely useful tool for understanding the conformational dynamics of macromolecules and for analyzing MD simulations in a quantitative fashion. They have been extensively used for peptide and protein folding, for small molecule binding, and for the study of native ensemble dynamics. Here, we adapt the MSM methodology to gain insight into the dynamics of misfolded states. To overcome possible flaws in root-mean-square deviation (RMSD)-based metrics, we introduce a novel discretization approach, based on coarse-grained contact maps. In addition, we extend the MSM methodology to include "sink" states in order to account for the irreversibility (on simulation time scales) of processes like protein misfolding. We apply this method to analyze the mechanism of misfolding of tandem repeats of titin domains, and how it is influenced by confinement in a chaperonin-like cavity.

Bayesian inference for Markov jump processes with informative observations.

Science.gov (United States)

Golightly, Andrew; Wilkinson, Darren J

2015-04-01

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

Chronic kidney disease Markov model comparing paricalcitol to calcitriol for secondary hyperparathyroidism: A US perspective

NARCIS (Netherlands)

M.J.C. Nuijten (Mark); D.L. Andress (Dennis); S.E. Marx (Steven); R. Sterz (Raimund)

2009-01-01

textabstractObjective: The objective of this study was to determine the cost effectiveness of paricalcitol versus calcitriol for the treatment of secondary hyperparathyroidism in patients with chronic kidney disease in the United States setting. Methods: A Markov process model was developed

Envelopes of Sets of Measures, Tightness, and Markov Control Processes

International Nuclear Information System (INIS)

Gonzalez-Hernandez, J.; Hernandez-Lerma, O.

1999-01-01

We introduce upper and lower envelopes for sets of measures on an arbitrary topological space, which are then used to give a tightness criterion. These concepts are applied to show the existence of optimal policies for a class of Markov control processes

Swallowing sound detection using hidden markov modeling of recurrence plot features

International Nuclear Information System (INIS)

Aboofazeli, Mohammad; Moussavi, Zahra

2009-01-01

Automated detection of swallowing sounds in swallowing and breath sound recordings is of importance for monitoring purposes in which the recording durations are long. This paper presents a novel method for swallowing sound detection using hidden Markov modeling of recurrence plot features. Tracheal sound recordings of 15 healthy and nine dysphagic subjects were studied. The multidimensional state space trajectory of each signal was reconstructed using the Taken method of delays. The sequences of three recurrence plot features of the reconstructed trajectories (which have shown discriminating capability between swallowing and breath sounds) were modeled by three hidden Markov models. The Viterbi algorithm was used for swallowing sound detection. The results were validated manually by inspection of the simultaneously recorded airflow signal and spectrogram of the sounds, and also by auditory means. The experimental results suggested that the performance of the proposed method using hidden Markov modeling of recurrence plot features was superior to the previous swallowing sound detection methods.

Swallowing sound detection using hidden markov modeling of recurrence plot features

Energy Technology Data Exchange (ETDEWEB)

Aboofazeli, Mohammad [Faculty of Engineering, Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba, R3T 5V6 (Canada)], E-mail: umaboofa@cc.umanitoba.ca; Moussavi, Zahra [Faculty of Engineering, Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba, R3T 5V6 (Canada)], E-mail: mousavi@ee.umanitoba.ca

2009-01-30

Automated detection of swallowing sounds in swallowing and breath sound recordings is of importance for monitoring purposes in which the recording durations are long. This paper presents a novel method for swallowing sound detection using hidden Markov modeling of recurrence plot features. Tracheal sound recordings of 15 healthy and nine dysphagic subjects were studied. The multidimensional state space trajectory of each signal was reconstructed using the Taken method of delays. The sequences of three recurrence plot features of the reconstructed trajectories (which have shown discriminating capability between swallowing and breath sounds) were modeled by three hidden Markov models. The Viterbi algorithm was used for swallowing sound detection. The results were validated manually by inspection of the simultaneously recorded airflow signal and spectrogram of the sounds, and also by auditory means. The experimental results suggested that the performance of the proposed method using hidden Markov modeling of recurrence plot features was superior to the previous swallowing sound detection methods.

Modelling of cyclical stratigraphy using Markov chains

Energy Technology Data Exchange (ETDEWEB)

Kulatilake, P.H.S.W.

1987-07-01

State-of-the-art on modelling of cyclical stratigraphy using first-order Markov chains is reviewed. Shortcomings of the presently available procedures are identified. A procedure which eliminates all the identified shortcomings is presented. Required statistical tests to perform this modelling are given in detail. An example (the Oficina formation in eastern Venezuela) is given to illustrate the presented procedure. 12 refs., 3 tabs. 1 fig.

Hidden Markov Model for quantitative prediction of snowfall

Indian Academy of Sciences (India)

A Hidden Markov Model (HMM) has been developed for prediction of quantitative snowfall in Pir-Panjal and Great Himalayan mountain ranges of Indian Himalaya. The model predicts snowfall for two days in advance using daily recorded nine meteorological variables of past 20 winters from 1992–2012. There are six ...

Learning to maximize reward rate: a model based on semi-Markov decision processes.

Science.gov (United States)

Khodadadi, Arash; Fakhari, Pegah; Busemeyer, Jerome R

2014-01-01

WHEN ANIMALS HAVE TO MAKE A NUMBER OF DECISIONS DURING A LIMITED TIME INTERVAL, THEY FACE A FUNDAMENTAL PROBLEM: how much time they should spend on each decision in order to achieve the maximum possible total outcome. Deliberating more on one decision usually leads to more outcome but less time will remain for other decisions. In the framework of sequential sampling models, the question is how animals learn to set their decision threshold such that the total expected outcome achieved during a limited time is maximized. The aim of this paper is to provide a theoretical framework for answering this question. To this end, we consider an experimental design in which each trial can come from one of the several possible "conditions." A condition specifies the difficulty of the trial, the reward, the penalty and so on. We show that to maximize the expected reward during a limited time, the subject should set a separate value of decision threshold for each condition. We propose a model of learning the optimal value of decision thresholds based on the theory of semi-Markov decision processes (SMDP). In our model, the experimental environment is modeled as an SMDP with each "condition" being a "state" and the value of decision thresholds being the "actions" taken in those states. The problem of finding the optimal decision thresholds then is cast as the stochastic optimal control problem of taking actions in each state in the corresponding SMDP such that the average reward rate is maximized. Our model utilizes a biologically plausible learning algorithm to solve this problem. The simulation results show that at the beginning of learning the model choses high values of decision threshold which lead to sub-optimal performance. With experience, however, the model learns to lower the value of decision thresholds till finally it finds the optimal values.

MODELING OF FUTURE LAND COVER LAND USE CHANGE IN NORTH CAROLINA USING MARKOV CHAIN AND CELLULAR AUTOMATA MODEL

OpenAIRE

Mohammad Sayemuzzaman; Manoj K. Jha

2014-01-01

State wide variant topographic features in North Carolina attract the hydro-climatologist. There is none modeling study found that predict future Land Cover Land Use (LCLU) change for whole North Carolina. In this study, satellite-derived land cover maps of year 1992, 2001 and 2006 of North Carolina were integrated within the framework of the Markov-Cellular Automata (Markov-CA) model which combines the Markov chain and Cellular Automata (CA) techniques. A Multi-Criteria Evaluation (MCE) was ...

Power plant reliability calculation with Markov chain models

International Nuclear Information System (INIS)

Senegacnik, A.; Tuma, M.

1998-01-01

In the paper power plant operation is modelled using continuous time Markov chains with discrete state space. The model is used to compute the power plant reliability and the importance and influence of individual states, as well as the transition probabilities between states. For comparison the model is fitted to data for coal and nuclear power plants recorded over several years. (orig.) [de

Control Design for Untimed Petri Nets Using Markov Decision Processes

Directory of Open Access Journals (Sweden)

Cherki Daoui

2017-01-01

Full Text Available Design of control sequences for discrete event systems (DESs has been presented modelled by untimed Petri nets (PNs. PNs are well-known mathematical and graphical models that are widely used to describe distributed DESs, including choices, synchronizations and parallelisms. The domains of application include, but are not restricted to, manufacturing systems, computer science and transportation networks. We are motivated by the observation that such systems need to plan their production or services. The paper is more particularly concerned with control issues in uncertain environments when unexpected events occur or when control errors disturb the behaviour of the system. To deal with such uncertainties, a new approach based on discrete time Markov decision processes (MDPs has been proposed that associates the modelling power of PNs with the planning power of MDPs. Finally, the simulation results illustrate the benefit of our method from the computational point of view. (original abstract

Stochastic differential equation model to Prendiville processes

International Nuclear Information System (INIS)

Granita; Bahar, Arifah

2015-01-01

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution

Stochastic differential equation model to Prendiville processes

Energy Technology Data Exchange (ETDEWEB)

Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)

2015-10-22

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

Piecewise deterministic processes in biological models

CERN Document Server

Rudnicki, Ryszard

2017-01-01

This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models. As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological processes into a unified mathematical theory, and...

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

DEFF Research Database (Denmark)

Berthelsen, Kasper Klitgaard; Møller, Jesper

2004-01-01

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

Transportation and concentration inequalities for bifurcating Markov chains

DEFF Research Database (Denmark)

Penda, S. Valère Bitseki; Escobar-Bach, Mikael; Guillin, Arnaud

2017-01-01

We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful...... concentration inequalities.We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive...

Abstract behaviour modelling and prognosis on the basis of spatially distributed sensor networks with Kohonen cards and Markov chains; Abstrakte Verhaltensmodellierung und -prognose auf der Basis raeumlich verteilter Sensornetze mit Kohonen-Karten und Markov-Ketten

Energy Technology Data Exchange (ETDEWEB)

Matthes, J.; Keller, H.B.; Mikut, R. [Forschungszentrum Karlsruhe GmbH Technik und Umwelt (Germany). Inst. fuer Angewandte Informatik

2000-10-01

Evironmental processes, e.g. local air quality changes in urban agglomerations, buildings and production halls are dynamic processes with regionally distributed physical variables. They can be monitored by networks of distributed measuring probes. Processes of this type form the basis of complex systems with many degrees of freedom and stochastic effects that are difficult to measure. The contribution presents an introduction to Markov chains, proposes a method of generating Markov chains as a prognostic model, and demonstrates the method using the example of an air quality monitoring process. [German] Fuer die Ueberwachung dynamischer Prozesse, deren physikalische Groessen raeumlich verteilt auftreten, werden oft Netze raeumlich verteilter Sensoren eingesetzt. Umweltprozesse, wie z.B. die oertliche Luftqualitaetsaenderung in Ballungsraeumen, Gebaeuden und Produktionsanlagen, aber auch verschiedene verfahrenstechnische Prozesse sind Vertreter dieser Prozessklasse. Solchen Prozessen hinterliegen komplexe Systeme, die durch eine hohe Anzahl an Freiheitsgraden und durch stochastische schwer messbare Einfluesse gekennzeichnet sind. Ziel dieses Vortrages ist es, - eine kurze Einfuehrung zu Markov-Ketten zu gegeben (Abschnitt 2); - ein datengestuetztes Verfahren vorzuschlagen, das nach einer Schaetzung abstrakter Prozesszustaende mit Hilfe von Kohonen-Karten Markov-Ketten als Prognosemodell generiert (Abschnitt 3), und - dieses Verfahren anhand eines Simulationsbeispiels zur Luftqualitaetsueberwachung zu demonstrieren (Abschnitt 4). (orig.)

A comparison of non-homogeneous Markov regression models with application to Alzheimer’s disease progression

Science.gov (United States)

Hubbard, R. A.; Zhou, X.H.

2011-01-01

Markov regression models are useful tools for estimating the impact of risk factors on rates of transition between multiple disease states. Alzheimer’s disease (AD) is an example of a multi-state disease process in which great interest lies in identifying risk factors for transition. In this context, non-homogeneous models are required because transition rates change as subjects age. In this report we propose a non-homogeneous Markov regression model that allows for reversible and recurrent disease states, transitions among multiple states between observations, and unequally spaced observation times. We conducted simulation studies to demonstrate performance of estimators for covariate effects from this model and compare performance with alternative models when the underlying non-homogeneous process was correctly specified and under model misspecification. In simulation studies, we found that covariate effects were biased if non-homogeneity of the disease process was not accounted for. However, estimates from non-homogeneous models were robust to misspecification of the form of the non-homogeneity. We used our model to estimate risk factors for transition to mild cognitive impairment (MCI) and AD in a longitudinal study of subjects included in the National Alzheimer’s Coordinating Center’s Uniform Data Set. Using our model, we found that subjects with MCI affecting multiple cognitive domains were significantly less likely to revert to normal cognition. PMID:22419833

Robust filtering and prediction for systems with embedded finite-state Markov-Chain dynamics

International Nuclear Information System (INIS)

Pate, E.B.

1986-01-01

This research developed new methodologies for the design of robust near-optimal filters/predictors for a class of system models that exhibit embedded finite-state Markov-chain dynamics. These methodologies are developed through the concepts and methods of stochastic model building (including time-series analysis), game theory, decision theory, and filtering/prediction for linear dynamic systems. The methodology is based on the relationship between the robustness of a class of time-series models and quantization which is applied to the time series as part of the model identification process. This relationship is exploited by utilizing the concept of an equivalence, through invariance of spectra, between the class of Markov-chain models and the class of autoregressive moving average (ARMA) models. This spectral equivalence permits a straightforward implementation of the desirable robust properties of the Markov-chain approximation in a class of models which may be applied in linear-recursive form in a linear Kalman filter/predictor structure. The linear filter/predictor structure is shown to provide asymptotically optimal estimates of states which represent one or more integrations of the Markov-chain state. The development of a new saddle-point theorem for a game based on the Markov-chain model structure gives rise to a technique for determining a worst case Markov-chain process, upon which a robust filter/predictor design if based

Using hidden Markov models to align multiple sequences.

Science.gov (United States)

Mount, David W

2009-07-01

A hidden Markov model (HMM) is a probabilistic model of a multiple sequence alignment (msa) of proteins. In the model, each column of symbols in the alignment is represented by a frequency distribution of the symbols (called a "state"), and insertions and deletions are represented by other states. One moves through the model along a particular path from state to state in a Markov chain (i.e., random choice of next move), trying to match a given sequence. The next matching symbol is chosen from each state, recording its probability (frequency) and also the probability of going to that state from a previous one (the transition probability). State and transition probabilities are multiplied to obtain a probability of the given sequence. The hidden nature of the HMM is due to the lack of information about the value of a specific state, which is instead represented by a probability distribution over all possible values. This article discusses the advantages and disadvantages of HMMs in msa and presents algorithms for calculating an HMM and the conditions for producing the best HMM.

Markov dynamic models for long-timescale protein motion.

KAUST Repository

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.

Markov dynamic models for long-timescale protein motion.

KAUST Repository

Chiang, Tsung-Han; Hsu, David; Latombe, Jean-Claude

2010-01-01

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.

Generalization bounds of ERM-based learning processes for continuous-time Markov chains.

Science.gov (United States)

Zhang, Chao; Tao, Dacheng

2012-12-01

Many existing results on statistical learning theory are based on the assumption that samples are independently and identically distributed (i.i.d.). However, the assumption of i.i.d. samples is not suitable for practical application to problems in which samples are time dependent. In this paper, we are mainly concerned with the empirical risk minimization (ERM) based learning process for time-dependent samples drawn from a continuous-time Markov chain. This learning process covers many kinds of practical applications, e.g., the prediction for a time series and the estimation of channel state information. Thus, it is significant to study its theoretical properties including the generalization bound, the asymptotic convergence, and the rate of convergence. It is noteworthy that, since samples are time dependent in this learning process, the concerns of this paper cannot (at least straightforwardly) be addressed by existing methods developed under the sample i.i.d. assumption. We first develop a deviation inequality for a sequence of time-dependent samples drawn from a continuous-time Markov chain and present a symmetrization inequality for such a sequence. By using the resultant deviation inequality and symmetrization inequality, we then obtain the generalization bounds of the ERM-based learning process for time-dependent samples drawn from a continuous-time Markov chain. Finally, based on the resultant generalization bounds, we analyze the asymptotic convergence and the rate of convergence of the learning process.

Multi-state reliability for pump group in system based on UGF and semi-Markov process

International Nuclear Information System (INIS)

Shang Yanlong; Cai Qi; Zhao Xinwen; Chen Ling

2012-01-01

In this paper, multi-state reliability value of pump group in nuclear power system is obtained by the combination method of the universal generating function (UGF) and Semi-Markov process. UGF arithmetic model of multi-state system reliability is studied, and the performance state probability expression of multi-state component is derived using semi-Markov theory. A quantificational model is defined to express the performance rate of the system and component. Different availability results by multi-state and binary state analysis method are compared under the condition whether the performance rate can satisfy the demanded value, and the mean value of system instantaneous output performance is also obtained. It shows that this combination method is an effective and feasible one which can quantify the effect of the partial failure on the system reliability, and the result of multi-state system reliability by this method deduces the modesty of the reliability value obtained by binary reliability analysis method. (authors)

Pemodelan Markov Switching Autoregressive

OpenAIRE

Ariyani, Fiqria Devi; Warsito, Budi; Yasin, Hasbi

2014-01-01

Transition from depreciation to appreciation of exchange rate is one of regime switching that ignored by classic time series model, such as ARIMA, ARCH, or GARCH. Therefore, economic variables are modeled by Markov Switching Autoregressive (MSAR) which consider the regime switching. MLE is not applicable to parameters estimation because regime is an unobservable variable. So that filtering and smoothing process are applied to see the regime probabilities of observation. Using this model, tran...

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

NARCIS (Netherlands)

U. Faigle; A. Schönhuth (Alexander)

2011-01-01

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

A simplified parsimonious higher order multivariate Markov chain model

Science.gov (United States)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, a simplified parsimonious higher-order multivariate Markov chain model (SPHOMMCM) is presented. Moreover, parameter estimation method of TPHOMMCM is give. Numerical experiments shows the effectiveness of TPHOMMCM.

Recombination Processes and Nonlinear Markov Chains.

Science.gov (United States)

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.

Algorithms for a parallel implementation of Hidden Markov Models with a small state space

DEFF Research Database (Denmark)

Nielsen, Jesper; Sand, Andreas

2011-01-01

Two of the most important algorithms for Hidden Markov Models are the forward and the Viterbi algorithms. We show how formulating these using linear algebra naturally lends itself to parallelization. Although the obtained algorithms are slow for Hidden Markov Models with large state spaces...

A statistical model for prediction of fuel element failure using the Markov process and entropy minimax principles

International Nuclear Information System (INIS)

Choi, K.Y.; Yoon, Y.K.; Chang, S.H.

1991-01-01

This paper reports on a new statistical fuel failure model developed to take into account the effects of damaging environmental conditions and the overall operating history of the fuel elements. The degradation of material properties and damage resistance of the fuel cladding is mainly caused by the combined effects of accumulated dynamic stresses, neutron irradiation, and chemical and stress corrosion at operating temperature. Since the degradation of material properties due to these effects can be considered as a stochastic process, a dynamic reliability function is derived based on the Markov process. Four damage parameters, namely, dynamic stresses, magnitude of power increase from the preceding power level and with ramp rate, and fatigue cycles, are used to build this model. The dynamic reliability function and damage parameters are used to obtain effective damage parameters. The entropy maximization principle is used to generate a probability density function of the effective damage parameters. The entropy minimization principle is applied to determine weighting factors for amalgamation of the failure probabilities due to the respective failure modes. In this way, the effects of operating history, damaging environmental conditions, and damage sequence are taken into account

Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach

Energy Technology Data Exchange (ETDEWEB)

Dufour, F., E-mail: dufour@math.u-bordeaux1.fr [Bordeaux INP, IMB, UMR CNRS 5251 (France); Piunovskiy, A. B., E-mail: piunov@liv.ac.uk [University of Liverpool, Department of Mathematical Sciences (United Kingdom)

2016-08-15

In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures of the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.

Students' Progress throughout Examination Process as a Markov Chain

Science.gov (United States)

Hlavatý, Robert; Dömeová, Ludmila

2014-01-01

The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…

Modelling and evaluation of surgical performance using hidden Markov models.

Science.gov (United States)

Megali, Giuseppe; Sinigaglia, Stefano; Tonet, Oliver; Dario, Paolo

2006-10-01

Minimally invasive surgery has become very widespread in the last ten years. Since surgeons experience difficulties in learning and mastering minimally invasive techniques, the development of training methods is of great importance. While the introduction of virtual reality-based simulators has introduced a new paradigm in surgical training, skill evaluation methods are far from being objective. This paper proposes a method for defining a model of surgical expertise and an objective metric to evaluate performance in laparoscopic surgery. Our approach is based on the processing of kinematic data describing movements of surgical instruments. We use hidden Markov model theory to define an expert model that describes expert surgical gesture. The model is trained on kinematic data related to exercises performed on a surgical simulator by experienced surgeons. Subsequently, we use this expert model as a reference model in the definition of an objective metric to evaluate performance of surgeons with different abilities. Preliminary results show that, using different topologies for the expert model, the method can be efficiently used both for the discrimination between experienced and novice surgeons, and for the quantitative assessment of surgical ability.

A competitive Markov decision process model for the energy–water–climate change nexus

International Nuclear Information System (INIS)

Nanduri, Vishnu; Saavedra-Antolínez, Ivan

2013-01-01

Highlights: • Developed a CMDP model for the energy–water–climate change nexus. • Solved the model using a reinforcement learning algorithm. • Study demonstrated on 30-bus IEEE electric power network using DCOPF formulation. • Sixty percentage drop in CO 2 and 40% drop in H 2 O use when coal replaced by wind (over 10 years). • Higher profits for nuclear and wind as well as higher LMPs under CO 2 and H 2 O taxes. - Abstract: Drought-like conditions in some parts of the US and around the world are causing water shortages that lead to power failures, becoming a source of concern to independent system operators. Water shortages can cause significant challenges in electricity production and thereby a direct socioeconomic impact on the surrounding region. Our paper presents a new, comprehensive quantitative model that examines the electricity–water–climate change nexus. We investigate the impact of a joint water and carbon tax proposal on the operation of a transmission-constrained power network operating in a wholesale power market setting. We develop a competitive Markov decision process (CMDP) model for the dynamic competition in wholesale electricity markets, and solve the model using reinforcement learning. Several cases, including the impact of different tax schemes, integration of stochastic wind energy resources, and capacity disruptions due to droughts are investigated. Results from the analysis on the sample power network show that electricity prices increased with the adoption of water and carbon taxes compared with locational marginal prices without taxes. As expected, wind energy integration reduced both CO 2 emissions and water usage. Capacity disruptions also caused locational marginal prices to increase. Other detailed analyses and results obtained using a 30-bus IEEE network are discussed in detail

A tridiagonal parsimonious higher order multivariate Markov chain model

Science.gov (United States)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

In this paper, we present a tridiagonal parsimonious higher-order multivariate Markov chain model (TPHOMMCM). Moreover, estimation method of the parameters in TPHOMMCM is give. Numerical experiments illustrate the effectiveness of TPHOMMCM.

Confluence reduction for Markov automata (extended version)

NARCIS (Netherlands)

Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette

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

Continuous-Time Semi-Markov Models in Health Economic Decision Making : An Illustrative Example in Heart Failure Disease Management

NARCIS (Netherlands)

Cao, Qi; Buskens, Erik; Feenstra, Talitha; Jaarsma, Tiny; Hillege, Hans; Postmus, Douwe

Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease

Regime-switching models to study psychological process

NARCIS (Netherlands)

Hamaker, E.L.; Grasman, R.P.P.P.; Kamphuis, J.H.

2010-01-01

Many psychological processes are characterized by recurrent shifts between different states. To model these processes at the level of the individual, regime-switching models may prove useful. In this chapter we discuss two of these models: the threshold autoregressive model and the Markov

The Logic of Adaptive Behavior - Knowledge Representation and Algorithms for the Markov Decision Process Framework in First-Order Domains

NARCIS (Netherlands)

van Otterlo, M.

2008-01-01

Learning and reasoning in large, structured, probabilistic worlds is at the heart of artificial intelligence. Markov decision processes have become the de facto standard in modeling and solving sequential decision making problems under uncertainty. Many efficient reinforcement learning and dynamic

Availability analysis of subsea blowout preventer using Markov model considering demand rate

Directory of Open Access Journals (Sweden)

Sunghee Kim

2014-12-01

Full Text Available Availabilities of subsea Blowout Preventers (BOP in the Gulf of Mexico Outer Continental Shelf (GoM OCS is investigated using a Markov method. An updated β factor model by SINTEF is used for common-cause failures in multiple redundant systems. Coefficient values of failure rates for the Markov model are derived using the β factor model of the PDS (reliability of computer-based safety systems, Norwegian acronym method. The blind shear ram preventer system of the subsea BOP components considers a demand rate to reflect reality more. Markov models considering the demand rate for one or two components are introduced. Two data sets are compared at the GoM OCS. The results show that three or four pipe ram preventers give similar availabilities, but redundant blind shear ram preventers or annular preventers enhance the availability of the subsea BOP. Also control systems (PODs and connectors are contributable components to improve the availability of the subsea BOPs based on sensitivity analysis.

Modelling the Errors of EIA’s Oil Prices and Production Forecasts by the Grey Markov Model

Directory of Open Access Journals (Sweden)

Gholam Hossein Hasantash

2012-01-01

Full Text Available Grey theory is about systematic analysis of limited information. The Grey-Markov model can improve the accuracy of forecast range in the random fluctuating data sequence. In this paper, we employed this model in energy system. The average errors of Energy Information Administrations predictions for world oil price and domestic crude oil production from 1982 to 2007 and from 1985 to 2008 respectively were used as two forecasted examples. We showed that the proposed Grey-Markov model can improve the forecast accuracy of original Grey forecast model.

Markov bridges, bisection and variance reduction

DEFF Research Database (Denmark)

Asmussen, Søren; Hobolth, Asger

. 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......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...

Incorporation of Markov reliability models for digital instrumentation and control systems into existing PRAs

International Nuclear Information System (INIS)

Bucci, P.; Mangan, L. A.; Kirschenbaum, J.; Mandelli, D.; Aldemir, T.; Arndt, S. A.

2006-01-01

Markov models have the ability to capture the statistical dependence between failure events that can arise in the presence of complex dynamic interactions between components of digital instrumentation and control systems. One obstacle to the use of such models in an existing probabilistic risk assessment (PRA) is that most of the currently available PRA software is based on the static event-tree/fault-tree methodology which often cannot represent such interactions. We present an approach to the integration of Markov reliability models into existing PRAs by describing the Markov model of a digital steam generator feedwater level control system, how dynamic event trees (DETs) can be generated from the model, and how the DETs can be incorporated into an existing PRA with the SAPHIRE software. (authors)

Combination of Markov state models and kinetic networks for the analysis of molecular dynamics simulations of peptide folding.

Science.gov (United States)

Radford, Isolde H; Fersht, Alan R; Settanni, Giovanni

2011-06-09

Atomistic molecular dynamics simulations of the TZ1 beta-hairpin peptide have been carried out using an implicit model for the solvent. The trajectories have been analyzed using a Markov state model defined on the projections along two significant observables and a kinetic network approach. The Markov state model allowed for an unbiased identification of the metastable states of the system, and provided the basis for commitment probability calculations performed on the kinetic network. The kinetic network analysis served to extract the main transition state for folding of the peptide and to validate the results from the Markov state analysis. The combination of the two techniques allowed for a consistent and concise characterization of the dynamics of the peptide. The slowest relaxation process identified is the exchange between variably folded and denatured species, and the second slowest process is the exchange between two different subsets of the denatured state which could not be otherwise identified by simple inspection of the projected trajectory. The third slowest process is the exchange between a fully native and a partially folded intermediate state characterized by a native turn with a proximal backbone H-bond, and frayed side-chain packing and termini. The transition state for the main folding reaction is similar to the intermediate state, although a more native like side-chain packing is observed.

Noise can speed convergence in Markov chains.

Science.gov (United States)

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.

Modeling promoter grammars with evolving hidden Markov models

DEFF Research Database (Denmark)

Won, Kyoung-Jae; Sandelin, Albin; Marstrand, Troels Torben

2008-01-01

MOTIVATION: Describing and modeling biological features of eukaryotic promoters remains an important and challenging problem within computational biology. The promoters of higher eukaryotes in particular display a wide variation in regulatory features, which are difficult to model. Often several...... factors are involved in the regulation of a set of co-regulated genes. If so, promoters can be modeled with connected regulatory features, where the network of connections is characteristic for a particular mode of regulation. RESULTS: With the goal of automatically deciphering such regulatory structures......, we present a method that iteratively evolves an ensemble of regulatory grammars using a hidden Markov Model (HMM) architecture composed of interconnected blocks representing transcription factor binding sites (TFBSs) and background regions of promoter sequences. The ensemble approach reduces the risk...

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

International Nuclear Information System (INIS)

Costa, O. L. V.; Dufour, F.

2011-01-01

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP’s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space ℝ n . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter ε>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as ε goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as ε goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

A fast exact simulation method for a class of Markov jump processes.

Science.gov (United States)

Li, Yao; Hu, Lili

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 semi-Markov model for the duration of stay in a non-homogenous ...

African Journals Online (AJOL)

The semi-Markov approach to a non-homogenous manpower system is considered. The mean duration of stay in a grade and the total duration of stay in the system are obtained. A renewal type equation is developed and used in deriving the limiting distribution of the semi – Markov process. Empirical estimators of the ...

Long memory of financial time series and hidden Markov models with time-varying parameters

DEFF Research Database (Denmark)

Nystrup, Peter; Madsen, Henrik; Lindström, Erik

Hidden Markov models are often used to capture stylized facts of daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time-varying behavior for the ability to reproduce the stylized...... facts have not been thoroughly examined. This paper presents an adaptive estimation approach that allows for the parameters of the estimated models to be time-varying. It is shown that a two-state Gaussian hidden Markov model with time-varying parameters is able to reproduce the long memory of squared...... daily returns that was previously believed to be the most difficult fact to reproduce with a hidden Markov model. Capturing the time-varying behavior of the parameters also leads to improved one-step predictions....

Optimisation of Hidden Markov Model using Baum–Welch algorithm ...

Indian Academy of Sciences (India)

The present work is a part of development of Hidden Markov Model. (HMM) based ... the Himalaya. In this work, HMMs have been developed for forecasting of maximum and minimum ..... data collection teams of Snow and Avalanche Study.

Cyclic Markov chains with an application to an intermediate ENSO model

Directory of Open Access Journals (Sweden)

R. A. Pasmanter

2003-01-01

Full Text Available We develop the theory of cyclic Markov chains and apply it to the El Niño-Southern Oscillation (ENSO predictability problem. At the core of Markov chain modelling is a partition of the state space such that the transition rates between different state space cells can be computed and used most efficiently. We apply a partition technique, which divides the state space into multidimensional cells containing an equal number of data points. This partition leads to mathematical properties of the transition matrices which can be exploited further such as to establish connections with the dynamical theory of unstable periodic orbits. We introduce the concept of most and least predictable states. The data basis of our analysis consists of a multicentury-long data set obtained from an intermediate coupled atmosphere-ocean model of the tropical Pacific. This cyclostationary Markov chain approach captures the spring barrier in ENSO predictability and gives insight also into the dependence of ENSO predictability on the climatic state.

Decision Making under Uncertainty: A Neural Model based on Partially Observable Markov Decision Processes

Directory of Open Access Journals (Sweden)

Rajesh P N Rao

2010-11-01

Full Text Available A fundamental problem faced by animals is learning to select actions based on noisy sensory information and incomplete knowledge of the world. It has been suggested that the brain engages in Bayesian inference during perception but how such probabilistic representations are used to select actions has remained unclear. Here we propose a neural model of action selection and decision making based on the theory of partially observable Markov decision processes (POMDPs. Actions are selected based not on a single optimal estimate of state but on the posterior distribution over states (the belief state. We show how such a model provides a unified framework for explaining experimental results in decision making that involve both information gathering and overt actions. The model utilizes temporal difference (TD learning for maximizing expected reward. The resulting neural architecture posits an active role for the neocortex in belief computation while ascribing a role to the basal ganglia in belief representation, value computation, and action selection. When applied to the random dots motion discrimination task, model neurons representing belief exhibit responses similar to those of LIP neurons in primate neocortex. The appropriate threshold for switching from information gathering to overt actions emerges naturally during reward maximization. Additionally, the time course of reward prediction error in the model shares similarities with dopaminergic responses in the basal ganglia during the random dots task. For tasks with a deadline, the model learns a decision making strategy that changes with elapsed time, predicting a collapsing decision threshold consistent with some experimental studies. The model provides a new framework for understanding neural decision making and suggests an important role for interactions between the neocortex and the basal ganglia in learning the mapping between probabilistic sensory representations and actions that maximize

Computer modeling of lung cancer diagnosis-to-treatment process.

Science.gov (United States)

Ju, Feng; Lee, Hyo Kyung; Osarogiagbon, Raymond U; Yu, Xinhua; Faris, Nick; Li, Jingshan

2015-08-01

We introduce an example of a rigorous, quantitative method for quality improvement in lung cancer care-delivery. Computer process modeling methods are introduced for lung cancer diagnosis, staging and treatment selection process. Two types of process modeling techniques, discrete event simulation (DES) and analytical models, are briefly reviewed. Recent developments in DES are outlined and the necessary data and procedures to develop a DES model for lung cancer diagnosis, leading up to surgical treatment process are summarized. The analytical models include both Markov chain model and closed formulas. The Markov chain models with its application in healthcare are introduced and the approach to derive a lung cancer diagnosis process model is presented. Similarly, the procedure to derive closed formulas evaluating the diagnosis process performance is outlined. Finally, the pros and cons of these methods are discussed.

Semi-Markov models for interval censored transient cognitive states with back transitions and a competing risk.

Science.gov (United States)

Wei, Shaoceng; Kryscio, Richard J

2016-12-01

Continuous-time multi-state stochastic processes are useful for modeling the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient cognitive states and death as a competing risk. Each subject's cognition is assessed periodically resulting in interval censoring for the cognitive states while death without dementia is not interval censored. Since back transitions among the transient states are possible, Markov chains are often applied to this type of panel data. In this manuscript, we apply a semi-Markov process in which we assume that the waiting times are Weibull distributed except for transitions from the baseline state, which are exponentially distributed and in which we assume no additional changes in cognition occur between two assessments. We implement a quasi-Monte Carlo (QMC) method to calculate the higher order integration needed for likelihood estimation. We apply our model to a real dataset, the Nun Study, a cohort of 461 participants. © The Author(s) 2014.

Influence of credit scoring on the dynamics of Markov chain

Science.gov (United States)

Galina, Timofeeva

2015-11-01

Markov processes are widely used to model the dynamics of a credit portfolio and forecast the portfolio risk and profitability. In the Markov chain model the loan portfolio is divided into several groups with different quality, which determined by presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is described by a multistage controlled system. The article outlines mathematical formalization of controls which reflect the actions of the bank's management in order to improve the loan portfolio quality. The most important control is the organization of approval procedure of loan applications. The credit scoring is studied as a control affecting to the dynamic system. Different formalizations of "good" and "bad" consumers are proposed in connection with the Markov chain model.

Markov Modeling with Soft Aggregation for Safety and Decision Analysis; TOPICAL

International Nuclear Information System (INIS)

COOPER, J. ARLIN

1999-01-01

The methodology in this report improves on some of the limitations of many conventional safety assessment and decision analysis methods. A top-down mathematical approach is developed for decomposing systems and for expressing imprecise individual metrics as possibilistic or fuzzy numbers. A ''Markov-like'' model is developed that facilitates combining (aggregating) inputs into overall metrics and decision aids, also portraying the inherent uncertainty. A major goal of Markov modeling is to help convey the top-down system perspective. One of the constituent methodologies allows metrics to be weighted according to significance of the attribute and aggregated nonlinearly as to contribution. This aggregation is performed using exponential combination of the metrics, since the accumulating effect of such factors responds less and less to additional factors. This is termed ''soft'' mathematical aggregation. Dependence among the contributing factors is accounted for by incorporating subjective metrics on ''overlap'' of the factors as well as by correspondingly reducing the overall contribution of these combinations to the overall aggregation. Decisions corresponding to the meaningfulness of the results are facilitated in several ways. First, the results are compared to a soft threshold provided by a sigmoid function. Second, information is provided on input ''Importance'' and ''Sensitivity,'' in order to know where to place emphasis on considering new controls that may be necessary. Third, trends in inputs and outputs are tracked in order to obtain significant information% including cyclic information for the decision process. A practical example from the air transportation industry is used to demonstrate application of the methodology. Illustrations are given for developing a structure (along with recommended inputs and weights) for air transportation oversight at three different levels, for developing and using cycle information, for developing Importance and

HMMEditor: a visual editing tool for profile hidden Markov model

Directory of Open Access Journals (Sweden)

Cheng Jianlin

2008-03-01

Full Text Available Abstract Background Profile Hidden Markov Model (HMM is a powerful statistical model to represent a family of DNA, RNA, and protein sequences. Profile HMM has been widely used in bioinformatics research such as sequence alignment, gene structure prediction, motif identification, protein structure prediction, and biological database search. However, few comprehensive, visual editing tools for profile HMM are publicly available. Results We develop a visual editor for profile Hidden Markov Models (HMMEditor. HMMEditor can visualize the profile HMM architecture, transition probabilities, and emission probabilities. Moreover, it provides functions to edit and save HMM and parameters. Furthermore, HMMEditor allows users to align a sequence against the profile HMM and to visualize the corresponding Viterbi path. Conclusion HMMEditor provides a set of unique functions to visualize and edit a profile HMM. It is a useful tool for biological sequence analysis and modeling. Both HMMEditor software and web service are freely available.

[Succession caused by beaver (Castor fiber L.) life activity: II. A refined Markov model].

Science.gov (United States)

Logofet; Evstigneev, O I; Aleinikov, A A; Morozova, A O

2015-01-01

The refined Markov model of cyclic zoogenic successions caused by beaver (Castor fiber L.) life activity represents a discrete chain of the following six states: flooded forest, swamped forest, pond, grassy swamp, shrubby swamp, and wet forest, which correspond to certain stages of succession. Those stages are defined, and a conceptual scheme of probable transitions between them for one time step is constructed from the knowledge of beaver behaviour in small river floodplains of "Bryanskii Les" Reserve. We calibrated the corresponding matrix of transition probabilities according to the optimization principle: minimizing differences between the model outcome and reality; the model generates a distribution of relative areas corresponding to the stages of succession, that has to be compared to those gained from case studies in the Reserve during 2002-2006. The time step is chosen to equal 2 years, and the first-step data in the sum of differences are given various weights, w (between 0 and 1). The value of w = 0.2 is selected due to its optimality and for some additional reasons. By the formulae of finite homogeneous Markov chain theory, we obtained the main results of the calibrated model, namely, a steady-state distribution of stage areas, indexes of cyclicity, and the mean durations (M(j)) of succession stages. The results of calibration give an objective quantitative nature to the expert knowledge of the course of succession and get a proper interpretation. The 2010 data, which are not involved in the calibration procedure, enabled assessing the quality of prediction by the homogeneous model in short-term (from the 2006 situation): the error of model area distribution relative to the distribution observed in 2010 falls into the range of 9-17%, the best prognosis being given by the least optimal matrices (rejected values of w). This indicates a formally heterogeneous nature of succession processes in time. Thus, the refined version of the homogeneous Markov chain

Synthesis of the Markov model of the thermochemical degradation of a polymer in solution

Directory of Open Access Journals (Sweden)

V. K. Bityukov

2017-01-01

Full Text Available The paper deals with the problem of mathematical modeling of thermochemical destruction process. The apparatus of Markov's chains is used to synthesize a mathematical model. The authors of the study suggest to consider the destruction process as a random one, where the system state changes, which is characterized by the proportion of macromolecules in each fraction of the molecular- and weight distribution. The intensities of transitions from one state to another characterize the corresponding rates of destruction processes for each fraction of the molecular- and weight distribution. The processes of crosslinking and polymerization in this work were neglected, and it was accepted that there is a probability of transition from any state with a lower order index (corresponding to fractions with higher molecular weights to any state with a higher index (corresponding to fractions with lower molecular weights. Markov's chain with discrete states and continuous time was taken as the mathematical model basis. Interactive graphical simulation environment MathWorksSimulink was used as a simulation environment. Experimental studies of polybutadiene destruction in solution were carried out to evaluate the mathematical model parameters. The GPC (gel-penetration chromatography data of the polybutadiene solution were used as the initial (starting data for estimating the polymer WMD (molecular weight distribution. Mean-square deviation of the calculated data from the experimental data for each fraction and at specified times was minimized for the numerical search of parameter values. The results of comparison of experimental and calculated on mathematical model data showed an error of calculations on the average about 5%, which indicates an acceptable error in estimating of polymer fractions proportions change during the process of destruction for the process under consideration and conditions.

Monte Carlo simulation of Markov unreliability models

International Nuclear Information System (INIS)

Lewis, E.E.; Boehm, F.

1984-01-01

A Monte Carlo method is formulated for the evaluation of the unrealibility of complex systems with known component failure and repair rates. The formulation is in terms of a Markov process allowing dependences between components to be modeled and computational efficiencies to be achieved in the Monte Carlo simulation. Two variance reduction techniques, forced transition and failure biasing, are employed to increase computational efficiency of the random walk procedure. For an example problem these result in improved computational efficiency by more than three orders of magnitudes over analog Monte Carlo. The method is generalized to treat problems with distributed failure and repair rate data, and a batching technique is introduced and shown to result in substantial increases in computational efficiency for an example problem. A method for separating the variance due to the data uncertainty from that due to the finite number of random walks is presented. (orig.)

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

Directory of Open Access Journals (Sweden)

Chongben Tao

2013-01-01

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

Verification of Open Interactive Markov Chains

OpenAIRE

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

2012-01-01

Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation....

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

Science.gov (United States)

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

2015-09-01

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

Improved hidden Markov model for nosocomial infections.

Science.gov (United States)

Khader, Karim; Leecaster, Molly; Greene, Tom; Samore, Matthew; Thomas, Alun

2014-12-01

We propose a novel hidden Markov model (HMM) for parameter estimation in hospital transmission models, and show that commonly made simplifying assumptions can lead to severe model misspecification and poor parameter estimates. A standard HMM that embodies two commonly made simplifying assumptions, namely a fixed patient count and binomially distributed detections is compared with a new alternative HMM that does not require these simplifying assumptions. Using simulated data, we demonstrate how each of the simplifying assumptions used by the standard model leads to model misspecification, whereas the alternative model results in accurate parameter estimates. © The Authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A Hybrid Generalized Hidden Markov Model-Based Condition Monitoring Approach for Rolling Bearings.

Science.gov (United States)

Liu, Jie; Hu, Youmin; Wu, Bo; Wang, Yan; Xie, Fengyun

2017-05-18

The operating condition of rolling bearings affects productivity and quality in the rotating machine process. Developing an effective rolling bearing condition monitoring approach is critical to accurately identify the operating condition. In this paper, a hybrid generalized hidden Markov model-based condition monitoring approach for rolling bearings is proposed, where interval valued features are used to efficiently recognize and classify machine states in the machine process. In the proposed method, vibration signals are decomposed into multiple modes with variational mode decomposition (VMD). Parameters of the VMD, in the form of generalized intervals, provide a concise representation for aleatory and epistemic uncertainty and improve the robustness of identification. The multi-scale permutation entropy method is applied to extract state features from the decomposed signals in different operating conditions. Traditional principal component analysis is adopted to reduce feature size and computational cost. With the extracted features' information, the generalized hidden Markov model, based on generalized interval probability, is used to recognize and classify the fault types and fault severity levels. Finally, the experiment results show that the proposed method is effective at recognizing and classifying the fault types and fault severity levels of rolling bearings. This monitoring method is also efficient enough to quantify the two uncertainty components.

A Hybrid Generalized Hidden Markov Model-Based Condition Monitoring Approach for Rolling Bearings

Directory of Open Access Journals (Sweden)

Jie Liu

2017-05-01

Full Text Available The operating condition of rolling bearings affects productivity and quality in the rotating machine process. Developing an effective rolling bearing condition monitoring approach is critical to accurately identify the operating condition. In this paper, a hybrid generalized hidden Markov model-based condition monitoring approach for rolling bearings is proposed, where interval valued features are used to efficiently recognize and classify machine states in the machine process. In the proposed method, vibration signals are decomposed into multiple modes with variational mode decomposition (VMD. Parameters of the VMD, in the form of generalized intervals, provide a concise representation for aleatory and epistemic uncertainty and improve the robustness of identification. The multi-scale permutation entropy method is applied to extract state features from the decomposed signals in different operating conditions. Traditional principal component analysis is adopted to reduce feature size and computational cost. With the extracted features’ information, the generalized hidden Markov model, based on generalized interval probability, is used to recognize and classify the fault types and fault severity levels. Finally, the experiment results show that the proposed method is effective at recognizing and classifying the fault types and fault severity levels of rolling bearings. This monitoring method is also efficient enough to quantify the two uncertainty components.

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

NARCIS (Netherlands)

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

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

Finding exact constants in a Markov model of Zipfs law generation

Science.gov (United States)

Bochkarev, V. V.; Lerner, E. Yu.; Nikiforov, A. A.; Pismenskiy, A. A.

2017-12-01

According to the classical Zipfs law, the word frequency is a power function of the word rank with an exponent -1. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [Bochkarev V V and Lerner E Yu 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. The search of the correct formulation of the Markov generalization of this results was performed using experiments with different ergodic matrices of transition probability P. Combinatory technique allowed taking into account all the words with probability of more than e -300 in case of 2 by 2 matrices. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row P with weights presenting the elements of the vector π of the stationary distribution of the Markov chain.

Speech-To-Text Conversion STT System Using Hidden Markov Model HMM

Directory of Open Access Journals (Sweden)

Su Myat Mon

2015-06-01

Full Text Available Abstract Speech is an easiest way to communicate with each other. Speech processing is widely used in many applications like security devices household appliances cellular phones ATM machines and computers. The human computer interface has been developed to communicate or interact conveniently for one who is suffering from some kind of disabilities. Speech-to-Text Conversion STT systems have a lot of benefits for the deaf or dumb people and find their applications in our daily lives. In the same way the aim of the system is to convert the input speech signals into the text output for the deaf or dumb students in the educational fields. This paper presents an approach to extract features by using Mel Frequency Cepstral Coefficients MFCC from the speech signals of isolated spoken words. And Hidden Markov Model HMM method is applied to train and test the audio files to get the recognized spoken word. The speech database is created by using MATLAB.Then the original speech signals are preprocessed and these speech samples are extracted to the feature vectors which are used as the observation sequences of the Hidden Markov Model HMM recognizer. The feature vectors are analyzed in the HMM depending on the number of states.

Data-based inference of generators for Markov jump processes using convex optimization

NARCIS (Netherlands)

D.T. Crommelin (Daan); E. Vanden-Eijnden (Eric)

2009-01-01

textabstractA variational approach to the estimation of generators for Markov jump processes from discretely sampled data is discussed and generalized. In this approach, one first calculates the spectrum of the discrete maximum likelihood estimator for the transition matrix consistent with

A joint logistic regression and covariate-adjusted continuous-time Markov chain model.

Science.gov (United States)

Rubin, Maria Laura; Chan, Wenyaw; Yamal, Jose-Miguel; Robertson, Claudia Sue

2017-12-10

The use of longitudinal measurements to predict a categorical outcome is an increasingly common goal in research studies. Joint models are commonly used to describe two or more models simultaneously by considering the correlated nature of their outcomes and the random error present in the longitudinal measurements. However, there is limited research on joint models with longitudinal predictors and categorical cross-sectional outcomes. Perhaps the most challenging task is how to model the longitudinal predictor process such that it represents the true biological mechanism that dictates the association with the categorical response. We propose a joint logistic regression and Markov chain model to describe a binary cross-sectional response, where the unobserved transition rates of a two-state continuous-time Markov chain are included as covariates. We use the method of maximum likelihood to estimate the parameters of our model. In a simulation study, coverage probabilities of about 95%, standard deviations close to standard errors, and low biases for the parameter values show that our estimation method is adequate. We apply the proposed joint model to a dataset of patients with traumatic brain injury to describe and predict a 6-month outcome based on physiological data collected post-injury and admission characteristics. Our analysis indicates that the information provided by physiological changes over time may help improve prediction of long-term functional status of these severely ill subjects. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

A Markov chain model for CANDU feeder pipe degradation

International Nuclear Information System (INIS)

Datla, S.; Dinnie, K.; Usmani, A.; Yuan, X.-X.

2008-01-01

There is need for risk based approach to manage feeder pipe degradation to ensure safe operation by minimizing the nuclear safety risk. The current lack of understanding of some fundamental degradation mechanisms will result in uncertainty in predicting the rupture frequency. There are still concerns caused by uncertainties in the inspection techniques and engineering evaluations which should be addressed in the current procedures. A probabilistic approach is therefore useful in quantifying the risk and also it provides a tool for risk based decision making. This paper discusses the application of Markov chain model for feeder pipes in order to predict and manage the risks associated with the existing and future aging-related feeder degradation mechanisms. The major challenge in the approach is the lack of service data in characterizing the transition probabilities of the Markov model. The paper also discusses various approaches in estimating plant specific degradation rates. (author)

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....

Shape Modelling Using Markov Random Field Restoration of Point Correspondences

DEFF Research Database (Denmark)

Paulsen, Rasmus Reinhold; Hilger, Klaus Baggesen

2003-01-01

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

Flux through a Markov chain

International Nuclear Information System (INIS)

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

2016-01-01

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

A theoretical Markov chain model for evaluating correctional ...

African Journals Online (AJOL)

In this paper a stochastic method is applied in the study of the long time effect of confinement in a correctional institution on the behaviour of a person with criminal tendencies. The approach used is Markov chain, which uses past history to predict the state of a system in the future. A model is developed for comparing the ...

A Markov deterioration model for predicting recurrent maintenance ...

African Journals Online (AJOL)

The parameters of the Markov chain model for predicting the condition of the road at a design · period for· the flexible pavement failures of wheel track rutting, cracks and pot holes were developed for the Niger State· road network . in Nigeria. Twelve sampled candidate roads were each subjected to standard inventory, traffic ...

Model checking conditional CSL for continuous-time Markov chains

DEFF Research Database (Denmark)

Gao, Yang; Xu, Ming; Zhan, Naijun

2013-01-01

In this paper, we consider the model-checking problem of continuous-time Markov chains (CTMCs) with respect to conditional logic. To the end, we extend Continuous Stochastic Logic introduced in Aziz et al. (2000) [1] to Conditional Continuous Stochastic Logic (CCSL) by introducing a conditional...

Basic problems solving for two-dimensional discrete 3 × 4 order hidden markov model

International Nuclear Information System (INIS)

Wang, Guo-gang; Gan, Zong-liang; Tang, Gui-jin; Cui, Zi-guan; Zhu, Xiu-chang

2016-01-01

A novel model is proposed to overcome the shortages of the classical hypothesis of the two-dimensional discrete hidden Markov model. In the proposed model, the state transition probability depends on not only immediate horizontal and vertical states but also on immediate diagonal state, and the observation symbol probability depends on not only current state but also on immediate horizontal, vertical and diagonal states. This paper defines the structure of the model, and studies the three basic problems of the model, including probability calculation, path backtracking and parameters estimation. By exploiting the idea that the sequences of states on rows or columns of the model can be seen as states of a one-dimensional discrete 1 × 2 order hidden Markov model, several algorithms solving the three questions are theoretically derived. Simulation results further demonstrate the performance of the algorithms. Compared with the two-dimensional discrete hidden Markov model, there are more statistical characteristics in the structure of the proposed model, therefore the proposed model theoretically can more accurately describe some practical problems.

Monte Carlo methods for the reliability analysis of Markov systems

International Nuclear Information System (INIS)

Buslik, A.J.

1985-01-01

This paper presents Monte Carlo methods for the reliability analysis of Markov systems. Markov models are useful in treating dependencies between components. The present paper shows how the adjoint Monte Carlo method for the continuous time Markov process can be derived from the method for the discrete-time Markov process by a limiting process. The straightforward extensions to the treatment of mean unavailability (over a time interval) are given. System unavailabilities can also be estimated; this is done by making the system failed states absorbing, and not permitting repair from them. A forward Monte Carlo method is presented in which the weighting functions are related to the adjoint function. In particular, if the exact adjoint function is known then weighting factors can be constructed such that the exact answer can be obtained with a single Monte Carlo trial. Of course, if the exact adjoint function is known, there is no need to perform the Monte Carlo calculation. However, the formulation is useful since it gives insight into choices of the weight factors which will reduce the variance of the estimator

Study of the seismic activity in central Ionian Islands via semi-Markov modelling

Science.gov (United States)

Pertsinidou, Christina Elisavet; Tsaklidis, George; Papadimitriou, Eleftheria

2017-06-01

The seismicity of the central Ionian Islands ( M ≥ 5.2, 1911-2014) is studied via a semi-Markov chain which is investigated in terms of the destination probabilities (occurrence probabilities). The interevent times are considered to follow geometric (in which case the semi-Markov model reduces to a Markov model) or Pareto distributions. The study of the destination probabilities is useful for forecasting purposes because they can provide the more probable earthquake magnitude and occurrence time. Using the first half of the data sample for the estimation procedure and the other half for forecasting purposes it is found that the time windows obtained by the destination probabilities include 72.9% of the observed earthquake occurrence times (for all magnitudes) and 71.4% for the larger ( M ≥ 6.0) ones.

Long Memory of Financial Time Series and Hidden Markov Models with Time-Varying Parameters

DEFF Research Database (Denmark)

Nystrup, Peter; Madsen, Henrik; Lindström, Erik

2016-01-01

Hidden Markov models are often used to model daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time-varying behavior have not been thoroughly examined. This paper presents an adaptive...... to reproduce with a hidden Markov model. Capturing the time-varying behavior of the parameters also leads to improved one-step density forecasts. Finally, it is shown that the forecasting performance of the estimated models can be further improved using local smoothing to forecast the parameter variations....

Bisimulation and Simulation Relations for Markov Chains

NARCIS (Netherlands)

Baier, Christel; Hermanns, H.; Katoen, Joost P.; Wolf, Verena; Aceto, L.; Gordon, A.

2006-01-01

Formal notions of bisimulation and simulation relation play a central role for any kind of process algebra. This short paper sketches the main concepts for bisimulation and simulation relations for probabilistic systems, modelled by discrete- or continuous-time Markov chains.

Reliability estimation of semi-Markov systems: a case study

International Nuclear Information System (INIS)

Ouhbi, Brahim; Limnios, Nikolaos

1997-01-01

In this article, we are concerned with the estimation of the reliability and the availability of a turbo-generator rotor using a set of data observed in a real engineering situation provided by Electricite De France (EDF). The rotor is modeled by a semi-Markov process, which is used to estimate the rotor's reliability and availability. To do this, we present a method for estimating the semi-Markov kernel from a censored data

Markov Tail Chains

OpenAIRE

janssen, Anja; Segers, Johan

2013-01-01

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

Optimisation of Hidden Markov Model using Baum–Welch algorithm

Indian Academy of Sciences (India)

Home; Journals; Journal of Earth System Science; Volume 126; Issue 1. Optimisation of Hidden Markov Model using Baum–Welch algorithm for prediction of maximum and minimum temperature over Indian Himalaya. J C Joshi Tankeshwar Kumar Sunita Srivastava Divya Sachdeva. Volume 126 Issue 1 February 2017 ...

Comparison of the kinetics of different Markov models for ligand binding under varying conditions

International Nuclear Information System (INIS)

Martini, Johannes W. R.; Habeck, Michael

2015-01-01

We recently derived a Markov model for macromolecular ligand binding dynamics from few physical assumptions and showed that its stationary distribution is the grand canonical ensemble [J. W. R. Martini, M. Habeck, and M. Schlather, J. Math. Chem. 52, 665 (2014)]. The transition probabilities of the proposed Markov process define a particular Glauber dynamics and have some similarity to the Metropolis-Hastings algorithm. Here, we illustrate that this model is the stochastic analog of (pseudo) rate equations and the corresponding system of differential equations. Moreover, it can be viewed as a limiting case of general stochastic simulations of chemical kinetics. Thus, the model links stochastic and deterministic approaches as well as kinetics and equilibrium described by the grand canonical ensemble. We demonstrate that the family of transition matrices of our model, parameterized by temperature and ligand activity, generates ligand binding kinetics that respond to changes in these parameters in a qualitatively similar way as experimentally observed kinetics. In contrast, neither the Metropolis-Hastings algorithm nor the Glauber heat bath reflects changes in the external conditions correctly. Both converge rapidly to the stationary distribution, which is advantageous when the major interest is in the equilibrium state, but fail to describe the kinetics of ligand binding realistically. To simulate cellular processes that involve the reversible stochastic binding of multiple factors, our pseudo rate equation model should therefore be preferred to the Metropolis-Hastings algorithm and the Glauber heat bath, if the stationary distribution is not of only interest

Comparison of the kinetics of different Markov models for ligand binding under varying conditions

Energy Technology Data Exchange (ETDEWEB)

Martini, Johannes W. R., E-mail: jmartin2@gwdg.de [Max Planck Institute for Developmental Biology, Tübingen (Germany); Felix Bernstein Institute for Mathematical Statistics in the Biosciences, University of Göttingen, Göttingen (Germany); Habeck, Michael, E-mail: mhabeck@gwdg.de [Felix Bernstein Institute for Mathematical Statistics in the Biosciences, University of Göttingen, Göttingen (Germany); Max Planck Institute for Biophysical Chemistry, Göttingen (Germany)

2015-03-07

We recently derived a Markov model for macromolecular ligand binding dynamics from few physical assumptions and showed that its stationary distribution is the grand canonical ensemble [J. W. R. Martini, M. Habeck, and M. Schlather, J. Math. Chem. 52, 665 (2014)]. The transition probabilities of the proposed Markov process define a particular Glauber dynamics and have some similarity to the Metropolis-Hastings algorithm. Here, we illustrate that this model is the stochastic analog of (pseudo) rate equations and the corresponding system of differential equations. Moreover, it can be viewed as a limiting case of general stochastic simulations of chemical kinetics. Thus, the model links stochastic and deterministic approaches as well as kinetics and equilibrium described by the grand canonical ensemble. We demonstrate that the family of transition matrices of our model, parameterized by temperature and ligand activity, generates ligand binding kinetics that respond to changes in these parameters in a qualitatively similar way as experimentally observed kinetics. In contrast, neither the Metropolis-Hastings algorithm nor the Glauber heat bath reflects changes in the external conditions correctly. Both converge rapidly to the stationary distribution, which is advantageous when the major interest is in the equilibrium state, but fail to describe the kinetics of ligand binding realistically. To simulate cellular processes that involve the reversible stochastic binding of multiple factors, our pseudo rate equation model should therefore be preferred to the Metropolis-Hastings algorithm and the Glauber heat bath, if the stationary distribution is not of only interest.

biomvRhsmm: Genomic Segmentation with Hidden Semi-Markov Model

Directory of Open Access Journals (Sweden)

Yang Du

2014-01-01

Full Text Available High-throughput technologies like tiling array and next-generation sequencing (NGS generate continuous homogeneous segments or signal peaks in the genome that represent transcripts and transcript variants (transcript mapping and quantification, regions of deletion and amplification (copy number variation, or regions characterized by particular common features like chromatin state or DNA methylation ratio (epigenetic modifications. However, the volume and output of data produced by these technologies present challenges in analysis. Here, a hidden semi-Markov model (HSMM is implemented and tailored to handle multiple genomic profile, to better facilitate genome annotation by assisting in the detection of transcripts, regulatory regions, and copy number variation by holistic microarray or NGS. With support for various data distributions, instead of limiting itself to one specific application, the proposed hidden semi-Markov model is designed to allow modeling options to accommodate different types of genomic data and to serve as a general segmentation engine. By incorporating genomic positions into the sojourn distribution of HSMM, with optional prior learning using annotation or previous studies, the modeling output is more biologically sensible. The proposed model has been compared with several other state-of-the-art segmentation models through simulation benchmarking, which shows that our efficient implementation achieves comparable or better sensitivity and specificity in genomic segmentation.

Markov chain solution of photon multiple scattering through turbid slabs.

Science.gov (United States)

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.

Markov-switching model for nonstationary runoff conditioned on El Nino information

DEFF Research Database (Denmark)

Gelati, Emiliano; Madsen, H.; Rosbjerg, Dan

2010-01-01

We define a Markov-modulated autoregressive model with exogenous input (MARX) to generate runoff scenarios using climatic information. Runoff parameterization is assumed to be conditioned on a hidden climate state following a Markov chain, where state transition probabilities are functions...... of the climatic input. MARX allows stochastic modeling of nonstationary runoff, as runoff anomalies are described by a mixture of autoregressive models with exogenous input, each one corresponding to a climate state. We apply MARX to inflow time series of the Daule Peripa reservoir (Ecuador). El Nino Southern...... Oscillation (ENSO) information is used to condition runoff parameterization. Among the investigated ENSO indexes, the NINO 1+2 sea surface temperature anomalies and the trans-Nino index perform best as predictors. In the perspective of reservoir optimization at various time scales, MARX produces realistic...

Bridge Deterioration Prediction Model Based On Hybrid Markov-System Dynamic

Directory of Open Access Journals (Sweden)

Widodo Soetjipto Jojok

2017-01-01

Full Text Available Instantaneous bridge failure tends to increase in Indonesia. To mitigate this condition, Indonesia’s Bridge Management System (I-BMS has been applied to continuously monitor the condition of bridges. However, I-BMS only implements visual inspection for maintenance priority of the bridge structure component instead of bridge structure system. This paper proposes a new bridge failure prediction model based on hybrid Markov-System Dynamic (MSD. System dynamic is used to represent the correlation among bridge structure components while Markov chain is used to calculate temporal probability of the bridge failure. Around 235 data of bridges in Indonesia were collected from Directorate of Bridge the Ministry of Public Works and Housing for calculating transition probability of the model. To validate the model, a medium span concrete bridge was used as a case study. The result shows that the proposed model can accurately predict the bridge condition. Besides predicting the probability of the bridge failure, this model can also be used as an early warning system for bridge monitoring activity.

Strategy Complexity of Finite-Horizon Markov Decision Processes and Simple Stochastic Games

DEFF Research Database (Denmark)

Ibsen-Jensen, Rasmus; Chatterjee, Krishnendu

2012-01-01

Markov decision processes (MDPs) and simple stochastic games (SSGs) provide a rich mathematical framework to study many important problems related to probabilistic systems. MDPs and SSGs with finite-horizon objectives, where the goal is to maximize the probability to reach a target state in a given...

Multivariate Markov chain modeling for stock markets

Science.gov (United States)

Maskawa, Jun-ichi

2003-06-01

We study a multivariate Markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes are coded into the sequences of up and down spins according to their signs. We start with the discussion for small portfolios consisting of two stock issues. The generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation. The resultant form of the joint probability of the stationary state coincides with Gibbs measure assigned to each configuration of spin glass model. Through the analysis of actual portfolios, it has been shown that the synchronization of the direction of the price changes is well described by the model.

Confluence reduction for Markov automata

NARCIS (Netherlands)

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