Metis: A Pure Metropolis Markov Chain Monte Carlo Bayesian Inference Library
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Bates, Cameron Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Mckigney, Edward Allen [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2018-01-09
The use of Bayesian inference in data analysis has become the standard for large scienti c experiments [1, 2]. The Monte Carlo Codes Group(XCP-3) at Los Alamos has developed a simple set of algorithms currently implemented in C++ and Python to easily perform at-prior Markov Chain Monte Carlo Bayesian inference with pure Metropolis sampling. These implementations are designed to be user friendly and extensible for customization based on speci c application requirements. This document describes the algorithmic choices made and presents two use cases.
Abdulla, Parosh Aziz; Henda, Noomene Ben; Mayr, Richard
2007-01-01
We consider qualitative and quantitative verification problems for infinite-state Markov chains. We call a Markov chain decisive w.r.t. a given set of target states F if it almost certainly eventually reaches either F or a state from which F can no longer be reached. While all finite Markov chains are trivially decisive (for every set F), this also holds for many classes of infinite Markov chains. Infinite Markov chains which contain a finite attractor are decisive w.r.t. every set F. In part...
Markov Chains and Markov Processes
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...
Quantum Enhanced Inference in Markov Logic Networks.
Wittek, Peter; Gogolin, Christian
2017-04-19
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.
Quantum Enhanced Inference in Markov Logic Networks
Wittek, Peter; Gogolin, Christian
2017-04-01
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
Cofré, Rodrigo; Maldonado, Cesar
2018-01-01
We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.
Markov Chain Estimation of Avian Seasonal Fecundity
To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...
Markov processes and controlled Markov chains
Filar, Jerzy; Chen, Anyue
2002-01-01
The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South Ameri...
Inferring animal densities from tracking data using Markov chains.
Whitehead, Hal; Jonsen, Ian D
2013-01-01
The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.
Inferring animal densities from tracking data using Markov chains.
Directory of Open Access Journals (Sweden)
Hal Whitehead
Full Text Available The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.
Observation uncertainty in reversible Markov chains.
Metzner, Philipp; Weber, Marcus; Schütte, Christof
2010-09-01
In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .
Multi-chain Markov chain Monte Carlo methods for computationally expensive models
Huang, M.; Ray, J.; Ren, H.; Hou, Z.; Bao, J.
2017-12-01
Markov chain Monte Carlo (MCMC) methods are used to infer model parameters from observational data. The parameters are inferred as probability densities, thus capturing estimation error due to sparsity of the data, and the shortcomings of the model. Multiple communicating chains executing the MCMC method have the potential to explore the parameter space better, and conceivably accelerate the convergence to the final distribution. We present results from tests conducted with the multi-chain method to show how the acceleration occurs i.e., for loose convergence tolerances, the multiple chains do not make much of a difference. The ensemble of chains also seems to have the ability to accelerate the convergence of a few chains that might start from suboptimal starting points. Finally, we show the performance of the chains in the estimation of O(10) parameters using computationally expensive forward models such as the Community Land Model, where the sampling burden is distributed over multiple chains.
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.
Mallak, Saed
1996-01-01
Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent University, 1996. Thesis (Master's) -- Bilkent University, 1996. Includes bibliographical references leaves leaf 29 In thi.s work, we studierl the Ergodicilv of Non-Stationary .Markov chains. We gave several e.xainples with different cases. We proved that given a sec[uence of Markov chains such that the limit of this sec|uence is an Ergodic Markov chain, then the limit of the combination ...
Process Algebra and Markov Chains
Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Process algebra and Markov chains
Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.
2001-01-01
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Geometry and Dynamics for Markov Chain Monte Carlo
Barp, Alessandro; Briol, Francois-Xavier; Kennedy, Anthony D.; Girolami, Mark
2017-01-01
Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains which can explore probability densities efficiently. The method emerges from physics and geometry and these links have been extensively studied by a series of authors through the last thirty years. However, there is currently a gap between the in...
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 ...
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.
Herbei, Radu; Kubatko, Laura
2013-03-26
Markov chains are widely used for modeling in many areas of molecular biology and genetics. As the complexity of such models advances, it becomes increasingly important to assess the rate at which a Markov chain converges to its stationary distribution in order to carry out accurate inference. A common measure of convergence to the stationary distribution is the total variation distance, but this measure can be difficult to compute when the state space of the chain is large. We propose a Monte Carlo method to estimate the total variation distance that can be applied in this situation, and we demonstrate how the method can be efficiently implemented by taking advantage of GPU computing techniques. We apply the method to two Markov chains on the space of phylogenetic trees, and discuss the implications of our findings for the development of algorithms for phylogenetic inference.
DEFF Research Database (Denmark)
Justesen, Jørn
2005-01-01
A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly.......A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly....
Hartfiel, Darald J
1998-01-01
In this study extending classical Markov chain theory to handle fluctuating transition matrices, the author develops a theory of Markov set-chains and provides numerous examples showing how that theory can be applied. Chapters are concluded with a discussion of related research. Readers who can benefit from this monograph are those interested in, or involved with, systems whose data is imprecise or that fluctuate with time. A background equivalent to a course in linear algebra and one in probability theory should be sufficient.
Regeneration and general Markov chains
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Vladimir V. Kalashnikov
1994-01-01
Full Text Available Ergodicity, continuity, finite approximations and rare visits of general Markov chains are investigated. The obtained results permit further quantitative analysis of characteristics, such as, rates of convergence, continuity (measured as a distance between perturbed and non-perturbed characteristics, deviations between Markov chains, accuracy of approximations and bounds on the distribution function of the first visit time to a chosen subset, etc. The underlying techniques use the embedding of the general Markov chain into a wide sense regenerative process with the help of splitting construction.
Markov chains theory and applications
Sericola, Bruno
2013-01-01
Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
Performance Modeling of Communication Networks with Markov Chains
Mo, Jeonghoon
2010-01-01
This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMe and continuous time Markov chain (CTMe. We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probab
Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation
Minasny, B.; Vrugt, J.A.; McBratney, A.B.
2011-01-01
This paper demonstrates for the first time the use of Markov Chain Monte Carlo (MCMC) simulation for parameter inference in model-based soil geostatistics. We implemented the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm to jointly summarize the posterior
Consistency and refinement for Interval Markov Chains
DEFF Research Database (Denmark)
Delahaye, Benoit; Larsen, Kim Guldstrand; Legay, Axel
2012-01-01
Interval Markov Chains (IMC), or Markov Chains with probability intervals in the transition matrix, are the base of a classic specification theory for probabilistic systems [18]. The standard semantics of IMCs assigns to a specification the set of all Markov Chains that satisfy its interval...
Data Analysis Recipes: Using Markov Chain Monte Carlo
Hogg, David W.; Foreman-Mackey, Daniel
2018-05-01
Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data. In this primarily pedagogical contribution, we give a brief overview of the most basic MCMC method and some practical advice for the use of MCMC in real inference problems. We give advice on method choice, tuning for performance, methods for initialization, tests of convergence, troubleshooting, and use of the chain output to produce or report parameter estimates with associated uncertainties. We argue that autocorrelation time is the most important test for convergence, as it directly connects to the uncertainty on the sampling estimate of any quantity of interest. We emphasize that sampling is a method for doing integrals; this guides our thinking about how MCMC output is best used. .
Spectral methods for quantum Markov chains
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Szehr, Oleg
2014-05-08
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Spectral methods for quantum Markov chains
International Nuclear Information System (INIS)
Szehr, Oleg
2014-01-01
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Verification of Open Interactive Markov Chains
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....
Approximate quantum Markov chains
Sutter, David
2018-01-01
This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...
Markov chains models, algorithms and applications
Ching, Wai-Ki; Ng, Michael K; Siu, Tak-Kuen
2013-01-01
This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods
Perturbation theory for Markov chains via Wasserstein distance
Rudolf, Daniel; Schweizer, Nikolaus
2017-01-01
Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the nth step distributions of two Markov chains
Quantum Markov Chain Mixing and Dissipative Engineering
DEFF Research Database (Denmark)
Kastoryano, Michael James
2012-01-01
This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state...... of the system at the present point in time, but not on the history of events. Very many important processes in nature are of this type, therefore a good understanding of their behaviour has turned out to be very fruitful for science. Markov chains always have a non-empty set of limiting distributions...... (stationary states). The aim of Markov chain mixing is to obtain (upper and/or lower) bounds on the number of steps it takes for the Markov chain to reach a stationary state. The natural quantum extensions of these notions are density matrices and quantum channels. We set out to develop a general mathematical...
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelli; Robert, Philippe
2012-01-01
If ($C_n$) a Markov chain on a discrete state space $S$, a Markov chain ($C_n, M_n$) on the product space $S \\times S$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain behaves like the original Markov chain and the second component changes only when both
Berlow, Noah; Pal, Ranadip
2011-01-01
Genetic Regulatory Networks (GRNs) are frequently modeled as Markov Chains providing the transition probabilities of moving from one state of the network to another. The inverse problem of inference of the Markov Chain from noisy and limited experimental data is an ill posed problem and often generates multiple model possibilities instead of a unique one. In this article, we address the issue of intervention in a genetic regulatory network represented by a family of Markov Chains. The purpose of intervention is to alter the steady state probability distribution of the GRN as the steady states are considered to be representative of the phenotypes. We consider robust stationary control policies with best expected behavior. The extreme computational complexity involved in search of robust stationary control policies is mitigated by using a sequential approach to control policy generation and utilizing computationally efficient techniques for updating the stationary probability distribution of a Markov chain following a rank one perturbation.
Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium
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.
Probability distributions for Markov chain based quantum walks
Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.
2018-01-01
We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelli; Robert, Philippe
Motivated by an original on-line page-ranking algorithm, starting from an arbitrary Markov chain $(C_n)$ on a discrete state space ${\\cal S}$, a Markov chain $(C_n,M_n)$ on the product space ${\\cal S}^2$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain
Markov chains analytic and Monte Carlo computations
Graham, Carl
2014-01-01
Markov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features: Numerous exercises with solutions as well as extended case studies.A detailed and rigorous presentation of Markov chains with discrete time and state space.An appendix presenting probabilistic notions that are nec
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.
Introduction to the numerical solutions of Markov chains
Stewart, Williams J
1994-01-01
A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse - and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here, Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing metho...
Markov chains and mixing times
Levin, David A; Wilmer, Elizabeth L
2009-01-01
This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of r
A New GMRES(m Method for Markov Chains
Directory of Open Access Journals (Sweden)
Bing-Yuan Pu
2013-01-01
Full Text Available This paper presents a class of new accelerated restarted GMRES method for calculating the stationary probability vector of an irreducible Markov chain. We focus on the mechanism of this new hybrid method by showing how to periodically combine the GMRES and vector extrapolation method into a much efficient one for improving the convergence rate in Markov chain problems. Numerical experiments are carried out to demonstrate the efficiency of our new algorithm on several typical Markov chain problems.
Quantitative risk stratification in Markov chains with limiting conditional distributions.
Chan, David C; Pollett, Philip K; Weinstein, Milton C
2009-01-01
Many clinical decisions require patient risk stratification. The authors introduce the concept of limiting conditional distributions, which describe the equilibrium proportion of surviving patients occupying each disease state in a Markov chain with death. Such distributions can quantitatively describe risk stratification. The authors first establish conditions for the existence of a positive limiting conditional distribution in a general Markov chain and describe a framework for risk stratification using the limiting conditional distribution. They then apply their framework to a clinical example of a treatment indicated for high-risk patients, first to infer the risk of patients selected for treatment in clinical trials and then to predict the outcomes of expanding treatment to other populations of risk. For the general chain, a positive limiting conditional distribution exists only if patients in the earliest state have the lowest combined risk of progression or death. The authors show that in their general framework, outcomes and population risk are interchangeable. For the clinical example, they estimate that previous clinical trials have selected the upper quintile of patient risk for this treatment, but they also show that expanded treatment would weakly dominate this degree of targeted treatment, and universal treatment may be cost-effective. Limiting conditional distributions exist in most Markov models of progressive diseases and are well suited to represent risk stratification quantitatively. This framework can characterize patient risk in clinical trials and predict outcomes for other populations of risk.
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...
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.
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
Sampling rare fluctuations of discrete-time Markov chains
Whitelam, Stephen
2018-03-01
We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.
Markov chain aggregation for agent-based models
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 Chain Monte Carlo Methods
Indian Academy of Sciences (India)
Keywords. Markov chain; state space; stationary transition probability; stationary distribution; irreducibility; aperiodicity; stationarity; M-H algorithm; proposal distribution; acceptance probability; image processing; Gibbs sampler.
Solan, Eilon; Vieille, Nicolas
2015-01-01
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.
Markov Chain Ontology Analysis (MCOA).
Frost, H Robert; McCray, Alexa T
2012-02-03
Biomedical ontologies have become an increasingly critical lens through which researchers analyze the genomic, clinical and bibliographic data that fuels scientific research. Of particular relevance are methods, such as enrichment analysis, that quantify the importance of ontology classes relative to a collection of domain data. Current analytical techniques, however, remain limited in their ability to handle many important types of structural complexity encountered in real biological systems including class overlaps, continuously valued data, inter-instance relationships, non-hierarchical relationships between classes, semantic distance and sparse data. In this paper, we describe a methodology called Markov Chain Ontology Analysis (MCOA) and illustrate its use through a MCOA-based enrichment analysis application based on a generative model of gene activation. MCOA models the classes in an ontology, the instances from an associated dataset and all directional inter-class, class-to-instance and inter-instance relationships as a single finite ergodic Markov chain. The adjusted transition probability matrix for this Markov chain enables the calculation of eigenvector values that quantify the importance of each ontology class relative to other classes and the associated data set members. On both controlled Gene Ontology (GO) data sets created with Escherichia coli, Drosophila melanogaster and Homo sapiens annotations and real gene expression data extracted from the Gene Expression Omnibus (GEO), the MCOA enrichment analysis approach provides the best performance of comparable state-of-the-art methods. A methodology based on Markov chain models and network analytic metrics can help detect the relevant signal within large, highly interdependent and noisy data sets and, for applications such as enrichment analysis, has been shown to generate superior performance on both real and simulated data relative to existing state-of-the-art approaches.
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.
Transition Effect Matrices and Quantum Markov Chains
Gudder, Stan
2009-06-01
A transition effect matrix (TEM) is a quantum generalization of a classical stochastic matrix. By employing a TEM we obtain a quantum generalization of a classical Markov chain. We first discuss state and operator dynamics for a quantum Markov chain. We then consider various types of TEMs and vector states. In particular, we study invariant, equilibrium and singular vector states and investigate projective, bistochastic, invertible and unitary TEMs.
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.
STATISTICAL ANALYSIS OF NOTATIONAL AFL DATA USING CONTINUOUS TIME MARKOV CHAINS
Directory of Open Access Journals (Sweden)
Denny Meyer
2006-12-01
Full Text Available Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs, with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated
Automated generation of partial Markov chain from high level descriptions
International Nuclear Information System (INIS)
Brameret, P.-A.; Rauzy, A.; Roussel, J.-M.
2015-01-01
We propose an algorithm to generate partial Markov chains from high level implicit descriptions, namely AltaRica models. This algorithm relies on two components. First, a variation on Dijkstra's algorithm to compute shortest paths in a graph. Second, the definition of a notion of distance to select which states must be kept and which can be safely discarded. The proposed method solves two problems at once. First, it avoids a manual construction of Markov chains, which is both tedious and error prone. Second, up the price of acceptable approximations, it makes it possible to push back dramatically the exponential blow-up of the size of the resulting chains. We report experimental results that show the efficiency of the proposed approach. - Highlights: • We generate Markov chains from a higher level safety modeling language (AltaRica). • We use a variation on Dijkstra's algorithm to generate partial Markov chains. • Hence we solve two problems: the first problem is the tedious manual construction of Markov chains. • The second problem is the blow-up of the size of the chains, at the cost of decent approximations. • The experimental results highlight the efficiency of the method
Markov chains and mixing times
Levin, David A
2017-01-01
Markov Chains and Mixing Times is a magical book, managing to be both friendly and deep. It gently introduces probabilistic techniques so that an outsider can follow. At the same time, it is the first book covering the geometric theory of Markov chains and has much that will be new to experts. It is certainly THE book that I will use to teach from. I recommend it to all comers, an amazing achievement. -Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University Mixing times are an active research topic within many fields from statistical physics to the theory of algorithms, as well as having intrinsic interest within mathematical probability and exploiting discrete analogs of important geometry concepts. The first edition became an instant classic, being accessible to advanced undergraduates and yet bringing readers close to current research frontiers. This second edition adds chapters on monotone chains, the exclusion process and hitting time parameters. Having both exercises...
Geometry and Dynamics for Markov Chain Monte Carlo
Barp, Alessandro; Briol, François-Xavier; Kennedy, Anthony D.; Girolami, Mark
2018-03-01
Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains which can explore probability densities efficiently. The method emerges from physics and geometry and these links have been extensively studied by a series of authors through the last thirty years. However, there is currently a gap between the intuitions and knowledge of users of the methodology and our deep understanding of these theoretical foundations. The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners and other users of the methodology with only a basic understanding of Monte Carlo methods. This will be complemented with some discussion of the most recent advances in the field which we believe will become increasingly relevant to applied scientists.
First hitting probabilities for semi markov chains and estimation
DEFF Research Database (Denmark)
Georgiadis, Stylianos
2017-01-01
We first consider a stochastic system described by an absorbing semi-Markov chain with finite state space and we introduce the absorption probability to a class of recurrent states. Afterwards, we study the first hitting probability to a subset of states for an irreducible semi-Markov chain...
Markov chains and semi-Markov models in time-to-event analysis.
Abner, Erin L; Charnigo, Richard J; Kryscio, Richard J
2013-10-25
A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields.
Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)
Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.
2018-05-01
A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.
Bayesian posterior distributions without Markov chains.
Cole, Stephen R; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B
2012-03-01
Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 3. Markov Chain Monte Carlo - Examples. Arnab Chakraborty. General Article Volume 7 Issue 3 March 2002 pp 25-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/007/03/0025-0034. Keywords.
Compositionality for Markov reward chains with fast and silent transitions
Markovski, J.; Sokolova, A.; Trcka, N.; Vink, de E.P.
2009-01-01
A parallel composition is defined for Markov reward chains with stochastic discontinuity, and with fast and silent transitions. In this setting, compositionality with respect to the relevant aggregation preorders is established. For Markov reward chains with fast transitions the preorders are
Singer, Philipp; Helic, Denis; Taraghi, Behnam; Strohmaier, Markus
2014-01-01
One of the most frequently used models for understanding human navigation on the Web is the Markov chain model, where Web pages are represented as states and hyperlinks as probabilities of navigating from one page to another. Predominantly, human navigation on the Web has been thought to satisfy the memoryless Markov property stating that the next page a user visits only depends on her current page and not on previously visited ones. This idea has found its way in numerous applications such as Google's PageRank algorithm and others. Recently, new studies suggested that human navigation may better be modeled using higher order Markov chain models, i.e., the next page depends on a longer history of past clicks. Yet, this finding is preliminary and does not account for the higher complexity of higher order Markov chain models which is why the memoryless model is still widely used. In this work we thoroughly present a diverse array of advanced inference methods for determining the appropriate Markov chain order. We highlight strengths and weaknesses of each method and apply them for investigating memory and structure of human navigation on the Web. Our experiments reveal that the complexity of higher order models grows faster than their utility, and thus we confirm that the memoryless model represents a quite practical model for human navigation on a page level. However, when we expand our analysis to a topical level, where we abstract away from specific page transitions to transitions between topics, we find that the memoryless assumption is violated and specific regularities can be observed. We report results from experiments with two types of navigational datasets (goal-oriented vs. free form) and observe interesting structural differences that make a strong argument for more contextual studies of human navigation in future work.
Directory of Open Access Journals (Sweden)
Philipp Singer
Full Text Available One of the most frequently used models for understanding human navigation on the Web is the Markov chain model, where Web pages are represented as states and hyperlinks as probabilities of navigating from one page to another. Predominantly, human navigation on the Web has been thought to satisfy the memoryless Markov property stating that the next page a user visits only depends on her current page and not on previously visited ones. This idea has found its way in numerous applications such as Google's PageRank algorithm and others. Recently, new studies suggested that human navigation may better be modeled using higher order Markov chain models, i.e., the next page depends on a longer history of past clicks. Yet, this finding is preliminary and does not account for the higher complexity of higher order Markov chain models which is why the memoryless model is still widely used. In this work we thoroughly present a diverse array of advanced inference methods for determining the appropriate Markov chain order. We highlight strengths and weaknesses of each method and apply them for investigating memory and structure of human navigation on the Web. Our experiments reveal that the complexity of higher order models grows faster than their utility, and thus we confirm that the memoryless model represents a quite practical model for human navigation on a page level. However, when we expand our analysis to a topical level, where we abstract away from specific page transitions to transitions between topics, we find that the memoryless assumption is violated and specific regularities can be observed. We report results from experiments with two types of navigational datasets (goal-oriented vs. free form and observe interesting structural differences that make a strong argument for more contextual studies of human navigation in future work.
Temperature scaling method for Markov chains.
Crosby, Lonnie D; Windus, Theresa L
2009-01-22
The use of ab initio potentials in Monte Carlo simulations aimed at investigating the nucleation kinetics of water clusters is complicated by the computational expense of the potential energy determinations. Furthermore, the common desire to investigate the temperature dependence of kinetic properties leads to an urgent need to reduce the expense of performing simulations at many different temperatures. A method is detailed that allows a Markov chain (obtained via Monte Carlo) at one temperature to be scaled to other temperatures of interest without the need to perform additional large simulations. This Markov chain temperature-scaling (TeS) can be generally applied to simulations geared for numerous applications. This paper shows the quality of results which can be obtained by TeS and the possible quantities which may be extracted from scaled Markov chains. Results are obtained for a 1-D analytical potential for which the exact solutions are known. Also, this method is applied to water clusters consisting of between 2 and 5 monomers, using Dynamical Nucleation Theory to determine the evaporation rate constant for monomer loss. Although ab initio potentials are not utilized in this paper, the benefit of this method is made apparent by using the Dang-Chang polarizable classical potential for water to obtain statistical properties at various temperatures.
A descriptive model of resting-state networks using Markov chains.
Xie, H; Pal, R; Mitra, S
2016-08-01
Resting-state functional connectivity (RSFC) studies considering pairwise linear correlations have attracted great interests while the underlying functional network structure still remains poorly understood. To further our understanding of RSFC, this paper presents an analysis of the resting-state networks (RSNs) based on the steady-state distributions and provides a novel angle to investigate the RSFC of multiple functional nodes. This paper evaluates the consistency of two networks based on the Hellinger distance between the steady-state distributions of the inferred Markov chain models. The results show that generated steady-state distributions of default mode network have higher consistency across subjects than random nodes from various RSNs.
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
Gbedo, Yémalin Gabin; Mangin-Brinet, Mariane
2017-07-01
We present a new procedure to determine parton distribution functions (PDFs), based on Markov chain Monte Carlo (MCMC) methods. The aim of this paper is to show that we can replace the standard χ2 minimization by procedures grounded on statistical methods, and on Bayesian inference in particular, thus offering additional insight into the rich field of PDFs determination. After a basic introduction to these techniques, we introduce the algorithm we have chosen to implement—namely Hybrid (or Hamiltonian) Monte Carlo. This algorithm, initially developed for Lattice QCD, turns out to be very interesting when applied to PDFs determination by global analyses; we show that it allows us to circumvent the difficulties due to the high dimensionality of the problem, in particular concerning the acceptance. A first feasibility study is performed and presented, which indicates that Markov chain Monte Carlo can successfully be applied to the extraction of PDFs and of their uncertainties.
On a Markov chain roulette-type game
International Nuclear Information System (INIS)
El-Shehawey, M A; El-Shreef, Gh A
2009-01-01
A Markov chain on non-negative integers which arises in a roulette-type game is discussed. The transition probabilities are p 01 = ρ, p Nj = δ Nj , p i,i+W = q, p i,i-1 = p = 1 - q, 1 ≤ W < N, 0 ≤ ρ ≤ 1, N - W < j ≤ N and i = 1, 2, ..., N - W. Using formulae for the determinant of a partitioned matrix, a closed form expression for the solution of the Markov chain roulette-type game is deduced. The present analysis is supported by two mathematical models from tumor growth and war with bargaining
Analysis of a quantum Markov chain
International Nuclear Information System (INIS)
Marbeau, J.; Gudder, S.
1990-01-01
A quantum chain is analogous to a classical stationary Markov chain except that the probability measure is replaced by a complex amplitude measure and the transition probability matrix is replaced by a transition amplitude matrix. After considering the general situation, we study a particular example of a quantum chain whose transition amplitude matrix has the form of a Dirichlet matrix. Such matrices generate a discrete analog of the usual continuum Feynman amplitude. We then compute the probability distribution for these quantum chains
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.
Computing continuous-time Markov chains as transformers of unbounded observables
DEFF Research Database (Denmark)
Danos, Vincent; Heindel, Tobias; Garnier, Ilias
2017-01-01
The paper studies continuous-time Markov chains (CTMCs) as transformers of real-valued functions on their state space, considered as generalised predicates and called observables. Markov chains are assumed to take values in a countable state space S; observables f: S → ℝ may be unbounded...
Exact goodness-of-fit tests for Markov chains.
Besag, J; Mondal, D
2013-06-01
Goodness-of-fit tests are useful in assessing whether a statistical model is consistent with available data. However, the usual χ² asymptotics often fail, either because of the paucity of the data or because a nonstandard test statistic is of interest. In this article, we describe exact goodness-of-fit tests for first- and higher order Markov chains, with particular attention given to time-reversible ones. The tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple Monte Carlo sampling or by Markov chain Monte Carlo. They apply both to single and to multiple sequences and allow a free choice of test statistic. Three examples are given. The first concerns multiple sequences of dry and wet January days for the years 1948-1983 at Snoqualmie Falls, Washington State, and suggests that standard analysis may be misleading. The second one is for a four-state DNA sequence and lends support to the original conclusion that a second-order Markov chain provides an adequate fit to the data. The last one is six-state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first-order reversible Markov chain at 6 picosecond time steps. © 2013, The International Biometric Society.
Martingales and Markov chains solved exercises and elements of theory
Baldi, Paolo; Priouret, Pierre
2002-01-01
CONDITIONAL EXPECTATIONSIntroductionDefinition and First PropertiesConditional Expectations and Conditional LawsExercisesSolutionsSTOCHASTIC PROCESSESGeneral FactsStopping TimesExercisesSolutionsMARTINGALESFirst DefinitionsFirst PropertiesThe Stopping TheoremMaximal InequalitiesSquare Integral MartingalesConvergence TheoremsRegular MartingalesExercisesProblemsSolutionsMARKOV CHAINSTransition Matrices, Markov ChainsConstruction and ExistenceComputations on the Canonical ChainPotential OperatorsPassage ProblemsRecurrence, TransienceRecurrent Irreducible ChainsPeriodicityExercisesProblemsSolution
Honest Importance Sampling with Multiple Markov Chains.
Tan, Aixin; Doss, Hani; Hobert, James P
2015-01-01
Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable
On almost-periodic points of a topological Markov chain
International Nuclear Information System (INIS)
Bogatyi, Semeon A; Redkozubov, Vadim V
2012-01-01
We prove that a transitive topological Markov chain has almost-periodic points of all D-periods. Moreover, every D-period is realized by continuously many distinct minimal sets. We give a simple constructive proof of the result which asserts that any transitive topological Markov chain has periodic points of almost all periods, and study the structure of the finite set of positive integers that are not periods.
Indian Academy of Sciences (India)
be obtained as a limiting value of a sample path of a suitable ... makes a mathematical model of chance and deals with the problem by .... Is the Markov chain aperiodic? It is! Here is how you can see it. Suppose that after you do the cut, you hold the top half in your right hand, and the bottom half in your left. Then there.
McNally, Kevin; Cotton, Richard; Cocker, John; Jones, Kate; Bartels, Mike; Rick, David; Price, Paul; Loizou, George
2012-01-01
There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure. PMID:22719759
Directory of Open Access Journals (Sweden)
Kevin McNally
2012-01-01
Full Text Available There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure.
Uncovering and testing the fuzzy clusters based on lumped Markov chain in complex network.
Jing, Fan; Jianbin, Xie; Jinlong, Wang; Jinshuai, Qu
2013-01-01
Identifying clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. By means of a lumped Markov chain model of a random walker, we propose two novel ways of inferring the lumped markov transition matrix. Furthermore, some useful results are proposed based on the analysis of the properties of the lumped Markov process. To find the best partition of complex networks, a novel framework including two algorithms for network partition based on the optimal lumped Markovian dynamics is derived to solve this problem. The algorithms are constructed to minimize the objective function under this framework. It is demonstrated by the simulation experiments that our algorithms can efficiently determine the probabilities with which a node belongs to different clusters during the learning process and naturally supports the fuzzy partition. Moreover, they are successfully applied to real-world network, including the social interactions between members of a karate club.
Monotone measures of ergodicity for Markov chains
Directory of Open Access Journals (Sweden)
J. Keilson
1998-01-01
Full Text Available The following paper, first written in 1974, was never published other than as part of an internal research series. Its lack of publication is unrelated to the merits of the paper and the paper is of current importance by virtue of its relation to the relaxation time. A systematic discussion is provided of the approach of a finite Markov chain to ergodicity by proving the monotonicity of an important set of norms, each measures of egodicity, whether or not time reversibility is present. The paper is of particular interest because the discussion of the relaxation time of a finite Markov chain [2] has only been clean for time reversible chains, a small subset of the chains of interest. This restriction is not present here. Indeed, a new relaxation time quoted quantifies the relaxation time for all finite ergodic chains (cf. the discussion of Q1(t below Equation (1.7]. This relaxation time was developed by Keilson with A. Roy in his thesis [6], yet to be published.
International Nuclear Information System (INIS)
Lucka, Felix
2012-01-01
Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in the prior distribution has attracted attention. Important questions about the relation between regularization theory and Bayesian inference still need to be addressed when using sparsity promoting inversion. A practical obstacle for these examinations is the lack of fast posterior sampling algorithms for sparse, high-dimensional Bayesian inversion. Accessing the full range of Bayesian inference methods requires being able to draw samples from the posterior probability distribution in a fast and efficient way. This is usually done using Markov chain Monte Carlo (MCMC) sampling algorithms. In this paper, we develop and examine a new implementation of a single component Gibbs MCMC sampler for sparse priors relying on L1-norms. We demonstrate that the efficiency of our Gibbs sampler increases when the level of sparsity or the dimension of the unknowns is increased. This property is contrary to the properties of the most commonly applied Metropolis–Hastings (MH) sampling schemes. We demonstrate that the efficiency of MH schemes for L1-type priors dramatically decreases when the level of sparsity or the dimension of the unknowns is increased. Practically, Bayesian inversion for L1-type priors using MH samplers is not feasible at all. As this is commonly believed to be an intrinsic feature of MCMC sampling, the performance of our Gibbs sampler also challenges common beliefs about the applicability of sample based Bayesian inference. (paper)
Applying Markov Chains for NDVI Time Series Forecasting of Latvian Regions
Directory of Open Access Journals (Sweden)
Stepchenko Arthur
2015-12-01
Full Text Available Time series of earth observation based estimates of vegetation inform about variations in vegetation at the scale of Latvia. A vegetation index is an indicator that describes the amount of chlorophyll (the green mass and shows the relative density and health of vegetation. NDVI index is an important variable for vegetation forecasting and management of various problems, such as climate change monitoring, energy usage monitoring, managing the consumption of natural resources, agricultural productivity monitoring, drought monitoring and forest fire detection. In this paper, we make a one-step-ahead prediction of 7-daily time series of NDVI index using Markov chains. The choice of a Markov chain is due to the fact that a Markov chain is a sequence of random variables where each variable is located in some state. And a Markov chain contains probabilities of moving from one state to other.
International Nuclear Information System (INIS)
Kim, Joo Yeon; Ryu, Hyung Joon; Jung, Gyu Hwan; Lee, Jai Ki
2011-01-01
The dependency within the sequential realizations in the generated Markov chains and their reliabilities are monitored by introducing the autocorrelation and the potential scale reduction factor (PSRF) by model parameters in the atmospheric dispersion. These two diagnostics have been applied for the posterior quantities of the release point and the release rate inferred through the inverse tracking of unknown model parameters for the Yonggwang atmospheric tracer experiment in Korea. The autocorrelations of model parameters are decreasing to low values approaching to zero with increase of lag, resulted in decrease of the dependencies within the two sequential realizations. Their PSRFs are reduced to within 1.2 and the adequate simulation number recognized from these results. From these two convergence diagnostics, the validation of Markov chains generated have been ensured and PSRF then is especially suggested as the efficient tool for convergence monitoring for the source reconstruction in atmospheric dispersion. (author)
A Markov Chain Estimator of Multivariate Volatility from High Frequency Data
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume; Lunde, Asger
We introduce a multivariate estimator of financial volatility that is based on the theory of Markov chains. The Markov chain framework takes advantage of the discreteness of high-frequency returns. We study the finite sample properties of the estimation in a simulation study and apply...
Energy Technology Data Exchange (ETDEWEB)
Frank, T D [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)
2008-07-18
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
International Nuclear Information System (INIS)
Frank, T D
2008-01-01
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
Improvement of Fuzzy Image Contrast Enhancement Using Simulated Ergodic Fuzzy Markov Chains
Directory of Open Access Journals (Sweden)
Behrouz Fathi-Vajargah
2014-01-01
Full Text Available This paper presents a novel fuzzy enhancement technique using simulated ergodic fuzzy Markov chains for low contrast brain magnetic resonance imaging (MRI. The fuzzy image contrast enhancement is proposed by weighted fuzzy expected value. The membership values are then modified to enhance the image using ergodic fuzzy Markov chains. The qualitative performance of the proposed method is compared to another method in which ergodic fuzzy Markov chains are not considered. The proposed method produces better quality image.
Markov chain solution of photon multiple scattering through turbid slabs.
Lin, Ying; Northrop, William F; Li, Xuesong
2016-11-14
This work introduces a Markov Chain solution to model photon multiple scattering through turbid slabs via anisotropic scattering process, i.e., Mie scattering. Results show that the proposed Markov Chain model agree with commonly used Monte Carlo simulation for various mediums such as medium with non-uniform phase functions and absorbing medium. The proposed Markov Chain solution method successfully converts the complex multiple scattering problem with practical phase functions into a matrix form and solves transmitted/reflected photon angular distributions by matrix multiplications. Such characteristics would potentially allow practical inversions by matrix manipulation or stochastic algorithms where widely applied stochastic methods such as Monte Carlo simulations usually fail, and thus enable practical diagnostics reconstructions such as medical diagnosis, spray analysis, and atmosphere sciences.
The spectral method and ergodic theorems for general Markov chains
International Nuclear Information System (INIS)
Nagaev, S V
2015-01-01
We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space
Operations and support cost modeling using Markov chains
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.
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.
Ragain, Stephen; Ugander, Johan
2016-01-01
As datasets capturing human choices grow in richness and scale---particularly in online domains---there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume any of the above axioms while still satisfying the foundational axiom of uniform expansio...
Distinguishing Hidden Markov Chains
Kiefer, Stefan; Sistla, A. Prasad
2015-01-01
Hidden Markov Chains (HMCs) are commonly used mathematical models of probabilistic systems. They are employed in various fields such as speech recognition, signal processing, and biological sequence analysis. We consider the problem of distinguishing two given HMCs based on an observation sequence that one of the HMCs generates. More precisely, given two HMCs and an observation sequence, a distinguishing algorithm is expected to identify the HMC that generates the observation sequence. Two HM...
Multi-dimensional quasitoeplitz Markov chains
Directory of Open Access Journals (Sweden)
Alexander N. Dudin
1999-01-01
Full Text Available This paper deals with multi-dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector-generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP-input, which operate in synchronous random environment.
Markov chain model for demersal fish catch analysis in Indonesia
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.
Adiabatic condition and the quantum hitting time of Markov chains
International Nuclear Information System (INIS)
Krovi, Hari; Ozols, Maris; Roland, Jeremie
2010-01-01
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P ' where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP ' and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.
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.
Volchenkov, Dima; Dawin, Jean René
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
An interlacing theorem for reversible Markov chains
International Nuclear Information System (INIS)
Grone, Robert; Salamon, Peter; Hoffmann, Karl Heinz
2008-01-01
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
An interlacing theorem for reversible Markov chains
Energy Technology Data Exchange (ETDEWEB)
Grone, Robert; Salamon, Peter [Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720 (United States); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet Chemnitz, D-09107 Chemnitz (Germany)
2008-05-30
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
Energy Technology Data Exchange (ETDEWEB)
Vrugt, Jasper A [Los Alamos National Laboratory; Hyman, James M [Los Alamos National Laboratory; Robinson, Bruce A [Los Alamos National Laboratory; Higdon, Dave [Los Alamos National Laboratory; Ter Braak, Cajo J F [NETHERLANDS; Diks, Cees G H [UNIV OF AMSTERDAM
2008-01-01
Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled DiffeRential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, high-dimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems.
A note on asymptotic expansions for Markov chains using operator theory
DEFF Research Database (Denmark)
Jensen, J.L.
1987-01-01
We consider asymptotic expansions for sums Sn on the form Sn = fhook0(X0) + fhook(X1, X0) + ... + fhook(Xn, Xn-1), where Xi is a Markov chain. Under different ergodicity conditions on the Markov chain and certain conditional moment conditions on fhook(Xi, Xi-1), a simple representation...
Model Checking Structured Infinite Markov Chains
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
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
Directory of Open Access Journals (Sweden)
Rodrigo Cofré
2018-01-01
Full Text Available The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.
Decomposition of conditional probability for high-order symbolic Markov chains
Melnik, S. S.; Usatenko, O. V.
2017-07-01
The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.
Optimization of Markov chains for a SUSY fitter: Fittino
Energy Technology Data Exchange (ETDEWEB)
Prudent, Xavier [IKTP, Technische Universitaet, Dresden (Germany); Bechtle, Philip [DESY, Hamburg (Germany); Desch, Klaus; Wienemann, Peter [Universitaet Bonn (Germany)
2010-07-01
A Markov chains is a ''random walk'' algorithm which allows an efficient scan of a given profile and the search of the absolute minimum, even when this profil suffers from the presence of many secondary minima. This property makes them particularly suited to the study of Supersymmetry (SUSY) models, where minima have to be found in up-to 18-dimensional space for the general MSSM. Hence the SUSY fitter ''Fittino'' uses a Metropolis*Hastings Markov chain in a frequentist interpretation to study the impact of current low -energy measurements, as well as expected measurements from LHC and ILC, on the SUSY parameter space. The expected properties of an optimal Markov chain should be the independence of final results with respect to the starting point and a fast convergence. These two points can be achieved by optimizing the width of the proposal distribution, that is the ''average step length'' between two links in the chain. We developped an algorithm for the optimization of the proposal width, by modifying iteratively the width so that the rejection rate be around fifty percent. This optimization leads to a starting point independent chain as well as a faster convergence.
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...
Model Checking Infinite-State Markov Chains
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
An Application of Graph Theory in Markov Chains Reliability Analysis
Directory of Open Access Journals (Sweden)
Pavel Skalny
2014-01-01
Full Text Available The paper presents reliability analysis which was realized for an industrial company. The aim of the paper is to present the usage of discrete time Markov chains and the flow in network approach. Discrete Markov chains a well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. Markov chains are used to describe transitions between the states of the process. The industrial process is described as a graph network. The maximal flow in the network corresponds to the production. The Ford-Fulkerson algorithm is used to quantify the production for each state. The combination of both methods are utilized to quantify the expected value of the amount of manufactured products for the given time period.
Kirkwood, James R
2015-01-01
Review of ProbabilityShort HistoryReview of Basic Probability DefinitionsSome Common Probability DistributionsProperties of a Probability DistributionProperties of the Expected ValueExpected Value of a Random Variable with Common DistributionsGenerating FunctionsMoment Generating FunctionsExercisesDiscrete-Time, Finite-State Markov ChainsIntroductionNotationTransition MatricesDirected Graphs: Examples of Markov ChainsRandom Walk with Reflecting BoundariesGamblerâ€™s RuinEhrenfest ModelCentral Problem of Markov ChainsCondition to Ensure a Unique Equilibrium StateFinding the Equilibrium StateTransient and Recurrent StatesIndicator FunctionsPerron-Frobenius TheoremAbsorbing Markov ChainsMean First Passage TimeMean Recurrence Time and the Equilibrium StateFundamental Matrix for Regular Markov ChainsDividing a Markov Chain into Equivalence ClassesPeriodic Markov ChainsReducible Markov ChainsSummaryExercisesDiscrete-Time, Infinite-State Markov ChainsRenewal ProcessesDelayed Renewal ProcessesEquilibrium State f...
Bayesian analysis for reversible Markov chains
Diaconis, P.; Rolles, S.W.W.
2006-01-01
We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Pólya’s urn. We give closed form normalizing constants, a simple
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
Masuyama, Hiroyuki
2014-01-01
In this paper we study the augmented truncation of discrete-time block-monotone Markov chains under geometric drift conditions. We first present a bound for the total variation distance between the stationary distributions of an original Markov chain and its augmented truncation. We also obtain such error bounds for more general cases, where an original Markov chain itself is not necessarily block monotone but is blockwise dominated by a block-monotone Markov chain. Finally,...
Noise can speed convergence in Markov chains.
Franzke, Brandon; Kosko, Bart
2011-10-01
A new theorem shows that noise can speed convergence to equilibrium in discrete finite-state Markov chains. The noise applies to the state density and helps the Markov chain explore improbable regions of the state space. The theorem ensures that a stochastic-resonance noise benefit exists for states that obey a vector-norm inequality. Such noise leads to faster convergence because the noise reduces the norm components. A corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality. This leads to a noise-benefit algorithm that requires knowledge of the steady state. An alternative blind algorithm uses only past state information to achieve a weaker noise benefit. Simulations illustrate the predicted noise benefits in three well-known Markov models. The first model is a two-parameter Ehrenfest diffusion model that shows how noise benefits can occur in the class of birth-death processes. The second model is a Wright-Fisher model of genotype drift in population genetics. The third model is a chemical reaction network of zeolite crystallization. A fourth simulation shows a convergence rate increase of 64% for states that satisfy the theorem and an increase of 53% for states that satisfy the corollary. A final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles. Noise benefits tend to be sharpest in Markov models that do not converge quickly and that do not have strong absorbing states.
Bisimulation and Simulation Relations for Markov Chains
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.
Model Checking Markov Chains: Techniques and Tools
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
Markov chains with quasitoeplitz transition matrix
Directory of Open Access Journals (Sweden)
Alexander M. Dukhovny
1989-01-01
Full Text Available This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.
Extreme event statistics in a drifting Markov chain
Kindermann, Farina; Hohmann, Michael; Lausch, Tobias; Mayer, Daniel; Schmidt, Felix; Widera, Artur
2017-07-01
We analyze extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one-dimensional periodic potential. Based on more than 500 individual atomic traces we verify the applicability of the Sparre Andersen theorem to our system despite the presence of a drift. We present detailed analysis of four different rare-event statistics for our system: the distributions of extreme values, of record values, of extreme value occurrence in the chain, and of the number of records in the chain. We observe that, for our data, the shape of the extreme event distributions is dominated by the underlying exponential distance distribution extracted from the atomic traces. Furthermore, we find that even small drifts influence the statistics of extreme events and record values, which is supported by numerical simulations, and we identify cases in which the drift can be determined without information about the underlying random variable distributions. Our results facilitate the use of extreme event statistics as a signal for small drifts in correlated trajectories.
Influence of credit scoring on the dynamics of Markov chain
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.
Fast-slow asymptotics for a Markov chain model of fast sodium current
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.
Markov Chain: A Predictive Model for Manpower Planning ...
African Journals Online (AJOL)
ADOWIE PERE
Keywords: Markov Chain, Transition Probability Matrix, Manpower Planning, Recruitment, Promotion, .... movement of the workforce in Jordan productivity .... Planning periods, with T being the horizon, the value of t represents a session.
Bayesian tomography by interacting Markov chains
Romary, T.
2017-12-01
In seismic tomography, we seek to determine the velocity of the undergound from noisy first arrival travel time observations. In most situations, this is an ill posed inverse problem that admits several unperfect solutions. Given an a priori distribution over the parameters of the velocity model, the Bayesian formulation allows to state this problem as a probabilistic one, with a solution under the form of a posterior distribution. The posterior distribution is generally high dimensional and may exhibit multimodality. Moreover, as it is known only up to a constant, the only sensible way to addressthis problem is to try to generate simulations from the posterior. The natural tools to perform these simulations are Monte Carlo Markov chains (MCMC). Classical implementations of MCMC algorithms generally suffer from slow mixing: the generated states are slow to enter the stationary regime, that is to fit the observations, and when one mode of the posterior is eventually identified, it may become difficult to visit others. Using a varying temperature parameter relaxing the constraint on the data may help to enter the stationary regime. Besides, the sequential nature of MCMC makes them ill fitted toparallel implementation. Running a large number of chains in parallel may be suboptimal as the information gathered by each chain is not mutualized. Parallel tempering (PT) can be seen as a first attempt to make parallel chains at different temperatures communicate but only exchange information between current states. In this talk, I will show that PT actually belongs to a general class of interacting Markov chains algorithm. I will also show that this class enables to design interacting schemes that can take advantage of the whole history of the chain, by authorizing exchanges toward already visited states. The algorithms will be illustrated with toy examples and an application to first arrival traveltime tomography.
The spectral method and the central limit theorem for general Markov chains
Nagaev, S. V.
2017-12-01
We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.
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
A Martingale Decomposition of Discrete Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard
We consider a multivariate time series whose increments are given from a homogeneous Markov chain. We show that the martingale component of this process can be extracted by a filtering method and establish the corresponding martingale decomposition in closed-form. This representation is useful fo...
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
DEFF Research Database (Denmark)
Hobolth, Asger
2008-01-01
-dimensional integrals required in the EM algorithm are estimated using MCMC sampling. The MCMC sampler requires simulation of sample paths from a continuous time Markov process, conditional on the beginning and ending states and the paths of the neighboring sites. An exact path sampling algorithm is developed......The evolution of DNA sequences can be described by discrete state continuous time Markov processes on a phylogenetic tree. We consider neighbor-dependent evolutionary models where the instantaneous rate of substitution at a site depends on the states of the neighboring sites. Neighbor......-dependent substitution models are analytically intractable and must be analyzed using either approximate or simulation-based methods. We describe statistical inference of neighbor-dependent models using a Markov chain Monte Carlo expectation maximization (MCMC-EM) algorithm. In the MCMC-EM algorithm, the high...
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...
Revisiting Weak Simulation for Substochastic Markov Chains
DEFF Research Database (Denmark)
Jansen, David N.; Song, Lei; Zhang, Lijun
2013-01-01
of the logic PCTL\\x, and its completeness was conjectured. We revisit this result and show that soundness does not hold in general, but only for Markov chains without divergence. It is refuted for some systems with substochastic distributions. Moreover, we provide a counterexample to completeness...
Algebraic decay in self-similar Markov chains
International Nuclear Information System (INIS)
Hanson, J.D.; Cary, J.R.; Meiss, J.D.
1985-01-01
A continuous-time Markov chain is used to model motion in the neighborhood of a critical invariant circle for a Hamiltonian map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. For the case of a noble frequency, the chain is self-similar and the nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to the critical noble circle, the decay proceeds as t/sup -4.05/
Bailer-Jones, Coryn A. L.
2017-04-01
Preface; 1. Probability basics; 2. Estimation and uncertainty; 3. Statistical models and inference; 4. Linear models, least squares, and maximum likelihood; 5. Parameter estimation: single parameter; 6. Parameter estimation: multiple parameters; 7. Approximating distributions; 8. Monte Carlo methods for inference; 9. Parameter estimation: Markov chain Monte Carlo; 10. Frequentist hypothesis testing; 11. Model comparison; 12. Dealing with more complicated problems; References; Index.
Maximum Kolmogorov-Sinai Entropy Versus Minimum Mixing Time in Markov Chains
Mihelich, M.; Dubrulle, B.; Paillard, D.; Kral, Q.; Faranda, D.
2018-01-01
We establish a link between the maximization of Kolmogorov Sinai entropy (KSE) and the minimization of the mixing time for general Markov chains. Since the maximisation of KSE is analytical and easier to compute in general than mixing time, this link provides a new faster method to approximate the minimum mixing time dynamics. It could be interesting in computer sciences and statistical physics, for computations that use random walks on graphs that can be represented as Markov chains.
State space orderings for Gauss-Seidel in Markov chains revisited
Energy Technology Data Exchange (ETDEWEB)
Dayar, T. [Bilkent Univ., Ankara (Turkey)
1996-12-31
Symmetric state space orderings of a Markov chain may be used to reduce the magnitude of the subdominant eigenvalue of the (Gauss-Seidel) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the Gauss-Seidel splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semi-convergent. On the other hand, there are semi-convergent symmetric state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. An algorithm that orders the states of a Markov chain so as to increase the likelihood of satisfying Property-R is presented. The computational complexity of the ordering algorithm is less than that of a single Gauss-Seidel iteration (for sparse matrices). In doing all this, the aim is to gain an insight for faster converging orderings. Results from a variety of applications improve the confidence in the algorithm.
Asymptotic evolution of quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)
2012-07-01
The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.
Algebraic decay in self-similar Markov chains
International Nuclear Information System (INIS)
Hanson, J.D.; Cary, J.R.; Meiss, J.D.
1984-10-01
A continuous time Markov chain is used to model motion in the neighborhood of a critical noble invariant circle in an area-preserving map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. The nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to Hamiltonian systems the decay proceeds as t -4 05
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...
Analysis of aerial survey data on Florida manatee using Markov chain Monte Carlo.
Craig, B A; Newton, M A; Garrott, R A; Reynolds, J E; Wilcox, J R
1997-06-01
We assess population trends of the Atlantic coast population of Florida manatee, Trichechus manatus latirostris, by reanalyzing aerial survey data collected between 1982 and 1992. To do so, we develop an explicit biological model that accounts for the method by which the manatees are counted, the mammals' movement between surveys, and the behavior of the population total over time. Bayesian inference, enabled by Markov chain Monte Carlo, is used to combine the survey data with the biological model. We compute marginal posterior distributions for all model parameters and predictive distributions for future counts. Several conclusions, such as a decreasing population growth rate and low sighting probabilities, are consistent across different prior specifications.
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...
Sumner, Jeremy G; Taylor, Amelia; Holland, Barbara R; Jarvis, Peter D
2017-12-01
Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site patterns that, in expectation value, either vanish for particular evolutionary trees (in the case of phylogenetic invariants) or have well understood transformation properties (in the case of Markov invariants). While both approaches have been valued for their intrinsic mathematical interest, it is not clear how they relate to each other, and to what extent they can be used as practical tools for inference of phylogenetic trees. In this paper, by focusing on the special case of binary sequence data and quartets of taxa, we are able to view these two different polynomial-based approaches within a common framework. To motivate the discussion, we present three desirable statistical properties that we argue any invariant-based phylogenetic method should satisfy: (1) sensible behaviour under reordering of input sequences; (2) stability as the taxa evolve independently according to a Markov process; and (3) explicit dependence on the assumption of a continuous-time process. Motivated by these statistical properties, we develop and explore several new phylogenetic inference methods. In particular, we develop a statistically bias-corrected version of the Markov invariants approach which satisfies all three properties. We also extend previous work by showing that the phylogenetic invariants can be implemented in such a way as to satisfy property (3). A simulation study shows that, in comparison to other methods, our new proposed approach based on bias-corrected Markov invariants is extremely powerful for phylogenetic inference. The binary case is of particular theoretical interest as-in this case only-the Markov invariants can be expressed as linear combinations of the phylogenetic invariants. A wider implication of this is that, for
Directory of Open Access Journals (Sweden)
Shi Zhiyan
2009-01-01
Full Text Available We study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain and a nonhomogeneous Markov chain indexed by a tree. As corollary, we obtain the property of the harmonic mean of random transition probability for a nonhomogeneous Markov chain.
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.
Counting of oligomers in sequences generated by markov chains for DNA motif discovery.
Shan, Gao; Zheng, Wei-Mou
2009-02-01
By means of the technique of the imbedded Markov chain, an efficient algorithm is proposed to exactly calculate first, second moments of word counts and the probability for a word to occur at least once in random texts generated by a Markov chain. A generating function is introduced directly from the imbedded Markov chain to derive asymptotic approximations for the problem. Two Z-scores, one based on the number of sequences with hits and the other on the total number of word hits in a set of sequences, are examined for discovery of motifs on a set of promoter sequences extracted from A. thaliana genome. Source code is available at http://www.itp.ac.cn/zheng/oligo.c.
A sufficiency property arising from the characterization of extremes of Markov chains
Bortot, Paola; Coles, Stuart
2000-01-01
At extreme levels, it is known that for a particular choice of marginal distribution, transitions of a Markov chain behave like a random walk. For a broad class of Markov chains, we give a characterization for the step length density of the limiting random walk, which leads to an interesting sufficiency property. This representation also leads us to propose a new technique for kernel density estimation for this class of models.
A Bayesian method for inferring transmission chains in a partially observed epidemic.
Energy Technology Data Exchange (ETDEWEB)
Marzouk, Youssef M.; Ray, Jaideep
2008-10-01
We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historical data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.
Elements of automata theory and the theory of Markov chains. [Self-organizing control systems
Energy Technology Data Exchange (ETDEWEB)
Lind, M
1975-03-01
Selected topics from automata theory and the theory of Markov chains are treated. In particular, finite-memory automata are discussed in detail, and the results are used to formulate an automation model of a class of continuous systems. Stochastic automata are introduced as a natural generalization of the deterministic automaton. Markov chains are shown to be closely related to stochastic automata. Results from Markov chain theory are thereby directly applicable to analysis of stochastic automata. This report provides the theoretical foundation for the investigation in Riso Report No. 315 of a class of self-organizing control systems. (25 figures) (auth)
Some remarks about the thermodynamics of discrete finite Markov chains
Energy Technology Data Exchange (ETDEWEB)
Siboni, S. [Trento Univ. (Italy). Facolta` di Ingegneria, Dip. di Ingegneria dei Materiali
1998-08-01
The Author propose a simple way to define a Hamiltonian for aperiodic Markov chains and to apply these chains in a thermodynamical context. The basic thermodynamic functions are correspondingly calculated. A quite intriguing and nontrivial application to stochastic automata is also pointed out.
A simplified parsimonious higher order multivariate Markov chain model
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.
Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo
Cheong, R. Y.; Gabda, D.
2017-09-01
Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.
DEFF Research Database (Denmark)
Møller, Jesper
2010-01-01
Chapter 9: This contribution concerns statistical inference for parametric models used in stochastic geometry and based on quick and simple simulation free procedures as well as more comprehensive methods based on a maximum likelihood or Bayesian approach combined with markov chain Monte Carlo...... (MCMC) techniques. Due to space limitations the focus is on spatial point processes....
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
Geometric allocation approaches in Markov chain Monte Carlo
International Nuclear Information System (INIS)
Todo, S; Suwa, H
2013-01-01
The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the selection of candidate states, the optimization of transition kernel, algorithm for choosing a configuration according to the transition probabilities. We show that the unconventional approaches based on the geometric allocation of probabilities or weights can improve the dynamics and scaling of the Monte Carlo simulation in several aspects. Particularly, the approach using the irreversible kernel can reduce or sometimes completely eliminate the rejection of trial move in the Markov chain. We also discuss how the space-time interchange technique together with Walker's method of aliases can reduce the computational time especially for the case where the number of candidates is large, such as models with long-range interactions
A tridiagonal parsimonious higher order multivariate Markov chain model
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.
Large deviations for Markov chains in the positive quadrant
Energy Technology Data Exchange (ETDEWEB)
Borovkov, A A; Mogul' skii, A A [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2001-10-31
The paper deals with so-called N-partially space-homogeneous time-homogeneous Markov chains X(y,n), n=0,1,2,..., X(y,0)=y, in the positive quadrant. These Markov chains are characterized by the following property of the transition probabilities P(y,A)=P(X(y,1) element of A): for some N{>=}0 the measure P(y,dx) depends only on x{sub 2}, y{sub 2}, and x{sub 1}-y{sub 1} in the domain x{sub 1}>N, y{sub 1}>N, and only on x{sub 1}, y{sub 1}, and x{sub 2}-y{sub 2} in the domain x{sub 2}>N, y{sub 2}>N. For such chains the asymptotic behaviour is found for a fixed set B as s{yields}{infinity}, |x|{yields}{infinity}, and n{yields}{infinity}. Some other conditions on the growth of parameters are also considered, for example, |x-y|{yields}{infinity}, |y|{yields}{infinity}. A study is made of the structure of the most probable trajectories, which give the main contribution to this asymptotics, and a number of other results pertaining to the topic are established. Similar results are obtained for the narrower class of 0-partially homogeneous ergodic chains under less restrictive moment conditions on the transition probabilities P(y,dx). Moreover, exact asymptotic expressions for the probabilities P(X(0,n) element of x+B) are found for 0-partially homogeneous ergodic chains under some additional conditions. The interest in partially homogeneous Markov chains in positive octants is due to the mathematical aspects (new and interesting problems arise in the framework of general large deviation theory) as well as applied issues, for such chains prove to be quite accurate mathematical models for numerous basic types of queueing and communication networks such as the widely known Jackson networks, polling systems, or communication networks associated with the ALOHA algorithm. There is a vast literature dealing with the analysis of these objects. The present paper is an attempt to find the extent to which an asymptotic analysis is possible for Markov chains of this type in their general
Markov chain: a predictive model for manpower planning | Ezugwu ...
African Journals Online (AJOL)
In respect of organizational management, numerous previous studies have ... and to forecast the academic staff structure of the university in the next five years. ... Keywords: Markov Chain, Transition Probability Matrix, Manpower Planning, ...
The How and Why of Interactive Markov Chains
Hermanns, H.; Katoen, Joost P.; de Boer, F.S; Bonsangue, S.H.; Leuschel, M
2010-01-01
This paper reviews the model of interactive Markov chains (IMCs, for short), an extension of labelled transition systems with exponentially delayed transitions. We show that IMCs are closed under parallel composition and hiding, and show how IMCs can be compositionally aggregated prior to analysis
Robust Dynamics and Control of a Partially Observed Markov Chain
International Nuclear Information System (INIS)
Elliott, R. J.; Malcolm, W. P.; Moore, J. P.
2007-01-01
In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721-734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear).Clark's method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established
Use of Markov chains for forecasting labor requirements in black coal mines
Energy Technology Data Exchange (ETDEWEB)
Penar, L.; Przybyla, H.
1987-01-01
Increasing mining depth, deterioration of mining conditions and technology development are causes of changes in labor requirements. In mines with stable coal output these changes in most cases are of a qualitative character, in mines with an increasing or decreasing coal output they are of a quantitative character. Methods for forecasting personnel needs, in particular professional requirements, are discussed. Quantitative and qualitative changes are accurately described by heterogenous Markov chains. A structure consisting of interdependent variables is the subject of a forecast. Changes that occur within the structure of time units is the subject of investigations. For a homogenous Markov chain probabilities of a transition from the i-state to the j-state are determined (the probabilities being time independent). For a heterogenous Markov chain probabilities of a transition from the i-state to the j-state are non-conditioned. The method was developed for the ODRA 1325 computers. 8 refs.
Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains
Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes
2018-03-01
We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.
Masuyama, Hiroyuki
2015-01-01
This paper studies the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of discrete-time block-monotone Markov chains under subgeometric drift conditions. The main result of this paper is to present an upper bound for the total variation distance between the stationary probability vectors of a block-monotone Markov chain and its LC-block-augmented truncation. The main result is extended to Markov chains that themselves may not be block monoton...
Classification of customer lifetime value models using Markov chain
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.
Simulation of daily rainfall through markov chain modeling
International Nuclear Information System (INIS)
Sadiq, N.
2015-01-01
Being an agricultural country, the inhabitants of dry land in cultivated areas mainly rely on the daily rainfall for watering their fields. A stochastic model based on first order Markov Chain was developed to simulate daily rainfall data for Multan, D. I. Khan, Nawabshah, Chilas and Barkhan for the period 1981-2010. Transitional probability matrices of first order Markov Chain was utilized to generate the daily rainfall occurrence while gamma distribution was used to generate the daily rainfall amount. In order to achieve the parametric values of mentioned cities, method of moments is used to estimate the shape and scale parameters which lead to synthetic sequence generation as per gamma distribution. In this study, unconditional and conditional probabilities of wet and dry days in sum with means and standard deviations are considered as the essential parameters for the simulated stochastic generation of daily rainfalls. It has been found that the computerized synthetic rainfall series concurred pretty well with the actual observed rainfall series. (author)
Prediction degradation trend of nuclear equipment based on GM (1, 1)-Markov chain
International Nuclear Information System (INIS)
Zhang Liming; Zhao Xinwen; Cai Qi; Wu Guangjiang
2010-01-01
The degradation trend prediction results are important references for nuclear equipment in-service inspection and maintenance plan. But it is difficult to predict the nuclear equipment degradation trend accurately by the traditional statistical probability due to the small samples, lack of degradation data and the wavy degradation locus. Therefore, a method of equipment degradation trend prediction based on GM (1, l)-Markov chain was proposed in this paper. The method which makes use of the advantages of both GM (1, 1) method and Markov chain could improve the prediction precision of nuclear equipment degradation trend. The paper collected degradation data as samples and accurately predicted the degradation trend of canned motor pump. Compared with the prediction results by GM (1, 1) method, the prediction precision by GM (1, l)-Markov chain is more accurate. (authors)
Energy Technology Data Exchange (ETDEWEB)
Balan, I.
2005-05-01
This work presents the implementation of the Adjoint Sensitivity Analysis Procedure (ASAP) for the Continuous Time, Discrete Space Markov chains (CTMC), as an alternative to the other computational expensive methods. In order to develop this procedure as an end product in reliability studies, the reliability of the physical systems is analyzed using a coupled Fault-Tree - Markov chain technique, i.e. the abstraction of the physical system is performed using as the high level interface the Fault-Tree and afterwards this one is automatically converted into a Markov chain. The resulting differential equations based on the Markov chain model are solved in order to evaluate the system reliability. Further sensitivity analyses using ASAP applied to CTMC equations are performed to study the influence of uncertainties in input data to the reliability measures and to get the confidence in the final reliability results. The methods to generate the Markov chain and the ASAP for the Markov chain equations have been implemented into the new computer code system QUEFT/MARKOMAGS/MCADJSEN for reliability and sensitivity analysis of physical systems. The validation of this code system has been carried out by using simple problems for which analytical solutions can be obtained. Typical sensitivity results show that the numerical solution using ASAP is robust, stable and accurate. The method and the code system developed during this work can be used further as an efficient and flexible tool to evaluate the sensitivities of reliability measures for any physical system analyzed using the Markov chain. Reliability and sensitivity analyses using these methods have been performed during this work for the IFMIF Accelerator System Facilities. The reliability studies using Markov chain have been concentrated around the availability of the main subsystems of this complex physical system for a typical mission time. The sensitivity studies for two typical responses using ASAP have been
2nd International Workshop on the Numerical Solution of Markov Chains
1995-01-01
Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.
Handbook of Markov chain Monte Carlo
Brooks, Steve
2011-01-01
""Handbook of Markov Chain Monte Carlo"" brings together the major advances that have occurred in recent years while incorporating enough introductory material for new users of MCMC. Along with thorough coverage of the theoretical foundations and algorithmic and computational methodology, this comprehensive handbook includes substantial realistic case studies from a variety of disciplines. These case studies demonstrate the application of MCMC methods and serve as a series of templates for the construction, implementation, and choice of MCMC methodology.
Exploring Mass Perception with Markov Chain Monte Carlo
Cohen, Andrew L.; Ross, Michael G.
2009-01-01
Several previous studies have examined the ability to judge the relative mass of objects in idealized collisions. With a newly developed technique of psychological Markov chain Monte Carlo sampling (A. N. Sanborn & T. L. Griffiths, 2008), this work explores participants; perceptions of different collision mass ratios. The results reveal…
''adding'' algorithm for the Markov chain formalism for radiation transfer
International Nuclear Information System (INIS)
Esposito, L.W.
1979-01-01
The Markov chain radiative transfer method of Esposito and House has been shown to be both efficient and accurate for calculation of the diffuse reflection from a homogeneous scattering planetary atmosphere. The use of a new algorithm similar to the ''adding'' formula of Hansen and Travis extends the application of this formalism to an arbitrarily deep atmosphere. The basic idea for this algorithm is to consider a preceding calculation as a single state of a new Markov chain. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. The time required for the algorithm is comparable to that for a doubling calculation for a homogeneous atmosphere, but for a non-homogeneous atmosphere the new method is considerably faster than the standard ''adding'' routine. As with he standard ''adding'' method, the information on the internal radiation field is lost during the calculation. This method retains the advantage of the earlier Markov chain method that the time required is relatively insensitive to the number of illumination angles or observation angles for which the diffuse reflection is calculated. A technical write-up giving fuller details of the algorithm and a sample code are available from the author
Mixed Vehicle Flow At Signalized Intersection: Markov Chain Analysis
Directory of Open Access Journals (Sweden)
Gertsbakh Ilya B.
2015-09-01
Full Text Available We assume that a Poisson flow of vehicles arrives at isolated signalized intersection, and each vehicle, independently of others, represents a random number X of passenger car units (PCU’s. We analyze numerically the stationary distribution of the queue process {Zn}, where Zn is the number of PCU’s in a queue at the beginning of the n-th red phase, n → ∞. We approximate the number Yn of PCU’s arriving during one red-green cycle by a two-parameter Negative Binomial Distribution (NBD. The well-known fact is that {Zn} follow an infinite-state Markov chain. We approximate its stationary distribution using a finite-state Markov chain. We show numerically that there is a strong dependence of the mean queue length E[Zn] in equilibrium on the input distribution of Yn and, in particular, on the ”over dispersion” parameter γ= Var[Yn]/E[Yn]. For Poisson input, γ = 1. γ > 1 indicates presence of heavy-tailed input. In reality it means that a relatively large ”portion” of PCU’s, considerably exceeding the average, may arrive with high probability during one red-green cycle. Empirical formulas are presented for an accurate estimation of mean queue length as a function of load and g of the input flow. Using the Markov chain technique, we analyze the mean ”virtual” delay time for a car which always arrives at the beginning of the red phase.
Variable context Markov chains for HIV protease cleavage site prediction.
Oğul, Hasan
2009-06-01
Deciphering the knowledge of HIV protease specificity and developing computational tools for detecting its cleavage sites in protein polypeptide chain are very desirable for designing efficient and specific chemical inhibitors to prevent acquired immunodeficiency syndrome. In this study, we developed a generative model based on a generalization of variable order Markov chains (VOMC) for peptide sequences and adapted the model for prediction of their cleavability by certain proteases. The new method, called variable context Markov chains (VCMC), attempts to identify the context equivalence based on the evolutionary similarities between individual amino acids. It was applied for HIV-1 protease cleavage site prediction problem and shown to outperform existing methods in terms of prediction accuracy on a common dataset. In general, the method is a promising tool for prediction of cleavage sites of all proteases and encouraged to be used for any kind of peptide classification problem as well.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
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 ...
Approximating Markov Chains: What and why
International Nuclear Information System (INIS)
Pincus, S.
1996-01-01
Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to open-quote open-quote solve,close-quote close-quote or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the attractor, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. copyright 1996 American Institute of Physics
Markov chain analysis of single spin flip Ising simulations
International Nuclear Information System (INIS)
Hennecke, M.
1997-01-01
The Markov processes defined by random and loop-based schemes for single spin flip attempts in Monte Carlo simulations of the 2D Ising model are investigated, by explicitly constructing their transition matrices. Their analysis reveals that loops over all lattice sites using a Metropolis-type single spin flip probability often do not define ergodic Markov chains, and have distorted dynamical properties even if they are ergodic. The transition matrices also enable a comparison of the dynamics of random versus loop spin selection and Glauber versus Metropolis probabilities
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.
Caching and interpolated likelihoods: accelerating cosmological Monte Carlo Markov chains
Energy Technology Data Exchange (ETDEWEB)
Bouland, Adam; Easther, Richard; Rosenfeld, Katherine, E-mail: adam.bouland@aya.yale.edu, E-mail: richard.easther@yale.edu, E-mail: krosenfeld@cfa.harvard.edu [Department of Physics, Yale University, New Haven CT 06520 (United States)
2011-05-01
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free parameters and computationally expensive to evaluate. We generate a high-order interpolating polynomial for the log-likelihood using the first points gathered by the Markov chains as a training set. This polynomial then accurately computes the majority of the likelihoods needed in the latter parts of the chains. We implement a simple version of this algorithm as a patch (InterpMC) to CosmoMC and show that it accelerates parameter estimatation by a factor of between two and four for well-converged chains. The current code is primarily intended as a ''proof of concept'', and we argue that there is considerable room for further performance gains. Unlike other approaches to accelerating parameter fits, we make no use of precomputed training sets or special choices of variables, and InterpMC is almost entirely transparent to the user.
Caching and interpolated likelihoods: accelerating cosmological Monte Carlo Markov chains
International Nuclear Information System (INIS)
Bouland, Adam; Easther, Richard; Rosenfeld, Katherine
2011-01-01
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free parameters and computationally expensive to evaluate. We generate a high-order interpolating polynomial for the log-likelihood using the first points gathered by the Markov chains as a training set. This polynomial then accurately computes the majority of the likelihoods needed in the latter parts of the chains. We implement a simple version of this algorithm as a patch (InterpMC) to CosmoMC and show that it accelerates parameter estimatation by a factor of between two and four for well-converged chains. The current code is primarily intended as a ''proof of concept'', and we argue that there is considerable room for further performance gains. Unlike other approaches to accelerating parameter fits, we make no use of precomputed training sets or special choices of variables, and InterpMC is almost entirely transparent to the user
Tokunaga and Horton self-similarity for level set trees of Markov chains
International Nuclear Information System (INIS)
Zaliapin, Ilia; Kovchegov, Yevgeniy
2012-01-01
Highlights: ► Self-similar properties of the level set trees for Markov chains are studied. ► Tokunaga and Horton self-similarity are established for symmetric Markov chains and regular Brownian motion. ► Strong, distributional self-similarity is established for symmetric Markov chains with exponential jumps. ► It is conjectured that fractional Brownian motions are Tokunaga self-similar. - Abstract: The Horton and Tokunaga branching laws provide a convenient framework for studying self-similarity in random trees. The Horton self-similarity is a weaker property that addresses the principal branching in a tree; it is a counterpart of the power-law size distribution for elements of a branching system. The stronger Tokunaga self-similarity addresses so-called side branching. The Horton and Tokunaga self-similarity have been empirically established in numerous observed and modeled systems, and proven for two paradigmatic models: the critical Galton–Watson branching process with finite progeny and the finite-tree representation of a regular Brownian excursion. This study establishes the Tokunaga and Horton self-similarity for a tree representation of a finite symmetric homogeneous Markov chain. We also extend the concept of Horton and Tokunaga self-similarity to infinite trees and establish self-similarity for an infinite-tree representation of a regular Brownian motion. We conjecture that fractional Brownian motions are also Tokunaga and Horton self-similar, with self-similarity parameters depending on the Hurst exponent.
Summary statistics for end-point conditioned continuous-time Markov chains
DEFF Research Database (Denmark)
Hobolth, Asger; Jensen, Jens Ledet
Continuous-time Markov chains are a widely used modelling tool. Applications include DNA sequence evolution, ion channel gating behavior and mathematical finance. We consider the problem of calculating properties of summary statistics (e.g. mean time spent in a state, mean number of jumps between...... two states and the distribution of the total number of jumps) for discretely observed continuous time Markov chains. Three alternative methods for calculating properties of summary statistics are described and the pros and cons of the methods are discussed. The methods are based on (i) an eigenvalue...... decomposition of the rate matrix, (ii) the uniformization method, and (iii) integrals of matrix exponentials. In particular we develop a framework that allows for analyses of rather general summary statistics using the uniformization method....
A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains
DEFF Research Database (Denmark)
Bacci, Giovanni; Bacci, Giorgio; Larsen, Kim Guldstrand
2017-01-01
In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS...... an axiom for dealing with the Kantorovich distance between probability distributions. The axiomatization is then used to propose a metric extension of a Kleene's style representation theorem for finite labelled Markov chains, that was proposed (in a more general coalgebraic fashion) by Silva et al. (Inf...
Directory of Open Access Journals (Sweden)
Bao Wang
2014-01-01
Full Text Available We study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by an infinite tree with uniformly bounded degree, which extends the corresponding results of countable Markov chains indexed by a Cayley tree and generalizes the relative results of finite Markov chains indexed by a uniformly bounded tree.
Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains
Directory of Open Access Journals (Sweden)
Francesca Biagini
2016-07-01
Full Text Available We study risk-minimization for a large class of insurance contracts. Given that the individual progress in time of visiting an insurance policy’s states follows an F -doubly stochastic Markov chain, we describe different state-dependent types of insurance benefits. These cover single payments at maturity, annuity-type payments and payments at the time of a transition. Based on the intensity of the F -doubly stochastic Markov chain, we provide the Galtchouk-Kunita-Watanabe decomposition for a general insurance contract and specify risk-minimizing strategies in a Brownian financial market setting. The results are further illustrated explicitly within an affine structure for the intensity.
Adjoint sensitivity analysis of dynamic reliability models based on Markov chains - I: Theory
International Nuclear Information System (INIS)
Cacuci, D. G.; Cacuci, D. G.; Ionescu-Bujor, M.
2008-01-01
The development of the adjoint sensitivity analysis procedure (ASAP) for generic dynamic reliability models based on Markov chains is presented, together with applications of this procedure to the analysis of several systems of increasing complexity. The general theory is presented in Part I of this work and is accompanied by a paradigm application to the dynamic reliability analysis of a simple binary component, namely a pump functioning on an 'up/down' cycle until it fails irreparably. This paradigm example admits a closed form analytical solution, which permits a clear illustration of the main characteristics of the ASAP for Markov chains. In particular, it is shown that the ASAP for Markov chains presents outstanding computational advantages over other procedures currently in use for sensitivity and uncertainty analysis of the dynamic reliability of large-scale systems. This conclusion is further underscored by the large-scale applications presented in Part II. (authors)
Adjoint sensitivity analysis of dynamic reliability models based on Markov chains - I: Theory
Energy Technology Data Exchange (ETDEWEB)
Cacuci, D. G. [Commiss Energy Atom, Direct Energy Nucl, Saclay, (France); Cacuci, D. G. [Univ Karlsruhe, Inst Nucl Technol and Reactor Safety, D-76021 Karlsruhe, (Germany); Ionescu-Bujor, M. [Forschungszentrum Karlsruhe, Fus Program, D-76021 Karlsruhe, (Germany)
2008-07-01
The development of the adjoint sensitivity analysis procedure (ASAP) for generic dynamic reliability models based on Markov chains is presented, together with applications of this procedure to the analysis of several systems of increasing complexity. The general theory is presented in Part I of this work and is accompanied by a paradigm application to the dynamic reliability analysis of a simple binary component, namely a pump functioning on an 'up/down' cycle until it fails irreparably. This paradigm example admits a closed form analytical solution, which permits a clear illustration of the main characteristics of the ASAP for Markov chains. In particular, it is shown that the ASAP for Markov chains presents outstanding computational advantages over other procedures currently in use for sensitivity and uncertainty analysis of the dynamic reliability of large-scale systems. This conclusion is further underscored by the large-scale applications presented in Part II. (authors)
Doss, Hani; Tan, Aixin
2014-09-01
In the classical biased sampling problem, we have k densities π 1 (·), …, π k (·), each known up to a normalizing constant, i.e. for l = 1, …, k , π l (·) = ν l (·)/ m l , where ν l (·) is a known function and m l is an unknown constant. For each l , we have an iid sample from π l , · and the problem is to estimate the ratios m l /m s for all l and all s . This problem arises frequently in several situations in both frequentist and Bayesian inference. An estimate of the ratios was developed and studied by Vardi and his co-workers over two decades ago, and there has been much subsequent work on this problem from many different perspectives. In spite of this, there are no rigorous results in the literature on how to estimate the standard error of the estimate. We present a class of estimates of the ratios of normalizing constants that are appropriate for the case where the samples from the π l 's are not necessarily iid sequences, but are Markov chains. We also develop an approach based on regenerative simulation for obtaining standard errors for the estimates of ratios of normalizing constants. These standard error estimates are valid for both the iid case and the Markov chain case.
A Parallel Solver for Large-Scale Markov Chains
Czech Academy of Sciences Publication Activity Database
Benzi, M.; Tůma, Miroslav
2002-01-01
Roč. 41, - (2002), s. 135-153 ISSN 0168-9274 R&D Projects: GA AV ČR IAA2030801; GA ČR GA101/00/1035 Keywords : parallel preconditioning * iterative methods * discrete Markov chains * generalized inverses * singular matrices * graph partitioning * AINV * Bi-CGSTAB Subject RIV: BA - General Mathematics Impact factor: 0.504, year: 2002
SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.
Thiede, Erik; VAN Koten, Brian; Weare, Jonathan
For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations.
Jamaluddin, Fadhilah; Rahim, Rahela Abdul
2015-12-01
Markov Chain has been introduced since the 1913 for the purpose of studying the flow of data for a consecutive number of years of the data and also forecasting. The important feature in Markov Chain is obtaining the accurate Transition Probability Matrix (TPM). However to obtain the suitable TPM is hard especially in involving long-term modeling due to unavailability of data. This paper aims to enhance the classical Markov Chain by introducing Exponential Smoothing technique in developing the appropriate TPM.
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)
Directory of Open Access Journals (Sweden)
Ning-bo Zhao
2014-01-01
Full Text Available Performance degradation forecast technology for quantitatively assessing degradation states of aeroengine using exhaust gas temperature is an important technology in the aeroengine health management. In this paper, a GM (1, 1 Markov chain-based approach is introduced to forecast exhaust gas temperature by taking the advantages of GM (1, 1 model in time series and the advantages of Markov chain model in dealing with highly nonlinear and stochastic data caused by uncertain factors. In this approach, firstly, the GM (1, 1 model is used to forecast the trend by using limited data samples. Then, Markov chain model is integrated into GM (1, 1 model in order to enhance the forecast performance, which can solve the influence of random fluctuation data on forecasting accuracy and achieving an accurate estimate of the nonlinear forecast. As an example, the historical monitoring data of exhaust gas temperature from CFM56 aeroengine of China Southern is used to verify the forecast performance of the GM (1, 1 Markov chain model. The results show that the GM (1, 1 Markov chain model is able to forecast exhaust gas temperature accurately, which can effectively reflect the random fluctuation characteristics of exhaust gas temperature changes over time.
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...
Markov chains with quasitoeplitz transition matrix: first zero hitting
Directory of Open Access Journals (Sweden)
Alexander M. Dukhovny
1989-01-01
Full Text Available This paper continues the investigation of Markov Chains with a quasitoeplitz transition matrix. Generating functions of first zero hitting probabilities and mean times are found by the solution of special Riemann boundary value problems on the unit circle. Duality is discussed.
On the Total Variation Distance of Semi-Markov Chains
DEFF Research Database (Denmark)
Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand
2015-01-01
Semi-Markov chains (SMCs) are continuous-time probabilistic transition systems where the residence time on states is governed by generic distributions on the positive real line. This paper shows the tight relation between the total variation distance on SMCs and their model checking problem over...
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 ...
RESEARCH ABSORBING STATES OF THE SYSTEM USING MARKOV CHAINS AND FUNDAMENTAL MATRIX
Directory of Open Access Journals (Sweden)
Тетяна Мефодіївна ОЛЕХ
2016-02-01
Full Text Available The article discusses the use Markov chains to research models that reflect the essential properties of systems, including methods of measuring the parameters of projects and assess their effectiveness. In the study carried out by its decomposition system for certain discrete state and create a diagram of transitions between these states. Specificity displays various objects Markov homogeneous chains with discrete states and discrete time determined by the method of calculation of transition probabilities. A model of success criteria for absorbing state system that is universal for all projects. A breakdown of passages to the matrix submatrices. The variation elements under matrix Q n with growth linked to the definition of important quantitative characteristics of absorbing circuits: 1 the probability of achieving the status of absorbing any given; 2 the mean number of steps needed to achieve the absorbing state; 3 the mean time that the system spends in each state to hit irreversible system in absorbing state. Built fundamental matrix that allowed calculating the different characteristics of the system. Considered fundamental matrix for supposedly modeled absorbing Markov chain, which gives the forecast for the behavior of the system in the future regardless of the absolute value of the time elapsed from the starting point. This property illustrates the fundamental matrix Markov process that characterizes it as a process without aftereffect.
Quasi-stationary distributions for reducible absorbing Markov chains in discrete time
van Doorn, Erik A.; Pollett, P.K.
2009-01-01
We consider discrete-time Markov chains with one coffin state and a finite set $S$ of transient states, and are interested in the limiting behaviour of such a chain as time $n \\to \\infty,$ conditional on survival up to $n$. It is known that, when $S$ is irreducible, the limiting conditional
Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique
International Nuclear Information System (INIS)
Destainville, N
2003-01-01
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium
Complete Axiomatization for the Bisimilarity Distance on Markov Chains
DEFF Research Database (Denmark)
Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand
2016-01-01
In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS...
Second Order Optimality in Markov Decision Chains
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2017-01-01
Roč. 53, č. 6 (2017), s. 1086-1099 ISSN 0023-5954 R&D Projects: GA ČR GA15-10331S Institutional support: RVO:67985556 Keywords : Markov decision chains * second order optimality * optimalilty conditions for transient, discounted and average models * policy and value iterations Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 0.379, year: 2016 http://library.utia.cas.cz/separaty/2017/E/sladky-0485146.pdf
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
DNA motif alignment by evolving a population of Markov chains.
Bi, Chengpeng
2009-01-30
Deciphering cis-regulatory elements or de novo motif-finding in genomes still remains elusive although much algorithmic effort has been expended. The Markov chain Monte Carlo (MCMC) method such as Gibbs motif samplers has been widely employed to solve the de novo motif-finding problem through sequence local alignment. Nonetheless, the MCMC-based motif samplers still suffer from local maxima like EM. Therefore, as a prerequisite for finding good local alignments, these motif algorithms are often independently run a multitude of times, but without information exchange between different chains. Hence it would be worth a new algorithm design enabling such information exchange. This paper presents a novel motif-finding algorithm by evolving a population of Markov chains with information exchange (PMC), each of which is initialized as a random alignment and run by the Metropolis-Hastings sampler (MHS). It is progressively updated through a series of local alignments stochastically sampled. Explicitly, the PMC motif algorithm performs stochastic sampling as specified by a population-based proposal distribution rather than individual ones, and adaptively evolves the population as a whole towards a global maximum. The alignment information exchange is accomplished by taking advantage of the pooled motif site distributions. A distinct method for running multiple independent Markov chains (IMC) without information exchange, or dubbed as the IMC motif algorithm, is also devised to compare with its PMC counterpart. Experimental studies demonstrate that the performance could be improved if pooled information were used to run a population of motif samplers. The new PMC algorithm was able to improve the convergence and outperformed other popular algorithms tested using simulated and biological motif sequences.
On the Metric-based Approximate Minimization of Markov Chains
DEFF Research Database (Denmark)
Bacci, Giovanni; Bacci, Giorgio; Larsen, Kim Guldstrand
2018-01-01
In this paper we address the approximate minimization problem of Markov Chains (MCs) from a behavioral metric-based perspective. Specifically, given a finite MC and a positive integer k, we are looking for an MC with at most k states having minimal distance to the original. The metric considered...
When are two Markov chains the same? | Cowen | Quaestiones ...
African Journals Online (AJOL)
Given two one-sided Markov chains, the authors illustrate a procedure for ascertaining whether they are essentially the same. Precisely, they show how one can determine whether they are block-isomorphic. An application to hydrology is investigated with an example. Quaestiones Mathematicae 23(2000), 507–513 ...
Finding metastabilities in reversible Markov chains based on incomplete sampling
Directory of Open Access Journals (Sweden)
Fackeldey Konstantin
2017-01-01
Full Text Available In order to fully characterize the state-transition behaviour of finite Markov chains one needs to provide the corresponding transition matrix P. In many applications such as molecular simulation and drug design, the entries of the transition matrix P are estimated by generating realizations of the Markov chain and determining the one-step conditional probability Pij for a transition from one state i to state j. This sampling can be computational very demanding. Therefore, it is a good idea to reduce the sampling effort. The main purpose of this paper is to design a sampling strategy, which provides a partial sampling of only a subset of the rows of such a matrix P. Our proposed approach fits very well to stochastic processes stemming from simulation of molecular systems or random walks on graphs and it is different from the matrix completion approaches which try to approximate the transition matrix by using a low-rank-assumption. It will be shown how Markov chains can be analyzed on the basis of a partial sampling. More precisely. First, we will estimate the stationary distribution from a partially given matrix P. Second, we will estimate the infinitesimal generator Q of P on the basis of this stationary distribution. Third, from the generator we will compute the leading invariant subspace, which should be identical to the leading invariant subspace of P. Forth, we will apply Robust Perron Cluster Analysis (PCCA+ in order to identify metastabilities using this subspace.
Density Control of Multi-Agent Systems with Safety Constraints: A Markov Chain Approach
Demirer, Nazli
The control of systems with autonomous mobile agents has been a point of interest recently, with many applications like surveillance, coverage, searching over an area with probabilistic target locations or exploring an area. In all of these applications, the main goal of the swarm is to distribute itself over an operational space to achieve mission objectives specified by the density of swarm. This research focuses on the problem of controlling the distribution of multi-agent systems considering a hierarchical control structure where the whole swarm coordination is achieved at the high-level and individual vehicle/agent control is managed at the low-level. High-level coordination algorithms uses macroscopic models that describes the collective behavior of the whole swarm and specify the agent motion commands, whose execution will lead to the desired swarm behavior. The low-level control laws execute the motion to follow these commands at the agent level. The main objective of this research is to develop high-level decision control policies and algorithms to achieve physically realizable commanding of the agents by imposing mission constraints on the distribution. We also make some connections with decentralized low-level motion control. This dissertation proposes a Markov chain based method to control the density distribution of the whole system where the implementation can be achieved in a decentralized manner with no communication between agents since establishing communication with large number of agents is highly challenging. The ultimate goal is to guide the overall density distribution of the system to a prescribed steady-state desired distribution while satisfying desired transition and safety constraints. Here, the desired distribution is determined based on the mission requirements, for example in the application of area search, the desired distribution should match closely with the probabilistic target locations. The proposed method is applicable for both
On the Metric-Based Approximate Minimization of Markov Chains
DEFF Research Database (Denmark)
Bacci, Giovanni; Bacci, Giorgio; Larsen, Kim Guldstrand
2017-01-01
We address the behavioral metric-based approximate minimization problem of Markov Chains (MCs), i.e., given a finite MC and a positive integer k, we are interested in finding a k-state MC of minimal distance to the original. By considering as metric the bisimilarity distance of Desharnais at al...
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, P.; van Doorn, E.A.
2001-01-01
The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, Pauline; van Doorn, Erik A.
2002-01-01
he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique
Energy Technology Data Exchange (ETDEWEB)
Destainville, N [Laboratoire de Physique Theorique - IRSAMC, CNRS/Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 04 (France)
2003-04-04
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium.
Rottman, Benjamin M; Hastie, Reid
2016-06-01
Making judgments by relying on beliefs about the causal relationships between events is a fundamental capacity of everyday cognition. In the last decade, Causal Bayesian Networks have been proposed as a framework for modeling causal reasoning. Two experiments were conducted to provide comprehensive data sets with which to evaluate a variety of different types of judgments in comparison to the standard Bayesian networks calculations. Participants were introduced to a fictional system of three events and observed a set of learning trials that instantiated the multivariate distribution relating the three variables. We tested inferences on chains X1→Y→X2, common cause structures X1←Y→X2, and common effect structures X1→Y←X2, on binary and numerical variables, and with high and intermediate causal strengths. We tested transitive inferences, inferences when one variable is irrelevant because it is blocked by an intervening variable (Markov Assumption), inferences from two variables to a middle variable, and inferences about the presence of one cause when the alternative cause was known to have occurred (the normative "explaining away" pattern). Compared to the normative account, in general, when the judgments should change, they change in the normative direction. However, we also discuss a few persistent violations of the standard normative model. In addition, we evaluate the relative success of 12 theoretical explanations for these deviations. Copyright © 2016 Elsevier Inc. All rights reserved.
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.
SDI and Markov Chains for Regional Drought Characteristics
Directory of Open Access Journals (Sweden)
Chen-Feng Yeh
2015-08-01
Full Text Available In recent years, global climate change has altered precipitation patterns, causing uneven spatial and temporal distribution of precipitation that gradually induces precipitation polarization phenomena. Taiwan is located in the subtropical climate zone, with distinct wet and dry seasons, which makes the polarization phenomenon more obvious; this has also led to a large difference between river flows during the wet and dry seasons, which is significantly influenced by precipitation, resulting in hydrological drought. Therefore, to effectively address the growing issue of water shortages, it is necessary to explore and assess the drought characteristics of river systems. In this study, the drought characteristics of northern Taiwan were studied using the streamflow drought index (SDI and Markov chains. Analysis results showed that the year 2002 was a turning point for drought severity in both the Lanyang River and Yilan River basins; the severity of rain events in the Lanyang River basin increased after 2002, and the severity of drought events in the Yilan River basin exhibited a gradual upward trend. In the study of drought severity, analysis results from periods of three months (November to January and six months (November to April have shown significant drought characteristics. In addition, analysis of drought occurrence probabilities using the method of Markov chains has shown that the occurrence probabilities of drought events are higher in the Lanyang River basin than in the Yilan River basin; particularly for extreme events, the occurrence probability of an extreme drought event is 20.6% during the dry season (November to April in the Lanyang River basin, and 3.4% in the Yilan River basin. This study shows that for analysis of drought/wet occurrence probabilities, the results obtained for the drought frequency and occurrence probability using short-term data with the method of Markov chains can be used to predict the long-term occurrence
Directory of Open Access Journals (Sweden)
Mokaedi V. Lekgari
2014-01-01
Full Text Available We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs. We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.
Bayesian inference for Markov jump processes with informative observations.
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.
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.
Application of Markov chains-entropy to analysis of depositional environments
Energy Technology Data Exchange (ETDEWEB)
Men Guizhen; Shi Xiaohong; Zhao Shuzhi
1989-01-01
The paper systematically and comprehensively discussed application of Markov chains-entropy to analysis of depositional environments of the upper Carboniferous series Taiyuan Formation in Anjialing, Pingshuo open-cast mine, Shanxi. Definite geological meanings were given respectively to calculated values of transition probability matrix, extremity probability matrix, substitution matrix and the entropy. The lithologic successions of coarse-fine-coarse grained layers from bottom upwards in the coal-bearing series made up the general symmetric cyclic patterns. It was suggested that the coal-bearing strata deposited in the coal-forming environment in delta plain-littoral swamps. Quantitative study of cyclic visibility and variation of formation was conducted. The assemblage relation among stratigraphic sequences and the significance of predicting vertical change were emphasized. Results of study showed that overall analysis of Markov chains was an effective method for analysis of depositional environments of coal-bearing strata. 2 refs., 5 figs.
Lithofacies cyclicity determination in the guaduas formation (Colombia using Markov chains
Directory of Open Access Journals (Sweden)
Jorge Eliecer Mariño Martinez
2016-07-01
Full Text Available Statistical embedded Markov Chain processes were used to analyze facies transitions and to determine the stacking pattern of the lithofacies of the Guaduas Formation. Twelve Lithofacies were found and characterized based on lithology and sedimentary structures in four stratigraphic sections. The findings were compared with a previous assemblage of lithofacies, interpretations of sedimentary environments, and depositional systems. As a result, four depositional Systems were established. Through the statistical analyses of facies transitions it was found that tidal facies are prevalent in the Socota section, especially in the upper part, whereas in the Sogamoso, Umbita and Peñas de Sutatausa sections, fluvial facies are prevalent in the upper part of the sections, and follow a regressive sequence with more continental deposits around the upper part of the sections. For each of these sections the Markov Chain transition matrices illustrates a strong interaction between tidal facies and fluvial facies, specially in the Peñas de Sutatausa matrix, where facies 6, made up of tidal deposits, appears several times. From the facies model and Markov Chain analyses, it is evident that the Guaduas Formation is a cyclic sequence in which the Markov facies repetitions are consistent with the lithofacies analyses conducted in previous stratigraphic studies. The results reveal that the Markov Chain statistical process can be used to predict stratigraphy in order to correlate contiguous geologically unexplored areas in the Guaduas Formation, where much work relating to correlation and the continuity of coal beds has yet to be done. Determinacion de la ciclicidad de las facies en la formacion Guaduas (Colombia usando las cadenas de Markov Resumen Se utilizaron los procesos estadísticos de las cadenas de Markov para analizar las transiciones de facies y para determinar el patrón de apilamiento de las litofacies de la formación Guaduas. Se encontraron y
Study on the Evolution of Weights on the Market of Competitive Products using Markov Chains
Directory of Open Access Journals (Sweden)
Daniel Mihai Amariei
2016-10-01
Full Text Available In this paper aims the application through the Markov Process mode, within the software product WinQSB, Markov chain in the establishment of the development on the market of five brands of athletic shoes.
A Cost-Effective Smoothed Multigrid with Modified Neighborhood-Based Aggregation for Markov Chains
Directory of Open Access Journals (Sweden)
Zhao-Li Shen
2015-01-01
Full Text Available Smoothed aggregation multigrid method is considered for computing stationary distributions of Markov chains. A judgement which determines whether to implement the whole aggregation procedure is proposed. Through this strategy, a large amount of time in the aggregation procedure is saved without affecting the convergence behavior. Besides this, we explain the shortage and irrationality of the Neighborhood-Based aggregation which is commonly used in multigrid methods. Then a modified version is presented to remedy and improve it. Numerical experiments on some typical Markov chain problems are reported to illustrate the performance of these methods.
International Nuclear Information System (INIS)
Hemi, Hanane; Ghouili, Jamel; Cheriti, Ahmed
2015-01-01
Highlights: • A combination of Markov chain and an optimal control solved by Pontryagin’s Minimum Principle is presented. • This strategy is applied to hybrid electric vehicle dynamic model. • The hydrogen consumption is analyzed for two different vehicle mass and drive cycle. • The supercapacitor and fuel cell behavior is analyzed at high or sudden required power. - Abstract: In this article, a real time optimal control strategy based on Pontryagin’s Minimum Principle (PMP) combined with the Markov chain approach is used for a fuel cell/supercapacitor electrical vehicle. In real time, at high power and at high speed, two phenomena are observed. The first is obtained at higher required power, and the second is observed at sudden power demand. To avoid these situations, the Markov chain model is proposed to predict the future power demand during a driving cycle. The optimal control problem is formulated as an equivalent consumption minimization strategy (ECMS), that has to be solved by using the Pontryagin’s Minimum Principle. A Markov chain model is added as a separate block for a prediction of required power. This approach and the whole system are modeled and implemented using the MATLAB/Simulink. The model without Markov chain block and the model is with it are compared. The results presented demonstrate the importance of a Markov chain block added to a model
Markov chain Monte Carlo with the Integrated Nested Laplace Approximation
Gómez-Rubio, Virgilio
2017-10-06
The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with
Markov chain Monte Carlo with the Integrated Nested Laplace Approximation
Gó mez-Rubio, Virgilio; Rue, Haavard
2017-01-01
The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with
Network Security Risk Assessment System Based on Attack Graph and Markov Chain
Sun, Fuxiong; Pi, Juntao; Lv, Jin; Cao, Tian
2017-10-01
Network security risk assessment technology can be found in advance of the network problems and related vulnerabilities, it has become an important means to solve the problem of network security. Based on attack graph and Markov chain, this paper provides a Network Security Risk Assessment Model (NSRAM). Based on the network infiltration tests, NSRAM generates the attack graph by the breadth traversal algorithm. Combines with the international standard CVSS, the attack probability of atomic nodes are counted, and then the attack transition probabilities of ones are calculated by Markov chain. NSRAM selects the optimal attack path after comprehensive measurement to assessment network security risk. The simulation results show that NSRAM can reflect the actual situation of network security objectively.
Students' Progress throughout Examination Process as a Markov Chain
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…
Markov chain Monte Carlo methods in radiotherapy treatment planning
International Nuclear Information System (INIS)
Hugtenburg, R.P.
2001-01-01
The Markov chain method can be used to incorporate measured data in Monte Carlo based radiotherapy treatment planning. This paper shows that convergence to the measured data, within the target precision, is achievable. Relative output factors for blocked fields and oblique beams are shown to compare well with independent measurements according to the same criterion. (orig.)
CSL Model Checking Algorithms for Infinite-state Structured Markov chains
Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Raskin, J.-F.; Thiagarajan, P.S.
2007-01-01
Jackson queueing networks (JQNs) are a very general class of queueing networks that find their application in a variety of settings. The state space of the continuous-time Markov chain (CTMC) that underlies such a JQN, is highly structured, however, of infinite size in as many dimensions as there
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...
Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion
DEFF Research Database (Denmark)
Zunino, Andrea; Lange, Katrine; Melnikova, Yulia
2014-01-01
We present a study on the inversion of seismic reflection data generated from a synthetic reservoir model. Our aim is to invert directly for rock facies and porosity of the target reservoir zone. We solve this inverse problem using a Markov chain Monte Carlo (McMC) method to handle the nonlinear...
Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media
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
Jia, Chen
2017-09-01
Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.
Molitor, John
2012-03-01
Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.
Utilizing Gaze Behavior for Inferring Task Transitions Using Abstract Hidden Markov Models
Directory of Open Access Journals (Sweden)
Daniel Fernando Tello Gamarra
2016-12-01
Full Text Available We demonstrate an improved method for utilizing observed gaze behavior and show that it is useful in inferring hand movement intent during goal directed tasks. The task dynamics and the relationship between hand and gaze behavior are learned using an Abstract Hidden Markov Model (AHMM. We show that the predicted hand movement transitions occur consistently earlier in AHMM models with gaze than those models that do not include gaze observations.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Directory of Open Access Journals (Sweden)
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.
Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng
2010-01-01
This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology. PMID:23554632
Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng
2010-05-01
This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology.
User's Manual MCnest - Markov Chain Nest Productivity Model Version 2.0
The Markov chain nest productivity model, or MCnest, is a set of algorithms for integrating the results of avian toxicity tests with reproductive life-history data to project the relative magnitude of chemical effects on avian reproduction. The mathematical foundation of MCnest i...
Generating intrinsically disordered protein conformational ensembles from a Markov chain
Cukier, Robert I.
2018-03-01
Intrinsically disordered proteins (IDPs) sample a diverse conformational space. They are important to signaling and regulatory pathways in cells. An entropy penalty must be payed when an IDP becomes ordered upon interaction with another protein or a ligand. Thus, the degree of conformational disorder of an IDP is of interest. We create a dichotomic Markov model that can explore entropic features of an IDP. The Markov condition introduces local (neighbor residues in a protein sequence) rotamer dependences that arise from van der Waals and other chemical constraints. A protein sequence of length N is characterized by its (information) entropy and mutual information, MIMC, the latter providing a measure of the dependence among the random variables describing the rotamer probabilities of the residues that comprise the sequence. For a Markov chain, the MIMC is proportional to the pair mutual information MI which depends on the singlet and pair probabilities of neighbor residue rotamer sampling. All 2N sequence states are generated, along with their probabilities, and contrasted with the probabilities under the assumption of independent residues. An efficient method to generate realizations of the chain is also provided. The chain entropy, MIMC, and state probabilities provide the ingredients to distinguish different scenarios using the terminologies: MoRF (molecular recognition feature), not-MoRF, and not-IDP. A MoRF corresponds to large entropy and large MIMC (strong dependence among the residues' rotamer sampling), a not-MoRF corresponds to large entropy but small MIMC, and not-IDP corresponds to low entropy irrespective of the MIMC. We show that MorFs are most appropriate as descriptors of IDPs. They provide a reasonable number of high-population states that reflect the dependences between neighbor residues, thus classifying them as IDPs, yet without very large entropy that might lead to a too high entropy penalty.
LISA data analysis using Markov chain Monte Carlo methods
International Nuclear Information System (INIS)
Cornish, Neil J.; Crowder, Jeff
2005-01-01
The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low-frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground based gravitational wave astronomy. LISA data analysis requires the identification of individual signals from a data stream containing an unknown number of overlapping signals. Because of the signal overlaps, a global fit to all the signals has to be performed in order to avoid biasing the solution. However, performing such a global fit requires the exploration of an enormous parameter space with a dimension upwards of 50 000. Markov Chain Monte Carlo (MCMC) methods offer a very promising solution to the LISA data analysis problem. MCMC algorithms are able to efficiently explore large parameter spaces, simultaneously providing parameter estimates, error analysis, and even model selection. Here we present the first application of MCMC methods to simulated LISA data and demonstrate the great potential of the MCMC approach. Our implementation uses a generalized F-statistic to evaluate the likelihoods, and simulated annealing to speed convergence of the Markov chains. As a final step we supercool the chains to extract maximum likelihood estimates, and estimates of the Bayes factors for competing models. We find that the MCMC approach is able to correctly identify the number of signals present, extract the source parameters, and return error estimates consistent with Fisher information matrix predictions
Bayesian clustering of DNA sequences using Markov chains and a stochastic partition model.
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.
Parallel algorithms for simulating continuous time Markov chains
Nicol, David M.; Heidelberger, Philip
1992-01-01
We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.
Markov Chain Analysis of Musical Dice Games
Volchenkov, D.; Dawin, J. R.
2012-07-01
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
Irreversible Markov chains in spin models: Topological excitations
Lei, Ze; Krauth, Werner
2018-01-01
We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain dynamics leads to slow decay of vortex-antivortex correlations while spin waves decorrelate very quickly. Using a Fréchet description of the maximum vortex-antivortex distance, we quantify the contributions of topological excitations to the equilibrium correlations, and show that they vary from a dynamical critical exponent z∼ 2 at the critical temperature to z∼ 0 in the limit of zero temperature. We confirm the event-chain algorithm's fast relaxation (corresponding to z = 0) of spin waves in the harmonic approximation to the XY model. Mixing times (describing the approach towards equilibrium from the least favorable initial state) however remain much larger than equilibrium correlation times at low temperatures. We also describe the respective influence of topological monopole-antimonopole excitations and of spin waves on the event-chain dynamics in the three-dimensional Heisenberg model.
Zhao, Ning-bo; Yang, Jia-long; Li, Shu-ying; Sun, Yue-wu
2014-01-01
Performance degradation forecast technology for quantitatively assessing degradation states of aeroengine using exhaust gas temperature is an important technology in the aeroengine health management. In this paper, a GM (1, 1) Markov chain-based approach is introduced to forecast exhaust gas temperature by taking the advantages of GM (1, 1) model in time series and the advantages of Markov chain model in dealing with highly nonlinear and stochastic data caused by uncertain factors. In this ap...
Directory of Open Access Journals (Sweden)
Huilin Huang
2014-01-01
Full Text Available We study strong limit theorems for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees. We mainly establish the strong law of large numbers for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees and give the strong limit law of the conditional sample entropy rate.
Markov Chain Model with Catastrophe to Determine Mean Time to Default of Credit Risky Assets
Dharmaraja, Selvamuthu; Pasricha, Puneet; Tardelli, Paola
2017-11-01
This article deals with the problem of probabilistic prediction of the time distance to default for a firm. To model the credit risk, the dynamics of an asset is described as a function of a homogeneous discrete time Markov chain subject to a catastrophe, the default. The behaviour of the Markov chain is investigated and the mean time to the default is expressed in a closed form. The methodology to estimate the parameters is given. Numerical results are provided to illustrate the applicability of the proposed model on real data and their analysis is discussed.
R Package clickstream: Analyzing Clickstream Data with Markov Chains
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Michael Scholz
2016-10-01
Full Text Available Clickstream analysis is a useful tool for investigating consumer behavior, market research and software testing. I present the clickstream package which provides functionality for reading, clustering, analyzing and writing clickstreams in R. The package allows for a modeling of lists of clickstreams as zero-, first- and higher-order Markov chains. I illustrate the application of clickstream for a list of representative clickstreams from an online store.
Predicting hepatitis B monthly incidence rates using weighted Markov chains and time series methods.
Shahdoust, Maryam; Sadeghifar, Majid; Poorolajal, Jalal; Javanrooh, Niloofar; Amini, Payam
2015-01-01
Hepatitis B (HB) is a major global mortality. Accurately predicting the trend of the disease can provide an appropriate view to make health policy disease prevention. This paper aimed to apply three different to predict monthly incidence rates of HB. This historical cohort study was conducted on the HB incidence data of Hamadan Province, the west of Iran, from 2004 to 2012. Weighted Markov Chain (WMC) method based on Markov chain theory and two time series models including Holt Exponential Smoothing (HES) and SARIMA were applied on the data. The results of different applied methods were compared to correct percentages of predicted incidence rates. The monthly incidence rates were clustered into two clusters as state of Markov chain. The correct predicted percentage of the first and second clusters for WMC, HES and SARIMA methods was (100, 0), (84, 67) and (79, 47) respectively. The overall incidence rate of HBV is estimated to decrease over time. The comparison of results of the three models indicated that in respect to existing seasonality trend and non-stationarity, the HES had the most accurate prediction of the incidence rates.
Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems
Antown, Fadi; Dragičević, Davor; Froyland, Gary
2018-03-01
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.
Fitting timeseries by continuous-time Markov chains: A quadratic programming approach
International Nuclear Information System (INIS)
Crommelin, D.T.; Vanden-Eijnden, E.
2006-01-01
Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows
Generalization bounds of ERM-based learning processes for continuous-time Markov chains.
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.
A Markov Chain Model for Contagion
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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.
Planning Tunnel Construction Using Markov Chain Monte Carlo (MCMC
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Juan P. Vargas
2015-01-01
Full Text Available Tunnels, drifts, drives, and other types of underground excavation are very common in mining as well as in the construction of roads, railways, dams, and other civil engineering projects. Planning is essential to the success of tunnel excavation, and construction time is one of the most important factors to be taken into account. This paper proposes a simulation algorithm based on a stochastic numerical method, the Markov chain Monte Carlo method, that can provide the best estimate of the opening excavation times for the classic method of drilling and blasting. Taking account of technical considerations that affect the tunnel excavation cycle, the simulation is developed through a computational algorithm. Using the Markov chain Monte Carlo method, the unit operations involved in the underground excavation cycle are identified and assigned probability distributions that, with random number input, make it possible to simulate the total excavation time. The results obtained with this method are compared with a real case of tunneling excavation. By incorporating variability in the planning, it is possible to determine with greater certainty the ranges over which the execution times of the unit operations fluctuate. In addition, the financial risks associated with planning errors can be reduced and the exploitation of resources maximized.
Evolution of probability measures by cellular automata on algebraic topological Markov chains
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ALEJANDRO MAASS
2003-01-01
Full Text Available In this paper we review some recent results on the evolution of probability measures under cellular automata acting on a fullshift. In particular we discuss the crucial role of the attractiveness of maximal measures. We enlarge the context of the results of a previous study of topological Markov chains that are Abelian groups; the shift map is an automorphism of this group. This is carried out by studying the dynamics of Markov measures by a particular additive cellular automata. Many of these topics were within the focus of Francisco Varela's mathematical interests.
Animal vocal sequences: not the Markov chains we thought they were.
Kershenbaum, Arik; Bowles, Ann E; Freeberg, Todd M; Jin, Dezhe Z; Lameira, Adriano R; Bohn, Kirsten
2014-10-07
Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the 'renewal process' (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica, Carolina chickadees Poecile carolinensis, free-tailed bats Tadarida brasiliensis, rock hyraxes Procavia capensis, pilot whales Globicephala macrorhynchus, killer whales Orcinus orca and orangutans Pongo spp. The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
International Nuclear Information System (INIS)
Kim, Joo Yeon; Jang, Han Ki; Jang, Sol Ah; Park, Tae Jin
2014-01-01
There is a question that the simulation actually leads to draws from its target distribution and the most basic one is whether such Markov chains can always be constructed and all chain values sampled from them. The problem to be solved is the determination of how large this iteration should be to achieve the target distribution. This problem can be answered as convergence monitoring. In this paper, two widely used methods, such as autocorrelation and potential scale reduction factor (PSRF) in MCMC are characterized. There is no general agreement on the subject of the convergence. Although it is generally agreed that running n parallel chains in practice is computationally inefficient and unnecessary, running multiple parallel chains is generally applied for the convergence monitoring due to easy implementation. The main debate is the number of parallel chains needed. If the convergence properties of the chain are well understood then clearly a single chain suffices. Therefore, autocorrelation using single chain and multiple parallel ones are tried and their results then compared with each other in this study. And, the following question is answered from the two convergence results: Have the Markov chain realizations for achieved the target distribution?
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Chudech Losiri
2016-07-01
Full Text Available Urban expansion is considered as one of the most important problems in several developing countries. Bangkok Metropolitan Region (BMR is the urbanized and agglomerated area of Bangkok Metropolis (BM and its vicinity, which confronts the expansion problem from the center of the city. Landsat images of 1988, 1993, 1998, 2003, 2008, and 2011 were used to detect the land use and land cover (LULC changes. The demographic and economic data together with corresponding maps were used to determine the driving factors for land conversions. This study applied Cellular Automata-Markov Chain (CA-MC and Multi-Layer Perceptron-Markov Chain (MLP-MC to model LULC and urban expansions. The performance of the CA-MC and MLP-MC yielded more than 90% overall accuracy to predict the LULC, especially the MLP-MC method. Further, the annual population and economic growth rates were considered to produce the land demand for the LULC in 2014 and 2035 using the statistical extrapolation and system dynamics (SD. It was evident that the simulated map in 2014 resulting from the SD yielded the highest accuracy. Therefore, this study applied the SD method to generate the land demand for simulating LULC in 2035. The outcome showed that urban occupied the land around a half of the BMR.
Stationary population flow of a semi-open Markov Chain. | Yakasai ...
African Journals Online (AJOL)
In this paper we study the state vector of a semi-open Markov chain of a stochastic population flow. We consider stationary inflow of new members into the system and derive the limiting value of the state vector X(n) = (X1(n),....,(Xm(n) ∈Z+ as n→ ∞ , when the system's capacity, is known. Journal of the Nigerian Association ...
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M. V. Serzhantova
2016-05-01
Full Text Available Subject of Research. We analyze the problems of finite Markov chains apparatus application for simulating a human operator activity in the quasi-static functional environment. It is shown that the functional environment stochastic nature is generated by a factor of interval character of human operator properties. Method. The problem is solved in the class of regular (recurrent finite Markov chains with three states of the human operator: with a favorable, median and unfavorable combination of the values of mathematical model parameters of the human operator in a quasi-static functional environment. The finite Markov chain is designed taking into account the factors of human operator tiredness and interval character of parameters of the model representation of his properties. The device is based on the usage of mathematical approximation of the standard curve of the human operator activity performance during work shift. The standard curve of the human operator activity performance is based on the extensive research experience of functional activity of the human operator with the help of photos of the day, his action timing and ergonomic generalizations. Main Results. The apparatus of regular finite Markov chains gave the possibility to evaluate correctly the human operator activity performance in a quasi-static functional environment with the use of the main information component of these chains as a vector of final probabilities. In addition, we managed to build an algorithmic basis for estimating the stationary time (time study for transit of human operator from arbitrary initial functional state into a state corresponding to a vector of final probabilities for a used chain after it reaches the final state based on the analysis of the eigenvalues spectrum of the matrix of transition probabilities for a regular (recurrent finite Markov chain. Practical Relevance. Obtained theoretical results are confirmed by illustrative examples, which
Tataru, Paula; Hobolth, Asger
2011-12-05
Continuous time Markov chains (CTMCs) is a widely used model for describing the evolution of DNA sequences on the nucleotide, amino acid or codon level. The sufficient statistics for CTMCs are the time spent in a state and the number of changes between any two states. In applications past evolutionary events (exact times and types of changes) are unaccessible and the past must be inferred from DNA sequence data observed in the present. We describe and implement three algorithms for computing linear combinations of expected values of the sufficient statistics, conditioned on the end-points of the chain, and compare their performance with respect to accuracy and running time. The first algorithm is based on an eigenvalue decomposition of the rate matrix (EVD), the second on uniformization (UNI), and the third on integrals of matrix exponentials (EXPM). The implementation in R of the algorithms is available at http://www.birc.au.dk/~paula/. We use two different models to analyze the accuracy and eight experiments to investigate the speed of the three algorithms. We find that they have similar accuracy and that EXPM is the slowest method. Furthermore we find that UNI is usually faster than EVD.
Vulnerability of networks of interacting Markov chains.
Kocarev, L; Zlatanov, N; Trajanov, D
2010-05-13
The concept of vulnerability is introduced for a model of random, dynamical interactions on networks. In this model, known as the influence model, the nodes are arranged in an arbitrary network, while the evolution of the status at a node is according to an internal Markov chain, but with transition probabilities that depend not only on the current status of that node but also on the statuses of the neighbouring nodes. Vulnerability is treated analytically and numerically for several networks with different topological structures, as well as for two real networks--the network of infrastructures and the EU power grid--identifying the most vulnerable nodes of these networks.
DEFF Research Database (Denmark)
Tataru, Paula Cristina; Hobolth, Asger
2011-01-01
past evolutionary events (exact times and types of changes) are unaccessible and the past must be inferred from DNA sequence data observed in the present. RESULTS: We describe and implement three algorithms for computing linear combinations of expected values of the sufficient statistics, conditioned......BACKGROUND: Continuous time Markov chains (CTMCs) is a widely used model for describing the evolution of DNA sequences on the nucleotide, amino acid or codon level. The sufficient statistics for CTMCs are the time spent in a state and the number of changes between any two states. In applications...... of the algorithms is available at www.birc.au.dk/~paula/. CONCLUSIONS: We use two different models to analyze the accuracy and eight experiments to investigate the speed of the three algorithms. We find that they have similar accuracy and that EXPM is the slowest method. Furthermore we find that UNI is usually...
Markov chain Monte Carlo methods for statistical analysis of RF photonic devices
DEFF Research Database (Denmark)
Piels, Molly; Zibar, Darko
2016-01-01
uncertainty is shown to give unsatisfactory and incorrect results due to the nonlinear relationship between the circuit parameters and the measured data. Markov chain Monte Carlo methods are shown to provide superior results, both for individual devices and for assessing within-die variation...
Markov chain aggregation and its applications to combinatorial reaction networks.
Ganguly, Arnab; Petrov, Tatjana; Koeppl, Heinz
2014-09-01
We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.
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)
Markov chain modeling of evolution of strains in reinforced concrete flexural beams
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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
A new Markov-chain-related statistical approach for modelling synthetic wind power time series
International Nuclear Information System (INIS)
Pesch, T; Hake, J F; Schröders, S; Allelein, H J
2015-01-01
The integration of rising shares of volatile wind power in the generation mix is a major challenge for the future energy system. To address the uncertainties involved in wind power generation, models analysing and simulating the stochastic nature of this energy source are becoming increasingly important. One statistical approach that has been frequently used in the literature is the Markov chain approach. Recently, the method was identified as being of limited use for generating wind time series with time steps shorter than 15–40 min as it is not capable of reproducing the autocorrelation characteristics accurately. This paper presents a new Markov-chain-related statistical approach that is capable of solving this problem by introducing a variable second lag. Furthermore, additional features are presented that allow for the further adjustment of the generated synthetic time series. The influences of the model parameter settings are examined by meaningful parameter variations. The suitability of the approach is demonstrated by an application analysis with the example of the wind feed-in in Germany. It shows that—in contrast to conventional Markov chain approaches—the generated synthetic time series do not systematically underestimate the required storage capacity to balance wind power fluctuation. (paper)
MARKOV CHAIN MODELING OF PERFORMANCE DEGRADATION OF PHOTOVOLTAIC SYSTEM
E. Suresh Kumar; Asis Sarkar; Dhiren kumar Behera
2012-01-01
Modern probability theory studies chance processes for which theknowledge of previous outcomes influence predictions for future experiments. In principle, when a sequence of chance experiments, all of the past outcomes could influence the predictions for the next experiment. In Markov chain type of chance, the outcome of a given experiment can affect the outcome of the next experiment. The system state changes with time and the state X and time t are two random variables. Each of these variab...
International Nuclear Information System (INIS)
Mikhailov, I.D.; Zhuravskii, L.V.
1987-01-01
A method is proposed for calculating the vibrational-state density averaged over all configurations for a polymer chain with Markov disorder. The method is based on using a group of centrally symmetric gauge transformations that reduce the dynamic matrix for along polymer chain to renormalized dynamic matrices for short fragments. The short-range order is incorporated exactly in the averaging procedure, while the long-range order is incorporated in the self-consistent field approximation. Results are given for a simple skeletal model for a polymer containing tacticity deviations of Markov type
Markov Chain Models for Stochastic Behavior in Resonance Overlap Regions
McCarthy, Morgan; Quillen, Alice
2018-01-01
We aim to predict lifetimes of particles in chaotic zoneswhere resonances overlap. A continuous-time Markov chain model isconstructed using mean motion resonance libration timescales toestimate transition times between resonances. The model is applied todiffusion in the co-rotation region of a planet. For particles begunat low eccentricity, the model is effective for early diffusion, butnot at later time when particles experience close encounters to the planet.
International Nuclear Information System (INIS)
Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Bao, Jie; Swiler, Laura
2017-01-01
In this paper we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.
Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Bao, Jie; Swiler, Laura
2017-12-01
In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated - reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.
Triangular M/G/1-type and tree-like QBD Markov chains
Van Houdt, B.; Leeuwaarden, van J.S.H.
2009-01-01
In applying matrix-analytic methods to M/G/1-type and tree-like QBD Markov chains, it is crucial to determine the solution to a (set of) nonlinear matrix equation(s). This is usually done via iterative methods. We consider the highly structured subclass of triangular M/G/1-type and tree-like QBD
A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis
Edwards, Michael C.
2010-01-01
Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…
Overshoot in biological systems modelled by Markov chains: a non-equilibrium dynamic phenomenon.
Jia, Chen; Qian, Minping; Jiang, Daquan
2014-08-01
A number of biological systems can be modelled by Markov chains. Recently, there has been an increasing concern about when biological systems modelled by Markov chains will perform a dynamic phenomenon called overshoot. In this study, the authors found that the steady-state behaviour of the system will have a great effect on the occurrence of overshoot. They showed that overshoot in general cannot occur in systems that will finally approach an equilibrium steady state. They further classified overshoot into two types, named as simple overshoot and oscillating overshoot. They showed that except for extreme cases, oscillating overshoot will occur if the system is far from equilibrium. All these results clearly show that overshoot is a non-equilibrium dynamic phenomenon with energy consumption. In addition, the main result in this study is validated with real experimental data.
Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains
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Erik Van der Straeten
2009-11-01
Full Text Available In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use one-dimensional classical spin systems to illustrate the theoretical ideas. The examples studied in this paper are: the Ising model, the Potts model and the Blume-Emery-Griffiths model.
A Multi-Armed Bandit Approach to Following a Markov Chain
2017-06-01
Introduction to online convex optimization ,” Foundations and Trends in Optimization , vol. 2, no. 3-4, pp. 157–325, 2016. [3] A. Mahajan and D. Teneketzis...stochastic optimization , machine learning, discrete time Markov chains, stochastic Multi-Armed Bandit, combinatorial Multi-Armed Bandit, online learning, and...fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OPERATIONS RESEARCH from the NAVAL POSTGRADUATE SCHOOL June 2017 Approved by: Roberto
DIM SUM: demography and individual migration simulated using a Markov chain.
Brown, Jeremy M; Savidge, Kevin; McTavish, Emily Jane B
2011-03-01
An increasing number of studies seek to infer demographic history, often jointly with genetic relationships. Despite numerous analytical methods for such data, few simulations have investigated the methods' power and robustness, especially when underlying assumptions have been violated. DIM SUM (Demography and Individual Migration Simulated Using a Markov chain) is a stand-alone Java program for the simulation of population demography and individual migration while recording ancestor-descendant relationships. It does not employ coalescent assumptions or discrete population boundaries. It is extremely flexible, allowing the user to specify border positions, reactions of organisms to borders, local and global carrying capacities, individual dispersal kernels, rates of reproduction and strategies for sampling individuals. Spatial variables may be specified using image files (e.g., as exported from gis software) and may vary through time. In combination with software for genetic marker simulation, DIM SUM will be useful for testing phylogeographic (e.g., nested clade phylogeographic analysis, coalescent-based tests and continuous-landscape frameworks) and landscape-genetic methods, specifically regarding violations of coalescent assumptions. It can also be used to explore the qualitative features of proposed demographic scenarios (e.g. regarding biological invasions) and as a pedagogical tool. DIM SUM (with user's manual) can be downloaded from http://code.google.com/p/bio-dimsum. © 2010 Blackwell Publishing Ltd.
APPLICATION OF HIDDEN MARKOV CHAINS IN QUALITY CONTROL
Directory of Open Access Journals (Sweden)
Hanife DEMIRALP
2013-01-01
Full Text Available The ever growing technological innovations and sophistication in industrial processes require adequate checks on quality. Thus, there is an increasing demand for simple and efficient quality control methods. In this regard the control charts stand out in simplicity and efficiency. In this paper, we propose a method of controlling quality based on the theory of hidden Markov chains. Based on samples drawn at different times from the production process, the method obtains the state of the process probabilistically. The main advantage of the method is that it requires no assumption on the normality of the process output.
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, we present a simplified parsimonious higher-order multivariate Markov chain model with new convergence condition. (TPHOMMCM-NCC). Moreover, estimation method of the parameters in TPHOMMCM-NCC is give. Numerical experiments illustrate the effectiveness of TPHOMMCM-NCC.
Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas behind the Algorithm
Stewart, Wayne; Stewart, Sepideh
2014-01-01
For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…
Directory of Open Access Journals (Sweden)
Nikola Trčka
2009-12-01
Full Text Available We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we consider Markov reward chains which are standardly presented in real matrix theory. By interpreting the obtained matrix conditions for bisimulations in this setting, we automatically obtain the definitions of strong, weak, and branching bisimulation for Markov reward chains. The obtained strong and weak bisimulations are shown to coincide with some existing notions, while the obtained branching bisimulation is new, but its usefulness is questionable.
Schmandt, Nicolaus T; Galán, Roberto F
2012-09-14
Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be replaced with their mean if state B is not directly connected to A, which shortens computing time considerably. We show the accuracy and efficacy of our approximation theoretically and in simulations of stochastic ion-channel gating in neurons.
A Graph-Algorithmic Approach for the Study of Metastability in Markov Chains
Gan, Tingyue; Cameron, Maria
2017-06-01
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry, and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical timescales at which the qualitative behavior of a given Markov chain changes, and give an effective description of the dynamics on each of them. This approach is valid for both time-reversible and time-irreversible Markov processes, with or without symmetry. Central to this approach are two graph algorithms, Algorithm 1 and Algorithm 2, for obtaining the sequences of the critical timescales and the hierarchies of Typical Transition Graphs or T-graphs indicating the most likely transitions in the system without and with symmetry, respectively. The sequence of critical timescales includes the subsequence of the reciprocals of the real parts of eigenvalues. Under a certain assumption, we prove sharp asymptotic estimates for eigenvalues (including pre-factors) and show how one can extract them from the output of Algorithm 1. We discuss the relationship between Algorithms 1 and 2 and explain how one needs to interpret the output of Algorithm 1 if it is applied in the case with symmetry instead of Algorithm 2. Finally, we analyze an example motivated by R. D. Astumian's model of the dynamics of kinesin, a molecular motor, by means of Algorithm 2.
Technical manual for basic version of the Markov chain nest productivity model (MCnest)
The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...
Learning Bayesian network classifiers for credit scoring using Markov Chain Monte Carlo search
Baesens, B.; Egmont-Petersen, M.; Castelo, R.; Vanthienen, J.
2001-01-01
In this paper, we will evaluate the power and usefulness of Bayesian network classifiers for credit scoring. Various types of Bayesian network classifiers will be evaluated and contrasted including unrestricted Bayesian network classifiers learnt using Markov Chain Monte Carlo (MCMC) search.
ON TESTING OF CRYPTOGRAPHYC GENERATORS OUTPUT SEQUENCES USING MARKOV CHAINS OF CONDITIONAL ORDER
Directory of Open Access Journals (Sweden)
M. V. Maltsev
2013-01-01
Full Text Available The paper deals with the Markov chain of conditional order, which is used for statisticaltesting of cryptographic generators. Statistical estimations of model parameters are given. Consistency of the order estimator is proved. Results of computer experiments are presented.
User’s manual for basic version of MCnest Markov chain nest productivity model
The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...
Liao, Weinan; Ren, Jie; Wang, Kun; Wang, Shun; Zeng, Feng; Wang, Ying; Sun, Fengzhu
2016-11-23
The comparison between microbial sequencing data is critical to understand the dynamics of microbial communities. The alignment-based tools analyzing metagenomic datasets require reference sequences and read alignments. The available alignment-free dissimilarity approaches model the background sequences with Fixed Order Markov Chain (FOMC) yielding promising results for the comparison of microbial communities. However, in FOMC, the number of parameters grows exponentially with the increase of the order of Markov Chain (MC). Under a fixed high order of MC, the parameters might not be accurately estimated owing to the limitation of sequencing depth. In our study, we investigate an alternative to FOMC to model background sequences with the data-driven Variable Length Markov Chain (VLMC) in metatranscriptomic data. The VLMC originally designed for long sequences was extended to apply to high-throughput sequencing reads and the strategies to estimate the corresponding parameters were developed. The flexible number of parameters in VLMC avoids estimating the vast number of parameters of high-order MC under limited sequencing depth. Different from the manual selection in FOMC, VLMC determines the MC order adaptively. Several beta diversity measures based on VLMC were applied to compare the bacterial RNA-Seq and metatranscriptomic datasets. Experiments show that VLMC outperforms FOMC to model the background sequences in transcriptomic and metatranscriptomic samples. A software pipeline is available at https://d2vlmc.codeplex.com.
Saliency Detection via Absorbing Markov Chain With Learnt Transition Probability.
Lihe Zhang; Jianwu Ai; Bowen Jiang; Huchuan Lu; Xiukui Li
2018-02-01
In this paper, we propose a bottom-up saliency model based on absorbing Markov chain (AMC). First, a sparsely connected graph is constructed to capture the local context information of each node. All image boundary nodes and other nodes are, respectively, treated as the absorbing nodes and transient nodes in the absorbing Markov chain. Then, the expected number of times from each transient node to all other transient nodes can be used to represent the saliency value of this node. The absorbed time depends on the weights on the path and their spatial coordinates, which are completely encoded in the transition probability matrix. Considering the importance of this matrix, we adopt different hierarchies of deep features extracted from fully convolutional networks and learn a transition probability matrix, which is called learnt transition probability matrix. Although the performance is significantly promoted, salient objects are not uniformly highlighted very well. To solve this problem, an angular embedding technique is investigated to refine the saliency results. Based on pairwise local orderings, which are produced by the saliency maps of AMC and boundary maps, we rearrange the global orderings (saliency value) of all nodes. Extensive experiments demonstrate that the proposed algorithm outperforms the state-of-the-art methods on six publicly available benchmark data sets.
Semi-Markov Arnason-Schwarz models.
King, Ruth; Langrock, Roland
2016-06-01
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis. © 2015, The International Biometric Society.
The computation of stationary distributions of Markov chains through perturbations
Directory of Open Access Journals (Sweden)
Jeffery J. Hunter
1991-01-01
Full Text Available An algorithmic procedure for the determination of the stationary distribution of a finite, m-state, irreducible Markov chain, that does not require the use of methods for solving systems of linear equations, is presented. The technique is based upon a succession of m, rank one, perturbations of the trivial doubly stochastic matrix whose known steady state vector is updated at each stage to yield the required stationary probability vector.
Directory of Open Access Journals (Sweden)
Tataru Paula
2011-12-01
Full Text Available Abstract Background Continuous time Markov chains (CTMCs is a widely used model for describing the evolution of DNA sequences on the nucleotide, amino acid or codon level. The sufficient statistics for CTMCs are the time spent in a state and the number of changes between any two states. In applications past evolutionary events (exact times and types of changes are unaccessible and the past must be inferred from DNA sequence data observed in the present. Results We describe and implement three algorithms for computing linear combinations of expected values of the sufficient statistics, conditioned on the end-points of the chain, and compare their performance with respect to accuracy and running time. The first algorithm is based on an eigenvalue decomposition of the rate matrix (EVD, the second on uniformization (UNI, and the third on integrals of matrix exponentials (EXPM. The implementation in R of the algorithms is available at http://www.birc.au.dk/~paula/. Conclusions We use two different models to analyze the accuracy and eight experiments to investigate the speed of the three algorithms. We find that they have similar accuracy and that EXPM is the slowest method. Furthermore we find that UNI is usually faster than EVD.
The combinational structure of non-homogeneous Markov chains with countable states
Directory of Open Access Journals (Sweden)
A. Mukherjea
1983-01-01
Full Text Available Let P(s,t denote a non-homogeneous continuous parameter Markov chain with countable state space E and parameter space [a,b], −∞0}. It is shown in this paper that R(s,t is reflexive, transitive, and independent of (s,t, s
Multivariate Markov chain modeling for stock markets
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.
DEFF Research Database (Denmark)
Møller, Jesper
(This text written by Jesper Møller, Aalborg University, is submitted for the collection ‘Stochastic Geometry: Highlights, Interactions and New Perspectives', edited by Wilfrid S. Kendall and Ilya Molchanov, to be published by ClarendonPress, Oxford, and planned to appear as Section 4.1 with the ......(This text written by Jesper Møller, Aalborg University, is submitted for the collection ‘Stochastic Geometry: Highlights, Interactions and New Perspectives', edited by Wilfrid S. Kendall and Ilya Molchanov, to be published by ClarendonPress, Oxford, and planned to appear as Section 4.......1 with the title ‘Inference'.) This contribution concerns statistical inference for parametric models used in stochastic geometry and based on quick and simple simulation free procedures as well as more comprehensive methods using Markov chain Monte Carlo (MCMC) simulations. Due to space limitations the focus...
International Nuclear Information System (INIS)
Mukhamedov, Farrukh; Saburov, Mansoor
2010-06-01
In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two distinct QMC for the given family of interaction operators {K }. (author)
Utilization of two web-based continuing education courses evaluated by Markov chain model.
Tian, Hao; Lin, Jin-Mann S; Reeves, William C
2012-01-01
To evaluate the web structure of two web-based continuing education courses, identify problems and assess the effects of web site modifications. Markov chain models were built from 2008 web usage data to evaluate the courses' web structure and navigation patterns. The web site was then modified to resolve identified design issues and the improvement in user activity over the subsequent 12 months was quantitatively evaluated. Web navigation paths were collected between 2008 and 2010. The probability of navigating from one web page to another was analyzed. The continuing education courses' sequential structure design was clearly reflected in the resulting actual web usage models, and none of the skip transitions provided was heavily used. The web navigation patterns of the two different continuing education courses were similar. Two possible design flaws were identified and fixed in only one of the two courses. Over the following 12 months, the drop-out rate in the modified course significantly decreased from 41% to 35%, but remained unchanged in the unmodified course. The web improvement effects were further verified via a second-order Markov chain model. The results imply that differences in web content have less impact than web structure design on how learners navigate through continuing education courses. Evaluation of user navigation can help identify web design flaws and guide modifications. This study showed that Markov chain models provide a valuable tool to evaluate web-based education courses. Both the results and techniques in this study would be very useful for public health education and research specialists.
Learning a Markov Logic network for supervised gene regulatory network inference.
Brouard, Céline; Vrain, Christel; Dubois, Julie; Castel, David; Debily, Marie-Anne; d'Alché-Buc, Florence
2013-09-12
Gene regulatory network inference remains a challenging problem in systems biology despite the numerous approaches that have been proposed. When substantial knowledge on a gene regulatory network is already available, supervised network inference is appropriate. Such a method builds a binary classifier able to assign a class (Regulation/No regulation) to an ordered pair of genes. Once learnt, the pairwise classifier can be used to predict new regulations. In this work, we explore the framework of Markov Logic Networks (MLN) that combine features of probabilistic graphical models with the expressivity of first-order logic rules. We propose to learn a Markov Logic network, e.g. a set of weighted rules that conclude on the predicate "regulates", starting from a known gene regulatory network involved in the switch proliferation/differentiation of keratinocyte cells, a set of experimental transcriptomic data and various descriptions of genes all encoded into first-order logic. As training data are unbalanced, we use asymmetric bagging to learn a set of MLNs. The prediction of a new regulation can then be obtained by averaging predictions of individual MLNs. As a side contribution, we propose three in silico tests to assess the performance of any pairwise classifier in various network inference tasks on real datasets. A first test consists of measuring the average performance on balanced edge prediction problem; a second one deals with the ability of the classifier, once enhanced by asymmetric bagging, to update a given network. Finally our main result concerns a third test that measures the ability of the method to predict regulations with a new set of genes. As expected, MLN, when provided with only numerical discretized gene expression data, does not perform as well as a pairwise SVM in terms of AUPR. However, when a more complete description of gene properties is provided by heterogeneous sources, MLN achieves the same performance as a black-box model such as a
Recursive estimation of high-order Markov chains: Approximation by finite mixtures
Czech Academy of Sciences Publication Activity Database
Kárný, Miroslav
2016-01-01
Roč. 326, č. 1 (2016), s. 188-201 ISSN 0020-0255 R&D Projects : GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Markov chain * Approximate parameter estimation * Bayesian recursive estimation * Adaptive systems * Kullback–Leibler divergence * Forgetting Subject RIV: BC - Control Systems Theory Impact factor: 4.832, year: 2016 http://library.utia.cas.cz/separaty/2015/AS/karny-0447119.pdf
Numerical approximations for speeding up mcmc inference in the infinite relational model
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Albers, Kristoffer Jon
2015-01-01
The infinite relational model (IRM) is a powerful model for discovering clusters in complex networks; however, the computational speed of Markov chain Monte Carlo inference in the model can be a limiting factor when analyzing large networks. We investigate how using numerical approximations...
Characterization of the rat exploratory behavior in the elevated plus-maze with Markov chains.
Tejada, Julián; Bosco, Geraldine G; Morato, Silvio; Roque, Antonio C
2010-11-30
The elevated plus-maze is an animal model of anxiety used to study the effect of different drugs on the behavior of the animal. It consists of a plus-shaped maze with two open and two closed arms elevated 50cm from the floor. The standard measures used to characterize exploratory behavior in the elevated plus-maze are the time spent and the number of entries in the open arms. In this work, we use Markov chains to characterize the exploratory behavior of the rat in the elevated plus-maze under three different conditions: normal and under the effects of anxiogenic and anxiolytic drugs. The spatial structure of the elevated plus-maze is divided into squares, which are associated with states of a Markov chain. By counting the frequencies of transitions between states during 5-min sessions in the elevated plus-maze, we constructed stochastic matrices for the three conditions studied. The stochastic matrices show specific patterns, which correspond to the observed behaviors of the rat under the three different conditions. For the control group, the stochastic matrix shows a clear preference for places in the closed arms. This preference is enhanced for the anxiogenic group. For the anxiolytic group, the stochastic matrix shows a pattern similar to a random walk. Our results suggest that Markov chains can be used together with the standard measures to characterize the rat behavior in the elevated plus-maze. Copyright © 2010 Elsevier B.V. All rights reserved.
An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains
Directory of Open Access Journals (Sweden)
Qihong Duan
2010-01-01
Full Text Available In many applications, the failure rate function may present a bathtub shape curve. In this paper, an expectation maximization algorithm is proposed to construct a suitable continuous-time Markov chain which models the failure time data by the first time reaching the absorbing state. Assume that a system is described by methods of supplementary variables, the device of stage, and so on. Given a data set, the maximum likelihood estimators of the initial distribution and the infinitesimal transition rates of the Markov chain can be obtained by our novel algorithm. Suppose that there are m transient states in the system and that there are n failure time data. The devised algorithm only needs to compute the exponential of m×m upper triangular matrices for O(nm2 times in each iteration. Finally, the algorithm is applied to two real data sets, which indicates the practicality and efficiency of our algorithm.
Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees
Directory of Open Access Journals (Sweden)
Weicai Peng
2016-02-01
Full Text Available Abstract In this paper, a kind of infinite, local finite tree T, named a controlled tree, is introduced. Some strong limit properties, such as the strong law of large numbers and the asymptotic equipartition property, for nonhomogeneous Markov chains indexed by T, are established. The outcomes are the generalizations of some well-known results.
Directory of Open Access Journals (Sweden)
Pablo J. Villacorta
2016-07-01
Full Text Available Markov chains are well-established probabilistic models of a wide variety of real systems that evolve along time. Countless examples of applications of Markov chains that successfully capture the probabilistic nature of real problems include areas as diverse as biology, medicine, social science, and engineering. One interesting feature which characterizes certain kinds of Markov chains is their stationary distribution, which stands for the global fraction of time the system spends in each state. The computation of the stationary distribution requires precise knowledge of the transition probabilities. When the only information available is a sequence of observations drawn from the system, such probabilities have to be estimated. Here we review an existing method to estimate fuzzy transition probabilities from observations and, with them, obtain the fuzzy stationary distribution of the resulting fuzzy Markov chain. The method also works when the user directly provides fuzzy transition probabilities. We provide an implementation in the R environment that is the first available to the community and serves as a proof of concept. We demonstrate the usefulness of our proposal with computational experiments on a toy problem, namely a time-homogeneous Markov chain that guides the randomized movement of an autonomous robot that patrols a small area.
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 ...
A Markov chain representation of the normalized Perron–Frobenius eigenvector
Cerf, Raphaël; Dalmau, Joseba
2017-01-01
We consider the problem of finding the Perron–Frobenius eigenvector of a primitive matrix. Dividing each of the rows of the matrix by the sum of the elements in the row, the resulting new matrix is stochastic. We give a formula for the normalized Perron–Frobenius eigenvector of the original matrix, in terms of a realization of the Markov chain defined by the associated stochastic matrix. This formula is a generalization of the classical formula for the invariant probability measure of a Marko...
Directory of Open Access Journals (Sweden)
Li Qiu
2013-01-01
unified Markov jump model. The random time delays and packet dropouts existed in feedback communication link are modeled by two independent Markov chains; the resulting closed-loop system is described by a new Markovian jump linear system (MJLS with Markov delays. Sufficient conditions of the stochastic stability for NCSs is obtained by constructing a novel Lyapunov functional, and the mode-dependent output feedback controller design method is presented based on linear matrix inequality (LMI technique. A numerical example is given to illustrate the effectiveness of the proposed method.
On Construction of Quantum Markov Chains on Cayley trees
International Nuclear Information System (INIS)
Accardi, Luigi; Mukhamedov, Farrukh; Souissi, Abdessatar
2016-01-01
The main aim of the present paper is to provide a new construction of quantum Markov chain (QMC) on arbitrary order Cayley tree. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Note that this construction reminds statistical mechanics models with competing interactions on trees. If one considers one dimensional tree, then the provided construction reduces to well-known one, which was studied by the first author. Our construction will allow to investigate phase transition problem in a quantum setting. (paper)
Avian life history profiles for use in the Markov chain nest productivity model (MCnest)
The Markov Chain nest productivity model, or MCnest, quantitatively estimates the effects of pesticides or other toxic chemicals on annual reproductive success of avian species (Bennett and Etterson 2013, Etterson and Bennett 2013). The Basic Version of MCnest was developed as a...
International Nuclear Information System (INIS)
Trias, Miquel; Vecchio, Alberto; Veitch, John
2009-01-01
Bayesian analysis of Laser Interferometer Space Antenna (LISA) data sets based on Markov chain Monte Carlo methods has been shown to be a challenging problem, in part due to the complicated structure of the likelihood function consisting of several isolated local maxima that dramatically reduces the efficiency of the sampling techniques. Here we introduce a new fully Markovian algorithm, a delayed rejection Metropolis-Hastings Markov chain Monte Carlo method, to efficiently explore these kind of structures and we demonstrate its performance on selected LISA data sets containing a known number of stellar-mass binary signals embedded in Gaussian stationary noise.
Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory
2016-05-12
Distribution Unlimited UU UU UU UU 12-05-2016 15-May-2014 14-Feb-2015 Final Report: Statistical Inference on Memory Structure of Processes and Its Applications ...ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 mathematical statistics ; time series; Markov chains; random...journals: Final Report: Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory Report Title Three areas
Block-accelerated aggregation multigrid for Markov chains with application to PageRank problems
Shen, Zhao-Li; Huang, Ting-Zhu; Carpentieri, Bruno; Wen, Chun; Gu, Xian-Ming
2018-06-01
Recently, the adaptive algebraic aggregation multigrid method has been proposed for computing stationary distributions of Markov chains. This method updates aggregates on every iterative cycle to keep high accuracies of coarse-level corrections. Accordingly, its fast convergence rate is well guaranteed, but often a large proportion of time is cost by aggregation processes. In this paper, we show that the aggregates on each level in this method can be utilized to transfer the probability equation of that level into a block linear system. Then we propose a Block-Jacobi relaxation that deals with the block system on each level to smooth error. Some theoretical analysis of this technique is presented, meanwhile it is also adapted to solve PageRank problems. The purpose of this technique is to accelerate the adaptive aggregation multigrid method and its variants for solving Markov chains and PageRank problems. It also attempts to shed some light on new solutions for making aggregation processes more cost-effective for aggregation multigrid methods. Numerical experiments are presented to illustrate the effectiveness of this technique.
Motif finding in DNA sequences based on skipping nonconserved positions in background Markov chains.
Zhao, Xiaoyan; Sze, Sing-Hoi
2011-05-01
One strategy to identify transcription factor binding sites is through motif finding in upstream DNA sequences of potentially co-regulated genes. Despite extensive efforts, none of the existing algorithms perform very well. We consider a string representation that allows arbitrary ignored positions within the nonconserved portion of single motifs, and use O(2(l)) Markov chains to model the background distributions of motifs of length l while skipping these positions within each Markov chain. By focusing initially on positions that have fixed nucleotides to define core occurrences, we develop an algorithm to identify motifs of moderate lengths. We compare the performance of our algorithm to other motif finding algorithms on a few benchmark data sets, and show that significant improvement in accuracy can be obtained when the sites are sufficiently conserved within a given sample, while comparable performance is obtained when the site conservation rate is low. A software program (PosMotif ) and detailed results are available online at http://faculty.cse.tamu.edu/shsze/posmotif.
Reliability measures for indexed semi-Markov chains applied to wind energy production
International Nuclear Information System (INIS)
D'Amico, Guglielmo; Petroni, Filippo; Prattico, Flavio
2015-01-01
The computation of the dependability measures is a crucial point in many engineering problems as well as in the planning and development of a wind farm. In this paper we address the issue of energy production by wind turbines by using an indexed semi-Markov chain as a model of wind speed. We present the mathematical model, the data and technical characteristics of a commercial wind turbine (Aircon HAWT-10kW). We show how to compute some of the main dependability measures such as reliability, availability and maintainability functions. We compare the results of the model with real energy production obtained from data available in the Lastem station (Italy) and sampled every 10 min. - Highlights: • Semi-Markov models. • Time series generation of wind speed. • Computation of availability, reliability and maintainability.
System reliability assessment via sensitivity analysis in the Markov chain scheme
International Nuclear Information System (INIS)
Gandini, A.
1988-01-01
Methods for reliability sensitivity analysis in the Markov chain scheme are presented, together with a new formulation which makes use of Generalized Perturbation Theory (GPT) methods. As well known, sensitivity methods are fundamental in system risk analysis, since they allow to identify important components, so to assist the analyst in finding weaknesses in design and operation and in suggesting optimal modifications for system upgrade. The relationship between the GPT sensitivity expression and the Birnbaum importance is also given [fr
Finite Markov processes and their applications
Iosifescu, Marius
2007-01-01
A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch
Fannes, Mark; Wouters, Jeroen
2012-01-01
We study a quantum process that can be considered as a quantum analogue for the classical Markov process. We specifically construct a version of these processes for free Fermions. For such free Fermionic processes we calculate the entropy density. This can be done either directly using Szeg\\"o's theorem for asymptotic densities of functions of Toeplitz matrices, or through an extension of said theorem to rates of functions, which we present in this article.
Memory functions and correlations in additive binary Markov chains
Energy Technology Data Exchange (ETDEWEB)
Melnyk, S S [A Ya Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov (Ukraine); Usatenko, O V [A Ya Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov (Ukraine); Yampol' skii, V A [A Ya Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov (Ukraine); Apostolov, S S [V N Karazin Kharkov National University, 4 Svoboda Sq., Kharkov 61077 (Ukraine); Maiselis, Z A [V N Karazin Kharkov National University, 4 Svoboda Sq., Kharkov 61077 (Ukraine)
2006-11-17
A theory of additive Markov chains with a long-range memory, proposed earlier in Usatenko et al (2003 Phys. Rev. E 68 061107), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, memory functions and their relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function.
Under-reported data analysis with INAR-hidden Markov chains.
Fernández-Fontelo, Amanda; Cabaña, Alejandra; Puig, Pedro; Moriña, David
2016-11-20
In this work, we deal with correlated under-reported data through INAR(1)-hidden Markov chain models. These models are very flexible and can be identified through its autocorrelation function, which has a very simple form. A naïve method of parameter estimation is proposed, jointly with the maximum likelihood method based on a revised version of the forward algorithm. The most-probable unobserved time series is reconstructed by means of the Viterbi algorithm. Several examples of application in the field of public health are discussed illustrating the utility of the models. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Memory functions and correlations in additive binary Markov chains
International Nuclear Information System (INIS)
Melnyk, S S; Usatenko, O V; Yampol'skii, V A; Apostolov, S S; Maiselis, Z A
2006-01-01
A theory of additive Markov chains with a long-range memory, proposed earlier in Usatenko et al (2003 Phys. Rev. E 68 061107), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, memory functions and their relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function
Surrogate based approaches to parameter inference in ocean models
Knio, Omar
2016-01-06
This talk discusses the inference of physical parameters using model surrogates. Attention is focused on the use of sampling schemes to build suitable representations of the dependence of the model response on uncertain input data. Non-intrusive spectral projections and regularized regressions are used for this purpose. A Bayesian inference formalism is then applied to update the uncertain inputs based on available measurements or observations. To perform the update, we consider two alternative approaches, based on the application of Markov Chain Monte Carlo methods or of adjoint-based optimization techniques. We outline the implementation of these techniques to infer dependence of wind drag, bottom drag, and internal mixing coefficients.
Surrogate based approaches to parameter inference in ocean models
Knio, Omar
2016-01-01
This talk discusses the inference of physical parameters using model surrogates. Attention is focused on the use of sampling schemes to build suitable representations of the dependence of the model response on uncertain input data. Non-intrusive spectral projections and regularized regressions are used for this purpose. A Bayesian inference formalism is then applied to update the uncertain inputs based on available measurements or observations. To perform the update, we consider two alternative approaches, based on the application of Markov Chain Monte Carlo methods or of adjoint-based optimization techniques. We outline the implementation of these techniques to infer dependence of wind drag, bottom drag, and internal mixing coefficients.
Directory of Open Access Journals (Sweden)
Yi-Chung Hu
2017-10-01
Full Text Available Grey prediction models for time series have been widely applied to demand forecasting because only limited data are required for them to build a time series model without any statistical assumptions. Previous studies have demonstrated that the combination of grey prediction with neural networks helps grey prediction perform better. Some methods have been presented to improve the prediction accuracy of the popular GM(1,1 model by using the Markov chain to estimate the residual needed to modify a predicted value. Compared to the previous Grey-Markov models, this study contributes to apply the functional-link net to estimate the degree to which a predicted value obtained from the GM(1,1 model can be adjusted. Furthermore, the troublesome number of states and their bounds that are not easily specified in Markov chain have been determined by a genetic algorithm. To verify prediction performance, the proposed grey prediction model was applied to an important grey system problem—foreign tourist forecasting. Experimental results show that the proposed model provides satisfactory results compared to the other Grey-Markov models considered.
Adaptive Markov Chain Monte Carlo
Jadoon, Khan
2016-08-08
A substantial interpretation of electromagnetic induction (EMI) measurements requires quantifying optimal model parameters and uncertainty of a nonlinear inverse problem. For this purpose, an adaptive Bayesian Markov chain Monte Carlo (MCMC) algorithm is used to assess multi-orientation and multi-offset EMI measurements in an agriculture field with non-saline and saline soil. In the MCMC simulations, posterior distribution was computed using Bayes rule. The electromagnetic forward model based on the full solution of Maxwell\\'s equations was used to simulate the apparent electrical conductivity measured with the configurations of EMI instrument, the CMD mini-Explorer. The model parameters and uncertainty for the three-layered earth model are investigated by using synthetic data. Our results show that in the scenario of non-saline soil, the parameters of layer thickness are not well estimated as compared to layers electrical conductivity because layer thicknesses in the model exhibits a low sensitivity to the EMI measurements, and is hence difficult to resolve. Application of the proposed MCMC based inversion to the field measurements in a drip irrigation system demonstrate that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil, and provide useful insight about parameter uncertainty for the assessment of the model outputs.
Figueiredo, Danilo Zucolli; Costa, Oswaldo Luiz do Valle
2017-10-01
This paper deals with the H2 optimal control problem of discrete-time Markov jump linear systems (MJLS) considering the case in which the Markov chain takes values in a general Borel space ?. It is assumed that the controller has access only to an output variable and to the jump parameter. The goal, in this case, is to design a dynamic Markov jump controller such that the H2-norm of the closed-loop system is minimised. It is shown that the H2-norm can be written as the sum of two H2-norms, such that one of them does not depend on the control, and the other one is obtained from the optimal filter for an infinite-horizon filtering problem. This result can be seen as a separation principle for MJLS with Markov chain in a Borel space ? considering the infinite time horizon case.
Kirchhoff, Michael
2018-03-01
Ramstead MJD, Badcock PB, Friston KJ. Answering Schrödinger's question: A free-energy formulation. Phys Life Rev 2018. https://doi.org/10.1016/j.plrev.2017.09.001 [this issue] motivate a multiscale characterisation of living systems in terms of hierarchically structured Markov blankets - a view of living systems as comprised of Markov blankets of Markov blankets [1-4]. It is effectively a treatment of what life is and how it is realised, cast in terms of how Markov blankets of living systems self-organise via active inference - a corollary of the free energy principle [5-7].
Nonequilibrium thermodynamic potentials for continuous-time Markov chains.
Verley, Gatien
2016-01-01
We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.
Stochastic model of milk homogenization process using Markov's chain
Directory of Open Access Journals (Sweden)
A. A. Khvostov
2016-01-01
Full Text Available The process of development of a mathematical model of the process of homogenization of dairy products is considered in the work. The theory of Markov's chains was used in the development of the mathematical model, Markov's chain with discrete states and continuous parameter for which the homogenisation pressure is taken, being the basis for the model structure. Machine realization of the model is implemented in the medium of structural modeling MathWorks Simulink™. Identification of the model parameters was carried out by minimizing the standard deviation calculated from the experimental data for each fraction of dairy products fat phase. As the set of experimental data processing results of the micrographic images of fat globules of whole milk samples distribution which were subjected to homogenization at different pressures were used. Pattern Search method was used as optimization method with the Latin Hypercube search algorithm from Global Optimization Тoolbox library. The accuracy of calculations averaged over all fractions of 0.88% (the relative share of units, the maximum relative error was 3.7% with the homogenization pressure of 30 MPa, which may be due to the very abrupt change in properties from the original milk in the particle size distribution at the beginning of the homogenization process and the lack of experimental data at homogenization pressures of below the specified value. The mathematical model proposed allows to calculate the profile of volume and mass distribution of the fat phase (fat globules in the product, depending on the homogenization pressure and can be used in the laboratory and research of dairy products composition, as well as in the calculation, design and modeling of the process equipment of the dairy industry enterprises.
HYDRA: a Java library for Markov Chain Monte Carlo
Directory of Open Access Journals (Sweden)
Gregory R. Warnes
2002-03-01
Full Text Available Hydra is an open-source, platform-neutral library for performing Markov Chain Monte Carlo. It implements the logic of standard MCMC samplers within a framework designed to be easy to use, extend, and integrate with other software tools. In this paper, we describe the problem that motivated our work, outline our goals for the Hydra pro ject, and describe the current features of the Hydra library. We then provide a step-by-step example of using Hydra to simulate from a mixture model drawn from cancer genetics, first using a variable-at-a-time Metropolis sampler and then a Normal Kernel Coupler. We conclude with a discussion of future directions for Hydra.
Snyder, Morgan E.; Waldron, John W. F.
2018-03-01
The deformation history of the Upper Paleozoic Maritimes Basin, Atlantic Canada, can be partially unraveled by examining fractures (joints, veins, and faults) that are well exposed on the shorelines of the macrotidal Bay of Fundy, in subsurface core, and on image logs. Data were collected from coastal outcrops and well core across the Windsor-Kennetcook subbasin, a subbasin in the Maritimes Basin, using the circular scan-line and vertical scan-line methods in outcrop, and FMI Image log analysis of core. We use cross-cutting and abutting relationships between fractures to understand relative timing of fracturing, followed by a statistical test (Markov chain analysis) to separate groups of fractures. This analysis, previously used in sedimentology, was modified to statistically test the randomness of fracture timing relationships. The results of the Markov chain analysis suggest that fracture initiation can be attributed to movement along the Minas Fault Zone, an E-W fault system that bounds the Windsor-Kennetcook subbasin to the north. Four sets of fractures are related to dextral strike slip along the Minas Fault Zone in the late Paleozoic, and four sets are related to sinistral reactivation of the same boundary in the Mesozoic.
Maximally reliable Markov chains under energy constraints.
Escola, Sean; Eisele, Michael; Miller, Kenneth; Paninski, Liam
2009-07-01
Signal-to-noise ratios in physical systems can be significantly degraded if the outputs of the systems are highly variable. Biological processes for which highly stereotyped signal generations are necessary features appear to have reduced their signal variabilities by employing multiple processing steps. To better understand why this multistep cascade structure might be desirable, we prove that the reliability of a signal generated by a multistate system with no memory (i.e., a Markov chain) is maximal if and only if the system topology is such that the process steps irreversibly through each state, with transition rates chosen such that an equal fraction of the total signal is generated in each state. Furthermore, our result indicates that by increasing the number of states, it is possible to arbitrarily increase the reliability of the system. In a physical system, however, an energy cost is associated with maintaining irreversible transitions, and this cost increases with the number of such transitions (i.e., the number of states). Thus, an infinite-length chain, which would be perfectly reliable, is infeasible. To model the effects of energy demands on the maximally reliable solution, we numerically optimize the topology under two distinct energy functions that penalize either irreversible transitions or incommunicability between states, respectively. In both cases, the solutions are essentially irreversible linear chains, but with upper bounds on the number of states set by the amount of available energy. We therefore conclude that a physical system for which signal reliability is important should employ a linear architecture, with the number of states (and thus the reliability) determined by the intrinsic energy constraints of the system.
On dynamic selection of households for direct marketing based on Markov chain models with memory
Otter, Pieter W.
A simple, dynamic selection procedure is proposed, based on conditional, expected profits using Markov chain models with memory. The method is easy to apply, only frequencies and mean values have to be calculated or estimated. The method is empirically illustrated using a data set from a charitable
spMC: an R-package for 3D lithological reconstructions based on spatial Markov chains
Sartore, Luca; Fabbri, Paolo; Gaetan, Carlo
2016-09-01
The paper presents the spatial Markov Chains (spMC) R-package and a case study of subsoil simulation/prediction located in a plain site of Northeastern Italy. spMC is a quite complete collection of advanced methods for data inspection, besides spMC implements Markov Chain models to estimate experimental transition probabilities of categorical lithological data. Furthermore, simulation methods based on most known prediction methods (as indicator Kriging and CoKriging) were implemented in spMC package. Moreover, other more advanced methods are available for simulations, e.g. path methods and Bayesian procedures, that exploit the maximum entropy. Since the spMC package was developed for intensive geostatistical computations, part of the code is implemented for parallel computations via the OpenMP constructs. A final analysis of this computational efficiency compares the simulation/prediction algorithms by using different numbers of CPU cores, and considering the example data set of the case study included in the package.
Weber, Juliane; Zachow, Christopher; Witthaut, Dirk
2018-03-01
Wind power generation exhibits a strong temporal variability, which is crucial for system integration in highly renewable power systems. Different methods exist to simulate wind power generation but they often cannot represent the crucial temporal fluctuations properly. We apply the concept of additive binary Markov chains to model a wind generation time series consisting of two states: periods of high and low wind generation. The only input parameter for this model is the empirical autocorrelation function. The two-state model is readily extended to stochastically reproduce the actual generation per period. To evaluate the additive binary Markov chain method, we introduce a coarse model of the electric power system to derive backup and storage needs. We find that the temporal correlations of wind power generation, the backup need as a function of the storage capacity, and the resting time distribution of high and low wind events for different shares of wind generation can be reconstructed.
Weber, Juliane; Zachow, Christopher; Witthaut, Dirk
2018-03-01
Wind power generation exhibits a strong temporal variability, which is crucial for system integration in highly renewable power systems. Different methods exist to simulate wind power generation but they often cannot represent the crucial temporal fluctuations properly. We apply the concept of additive binary Markov chains to model a wind generation time series consisting of two states: periods of high and low wind generation. The only input parameter for this model is the empirical autocorrelation function. The two-state model is readily extended to stochastically reproduce the actual generation per period. To evaluate the additive binary Markov chain method, we introduce a coarse model of the electric power system to derive backup and storage needs. We find that the temporal correlations of wind power generation, the backup need as a function of the storage capacity, and the resting time distribution of high and low wind events for different shares of wind generation can be reconstructed.
Short-term droughts forecast using Markov chain model in Victoria, Australia
Rahmat, Siti Nazahiyah; Jayasuriya, Niranjali; Bhuiyan, Muhammed A.
2017-07-01
A comprehensive risk management strategy for dealing with drought should include both short-term and long-term planning. The objective of this paper is to present an early warning method to forecast drought using the Standardised Precipitation Index (SPI) and a non-homogeneous Markov chain model. A model such as this is useful for short-term planning. The developed method has been used to forecast droughts at a number of meteorological monitoring stations that have been regionalised into six (6) homogenous clusters with similar drought characteristics based on SPI. The non-homogeneous Markov chain model was used to estimate drought probabilities and drought predictions up to 3 months ahead. The drought severity classes defined using the SPI were computed at a 12-month time scale. The drought probabilities and the predictions were computed for six clusters that depict similar drought characteristics in Victoria, Australia. Overall, the drought severity class predicted was quite similar for all the clusters, with the non-drought class probabilities ranging from 49 to 57 %. For all clusters, the near normal class had a probability of occurrence varying from 27 to 38 %. For the more moderate and severe classes, the probabilities ranged from 2 to 13 % and 3 to 1 %, respectively. The developed model predicted drought situations 1 month ahead reasonably well. However, 2 and 3 months ahead predictions should be used with caution until the models are developed further.
Vrugt, J.A.; Braak, ter C.J.F.; Clark, M.P.; Hyman, J.M.; Robinson, B.A.
2008-01-01
There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled
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
Bayesian inference in probabilistic risk assessment-The current state of the art
International Nuclear Information System (INIS)
Kelly, Dana L.; Smith, Curtis L.
2009-01-01
Markov chain Monte Carlo (MCMC) approaches to sampling directly from the joint posterior distribution of aleatory model parameters have led to tremendous advances in Bayesian inference capability in a wide variety of fields, including probabilistic risk analysis. The advent of freely available software coupled with inexpensive computing power has catalyzed this advance. This paper examines where the risk assessment community is with respect to implementing modern computational-based Bayesian approaches to inference. Through a series of examples in different topical areas, it introduces salient concepts and illustrates the practical application of Bayesian inference via MCMC sampling to a variety of important problems
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)
Bayesian inference for Hawkes processes
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Bayesian inference for Hawkes processes
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl
2013-01-01
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...... intensity function, while the second approach is based on an underlying clustering and branching structure in the Hawkes process. For practical use, MCMC (Markov chain Monte Carlo) methods are employed. The two approaches are compared numerically using three examples of the Hawkes process....
Zaib Jadoon, Khan; Umer Altaf, Muhammad; McCabe, Matthew Francis; Hoteit, Ibrahim; Muhammad, Nisar; Moghadas, Davood; Weihermüller, Lutz
2017-10-01
A substantial interpretation of electromagnetic induction (EMI) measurements requires quantifying optimal model parameters and uncertainty of a nonlinear inverse problem. For this purpose, an adaptive Bayesian Markov chain Monte Carlo (MCMC) algorithm is used to assess multi-orientation and multi-offset EMI measurements in an agriculture field with non-saline and saline soil. In MCMC the posterior distribution is computed using Bayes' rule. The electromagnetic forward model based on the full solution of Maxwell's equations was used to simulate the apparent electrical conductivity measured with the configurations of EMI instrument, the CMD Mini-Explorer. Uncertainty in the parameters for the three-layered earth model are investigated by using synthetic data. Our results show that in the scenario of non-saline soil, the parameters of layer thickness as compared to layers electrical conductivity are not very informative and are therefore difficult to resolve. Application of the proposed MCMC-based inversion to field measurements in a drip irrigation system demonstrates that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil, and provides useful insight about parameter uncertainty for the assessment of the model outputs.
Directory of Open Access Journals (Sweden)
K. Z. Jadoon
2017-10-01
Full Text Available A substantial interpretation of electromagnetic induction (EMI measurements requires quantifying optimal model parameters and uncertainty of a nonlinear inverse problem. For this purpose, an adaptive Bayesian Markov chain Monte Carlo (MCMC algorithm is used to assess multi-orientation and multi-offset EMI measurements in an agriculture field with non-saline and saline soil. In MCMC the posterior distribution is computed using Bayes' rule. The electromagnetic forward model based on the full solution of Maxwell's equations was used to simulate the apparent electrical conductivity measured with the configurations of EMI instrument, the CMD Mini-Explorer. Uncertainty in the parameters for the three-layered earth model are investigated by using synthetic data. Our results show that in the scenario of non-saline soil, the parameters of layer thickness as compared to layers electrical conductivity are not very informative and are therefore difficult to resolve. Application of the proposed MCMC-based inversion to field measurements in a drip irrigation system demonstrates that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil, and provides useful insight about parameter uncertainty for the assessment of the model outputs.
Jadoon, Khan Zaib
2017-10-26
A substantial interpretation of electromagnetic induction (EMI) measurements requires quantifying optimal model parameters and uncertainty of a nonlinear inverse problem. For this purpose, an adaptive Bayesian Markov chain Monte Carlo (MCMC) algorithm is used to assess multi-orientation and multi-offset EMI measurements in an agriculture field with non-saline and saline soil. In MCMC the posterior distribution is computed using Bayes\\' rule. The electromagnetic forward model based on the full solution of Maxwell\\'s equations was used to simulate the apparent electrical conductivity measured with the configurations of EMI instrument, the CMD Mini-Explorer. Uncertainty in the parameters for the three-layered earth model are investigated by using synthetic data. Our results show that in the scenario of non-saline soil, the parameters of layer thickness as compared to layers electrical conductivity are not very informative and are therefore difficult to resolve. Application of the proposed MCMC-based inversion to field measurements in a drip irrigation system demonstrates that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil, and provides useful insight about parameter uncertainty for the assessment of the model outputs.
Markov chain-based mass estimation method for loose part monitoring system and its performance
Directory of Open Access Journals (Sweden)
Sung-Hwan Shin
2017-10-01
Full Text Available A loose part monitoring system is used to identify unexpected loose parts in a nuclear reactor vessel or steam generator. It is still necessary for the mass estimation of loose parts, one function of a loose part monitoring system, to develop a new method due to the high estimation error of conventional methods such as Hertz's impact theory and the frequency ratio method. The purpose of this study is to propose a mass estimation method using a Markov decision process and compare its performance with a method using an artificial neural network model proposed in a previous study. First, how to extract feature vectors using discrete cosine transform was explained. Second, Markov chains were designed with codebooks obtained from the feature vector. A 1/8-scaled mockup of the reactor vessel for OPR1000 was employed, and all used signals were obtained by impacting its surface with several solid spherical masses. Next, the performance of mass estimation by the proposed Markov model was compared with that of the artificial neural network model. Finally, it was investigated that the proposed Markov model had matching error below 20% in mass estimation. That was a similar performance to the method using an artificial neural network model and considerably improved in comparison with the conventional methods.
Trcka, N.; Andova, S.; McIver, A.; D'Argenio, P.; Cuijpers, P.J.L.; Markovski, J.; Morgan, C.; Núñez, M.
2009-01-01
We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we consider Markov reward chains which are
Distance between configurations in Markov chain Monte Carlo simulations
Fukuma, Masafumi; Matsumoto, Nobuyuki; Umeda, Naoya
2017-12-01
For a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal form for the class of algorithms which generate local moves in the configuration space. We explicitly calculate the distance for the Langevin algorithm, and show that it certainly has desired and expected properties as distance. We further show that the distance for a multimodal distribution gets dramatically reduced from a large value by the introduction of a tempering method. We also argue that, when the original distribution is highly multimodal with large number of degenerate vacua, an anti-de Sitter-like geometry naturally emerges in the extended configuration space.
The behavior of Metropolis-coupled Markov chains when sampling rugged phylogenetic distributions.
Brown, Jeremy M; Thomson, Robert C
2018-02-15
Bayesian phylogenetic inference involves sampling from posterior distributions of trees, which sometimes exhibit local optima, or peaks, separated by regions of low posterior density. Markov chain Monte Carlo (MCMC) algorithms are the most widely used numerical method for generating samples from these posterior distributions, but they are susceptible to entrapment on individual optima in rugged distributions when they are unable to easily cross through or jump across regions of low posterior density. Ruggedness of posterior distributions can result from a variety of factors, including unmodeled variation in evolutionary processes and unrecognized variation in the true topology across sites or genes. Ruggedness can also become exaggerated when constraints are placed on topologies that require the presence or absence of particular bipartitions (often referred to as positive or negative constraints, respectively). These types of constraints are frequently employed when conducting tests of topological hypotheses (Bergsten et al. 2013; Brown and Thomson 2017). Negative constraints can lead to particularly rugged distributions when the data strongly support a forbidden clade, because monophyly of the clade can be disrupted by inserting outgroup taxa in many different ways. However, topological moves between the alternative disruptions are very difficult, because they require swaps between the inserted outgroup taxa while the data constrain taxa from the forbidden clade to remain close together on the tree. While this precise form of ruggedness is particular to negative constraints, trees with high posterior density can be separated by similarly complicated topological rearrangements, even in the absence of constraints.
Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness
Hervé, Loïc
2001-01-01
This book shows how techniques from the perturbation theory of operators, applied to a quasi-compact positive kernel, may be used to obtain limit theorems for Markov chains or to describe stochastic properties of dynamical systems. A general framework for this method is given and then applied to treat several specific cases. An essential element of this work is the description of the peripheral spectra of a quasi-compact Markov kernel and of its Fourier-Laplace perturbations. This is first done in the ergodic but non-mixing case. This work is extended by the second author to the non-ergodic case. The only prerequisites for this book are a knowledge of the basic techniques of probability theory and of notions of elementary functional analysis.
Strong diffusion formulation of Markov chain ensembles and its optimal weaker reductions
Güler, Marifi
2017-10-01
Two self-contained diffusion formulations, in the form of coupled stochastic differential equations, are developed for the temporal evolution of state densities over an ensemble of Markov chains evolving independently under a common transition rate matrix. Our first formulation derives from Kurtz's strong approximation theorem of density-dependent Markov jump processes [Stoch. Process. Their Appl. 6, 223 (1978), 10.1016/0304-4149(78)90020-0] and, therefore, strongly converges with an error bound of the order of lnN /N for ensemble size N . The second formulation eliminates some fluctuation variables, and correspondingly some noise terms, within the governing equations of the strong formulation, with the objective of achieving a simpler analytic formulation and a faster computation algorithm when the transition rates are constant or slowly varying. There, the reduction of the structural complexity is optimal in the sense that the elimination of any given set of variables takes place with the lowest attainable increase in the error bound. The resultant formulations are supported by numerical simulations.
Markov Chain Monte Carlo Methods
Indian Academy of Sciences (India)
Systat Software Asia-Pacific. Ltd., in Bangalore, where the technical work for the development of the statistical software Systat takes ... In Part 4, we discuss some applications of the Markov ... one can construct the joint probability distribution of.
Respondent-driven sampling as Markov chain Monte Carlo.
Goel, Sharad; Salganik, Matthew J
2009-07-30
Respondent-driven sampling (RDS) is a recently introduced, and now widely used, technique for estimating disease prevalence in hidden populations. RDS data are collected through a snowball mechanism, in which current sample members recruit future sample members. In this paper we present RDS as Markov chain Monte Carlo importance sampling, and we examine the effects of community structure and the recruitment procedure on the variance of RDS estimates. Past work has assumed that the variance of RDS estimates is primarily affected by segregation between healthy and infected individuals. We examine an illustrative model to show that this is not necessarily the case, and that bottlenecks anywhere in the networks can substantially affect estimates. We also show that variance is inflated by a common design feature in which the sample members are encouraged to recruit multiple future sample members. The paper concludes with suggestions for implementing and evaluating RDS studies.
Dettmer, Jan; Dosso, Stan E
2012-10-01
This paper develops a trans-dimensional approach to matched-field geoacoustic inversion, including interacting Markov chains to improve efficiency and an autoregressive model to account for correlated errors. The trans-dimensional approach and hierarchical seabed model allows inversion without assuming any particular parametrization by relaxing model specification to a range of plausible seabed models (e.g., in this case, the number of sediment layers is an unknown parameter). Data errors are addressed by sampling statistical error-distribution parameters, including correlated errors (covariance), by applying a hierarchical autoregressive error model. The well-known difficulty of low acceptance rates for trans-dimensional jumps is addressed with interacting Markov chains, resulting in a substantial increase in efficiency. The trans-dimensional seabed model and the hierarchical error model relax the degree of prior assumptions required in the inversion, resulting in substantially improved (more realistic) uncertainty estimates and a more automated algorithm. In particular, the approach gives seabed parameter uncertainty estimates that account for uncertainty due to prior model choice (layering and data error statistics). The approach is applied to data measured on a vertical array in the Mediterranean Sea.
Physical time scale in kinetic Monte Carlo simulations of continuous-time Markov chains.
Serebrinsky, Santiago A
2011-03-01
We rigorously establish a physical time scale for a general class of kinetic Monte Carlo algorithms for the simulation of continuous-time Markov chains. This class of algorithms encompasses rejection-free (or BKL) and rejection (or "standard") algorithms. For rejection algorithms, it was formerly considered that the availability of a physical time scale (instead of Monte Carlo steps) was empirical, at best. Use of Monte Carlo steps as a time unit now becomes completely unnecessary.
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...
Duan, Jinli; Jiao, Feng; Zhang, Qishan; Lin, Zhibin
2017-08-06
The sharp increase of the aging population has raised the pressure on the current limited medical resources in China. To better allocate resources, a more accurate prediction on medical service demand is very urgently needed. This study aims to improve the prediction on medical services demand in China. To achieve this aim, the study combines Taylor Approximation into the Grey Markov Chain model, and develops a new model named Taylor-Markov Chain GM (1,1) (T-MCGM (1,1)). The new model has been tested by adopting the historical data, which includes the medical service on treatment of diabetes, heart disease, and cerebrovascular disease from 1997 to 2015 in China. The model provides a predication on medical service demand of these three types of disease up to 2022. The results reveal an enormous growth of urban medical service demand in the future. The findings provide practical implications for the Health Administrative Department to allocate medical resources, and help hospitals to manage investments on medical facilities.
Inference of R 0 and Transmission Heterogeneity from the Size Distribution of Stuttering Chains
Blumberg, Seth; Lloyd-Smith, James O.
2013-01-01
For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer , but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, ) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in is detectable. In addition, by allowing for superspreading events, inference of shifts the threshold above which a transmission chain should be considered anomalously large for a given value of (thus reducing the probability of false alarms about pathogen adaptation). Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results. PMID:23658504
Zipf exponent of trajectory distribution in the hidden Markov model
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
DEFF Research Database (Denmark)
Xu, Shenzhi; Ai, Xiaomeng; Fang, Jiakun
2017-01-01
Photovoltaic (PV) power generation has made considerable developments in recent years. But its intermittent and volatility of its output has seriously affected the security operation of the power system. In order to better understand the PV generation and provide sufficient data support...... for analysis the impacts, a novel generation method for PV power time series combining decomposition technique and Markov chain theory is presented in this paper. It digs important factors from historical data from existing PV plants and then reproduce new data with similar patterns. In detail, the proposed...... method first decomposes the PV power time series into ideal output curve, amplitude parameter series and random fluctuating component three parts. Then generating daily ideal output curve by the extraction of typical daily data, amplitude parameter series based on the Markov chain Monte Carlo (MCMC...
International Nuclear Information System (INIS)
Mayzelis, Z.A.; Apostolov, S.S.; Melnyk, S.S.; Usatenko, O.V.; Yampol'skii, V.A.
2007-01-01
A theory of symbolic dynamic systems with long-range correlations based on the consideration of the binary N-step Markov chains developed earlier in Phys Rev Lett 2003;90:110601 is generalized to the biased case (non-equal numbers of zeros and unities in the chain). In the model, the conditional probability that the ith symbol in the chain equals zero (or unity) is a linear function of the number of unities (zeros) among the preceding N symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length L are obtained analytically and verified by numerical simulations. A self-similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented. The diffusion Fokker-Planck equation governing the distribution function of the L-words is explored. If the persistent correlations are not extremely strong, the distribution function is shown to be the Gaussian with the variance being nonlinearly dependent on L. An equation connecting the memory and correlation function of the additive Markov chain is presented. This equation allows reconstructing a memory function using a correlation function of the system. Effectiveness and robustness of the proposed method is demonstrated by simple model examples. Memory functions of concrete coarse-grained literary texts are found and their universal power-law behavior at long distances is revealed
Energy Technology Data Exchange (ETDEWEB)
Mayzelis, Z.A. [Department of Physics, Kharkov National University, 4 Svoboda Sq., Kharkov 61077 (Ukraine); Apostolov, S.S. [Department of Physics, Kharkov National University, 4 Svoboda Sq., Kharkov 61077 (Ukraine); Melnyk, S.S. [A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov (Ukraine); Usatenko, O.V. [A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov (Ukraine)]. E-mail: usatenko@ire.kharkov.ua; Yampol' skii, V.A. [A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov (Ukraine)
2007-10-15
A theory of symbolic dynamic systems with long-range correlations based on the consideration of the binary N-step Markov chains developed earlier in Phys Rev Lett 2003;90:110601 is generalized to the biased case (non-equal numbers of zeros and unities in the chain). In the model, the conditional probability that the ith symbol in the chain equals zero (or unity) is a linear function of the number of unities (zeros) among the preceding N symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length L are obtained analytically and verified by numerical simulations. A self-similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented. The diffusion Fokker-Planck equation governing the distribution function of the L-words is explored. If the persistent correlations are not extremely strong, the distribution function is shown to be the Gaussian with the variance being nonlinearly dependent on L. An equation connecting the memory and correlation function of the additive Markov chain is presented. This equation allows reconstructing a memory function using a correlation function of the system. Effectiveness and robustness of the proposed method is demonstrated by simple model examples. Memory functions of concrete coarse-grained literary texts are found and their universal power-law behavior at long distances is revealed.
Entropy and long-range memory in random symbolic additive Markov chains.
Melnik, S S; Usatenko, O V
2016-06-01
The goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov chain with long-range memory. Supposing that the correlations between random elements of the chain are weak, we express the conditional entropy of the sequence by means of the symbolic pair correlation function. We also examine an algorithm for estimating the conditional entropy of finite symbolic sequences. We show that the entropy contains two contributions, i.e., the correlation and the fluctuation. The obtained analytical results are used for numerical evaluation of the entropy of written English texts and DNA nucleotide sequences. The developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short-range and weak long-range memory.
Application of the Markov chain approximation to the sunspot observations
International Nuclear Information System (INIS)
Onal, M.
1988-01-01
The positions of the 13,588 sunspot groups observed during the cycle of 1950-1960 at the Istanbul University Observatory have been corrected for the effect of differential rotation. The evolution probability of a sunspot group to the other one in the same region have been determined. By using the Markov chain approximation, the types of these groups and their transition probabilities during the following activity cycle (1950-1960), and the concentration of active regions during 1950-1960 have been estimated. The transition probabilities from the observations of the activity cycle 1960-1970 have been compared with the predicted transition probabilities and a good correlation has been noted. 5 refs.; 2 tabs
Exact Markov chains versus diffusion theory for haploid random mating.
Tyvand, Peder A; Thorvaldsen, Steinar
2010-05-01
Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck. 2010 Elsevier Inc. All rights reserved.
A high-fidelity weather time series generator using the Markov Chain process on a piecewise level
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.
A joint logistic regression and covariate-adjusted continuous-time Markov chain model.
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.
Characterizing Quality Factor of Niobium Resonators Using a Markov Chain Monte Carlo Approach
Energy Technology Data Exchange (ETDEWEB)
Basu Thakur, Ritoban; Tang, Qing Yang; McGeehan, Ryan; Carter, Faustin; Shirokoff, Erik
2017-06-01
The next generation of radiation detectors in high precision Cosmology, Astronomy, and particle-astrophysics experiments will rely heavily on superconducting microwave resonators and kinetic inductance devices. Understanding the physics of energy loss in these devices, in particular at low temperatures and powers, is vital. We present a comprehensive analysis framework, using Markov Chain Monte Carlo methods, to characterize loss due to two-level system in concert with quasi-particle dynamics in thin-film Nb resonators in the GHz range.
Inhomogeneous Markov point processes by transformation
DEFF Research Database (Denmark)
Jensen, Eva B. Vedel; Nielsen, Linda Stougaard
2000-01-01
We construct parametrized models for point processes, allowing for both inhomogeneity and interaction. The inhomogeneity is obtained by applying parametrized transformations to homogeneous Markov point processes. An interesting model class, which can be constructed by this transformation approach......, is that of exponential inhomogeneous Markov point processes. Statistical inference For such processes is discussed in some detail....
Optimization of hospital ward resources with patient relocation using Markov chain modeling
DEFF Research Database (Denmark)
Andersen, Anders Reenberg; Nielsen, Bo Friis; Reinhardt, Line Blander
2017-01-01
available to the hospital. Patient flow is modeled using a homogeneous continuous-time Markov chain and optimization is conducted using a local search heuristic. Our model accounts for patient relocation, which has not been done analytically in literature with similar scope. The study objective is to ensure...... are distributed. Furthermore, our heuristic is found to efficiently derive the optimal solution. Applying our model to the hospital case, we found that relocation of daily arrivals can be reduced by 11.7% by re-distributing beds that are already available to the hospital....
Inference of R(0 and transmission heterogeneity from the size distribution of stuttering chains.
Directory of Open Access Journals (Sweden)
Seth Blumberg
Full Text Available For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, [Formula: see text] and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring [Formula: see text] and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer [Formula: see text], but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, [Formula: see text] has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both [Formula: see text] and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for [Formula: see text] is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in [Formula: see text] is detectable. In addition, by allowing for superspreading events, inference of [Formula: see text] shifts the threshold above which a transmission chain should be considered anomalously large for a given value of [Formula: see text] (thus reducing the probability of false alarms about pathogen adaptation. Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results.
Inference on inspiral signals using LISA MLDC data
International Nuclear Information System (INIS)
Roever, Christian; Stroeer, Alexander; Bloomer, Ed; Christensen, Nelson; Clark, James; Hendry, Martin; Messenger, Chris; Meyer, Renate; Pitkin, Matt; Toher, Jennifer; Umstaetter, Richard; Vecchio, Alberto; Veitch, John; Woan, Graham
2007-01-01
In this paper, we describe a Bayesian inference framework for the analysis of data obtained by LISA. We set up a model for binary inspiral signals as defined for the Mock LISA Data Challenge 1.2 (MLDC), and implemented a Markov chain Monte Carlo (MCMC) algorithm to facilitate exploration and integration of the posterior distribution over the nine-dimensional parameter space. Here, we present intermediate results showing how, using this method, information about the nine parameters can be extracted from the data
[Analysis and modelling of safety culture in a Mexican hospital by Markov chains].
Velázquez-Martínez, J D; Cruz-Suárez, H; Santos-Reyes, J
2016-01-01
The objective of this study was to analyse and model the safety culture with Markov chains, as well as predicting and/or prioritizing over time the evolutionary behaviour of the safety culture of the health's staff in one Mexican hospital. The Markov chain theory has been employed in the analysis, and the input data has been obtained from a previous study based on the Safety Attitude Questionnaire (CAS-MX-II), by considering the following 6 dimensions: safety climate, teamwork, job satisfaction, recognition of stress, perception of management, and work environment. The results highlighted the predictions and/or prioritisation of the approximate time for the possible integration into the evolutionary behaviour of the safety culture as regards the "slightly agree" (Likert scale) for: safety climate (in 12 years; 24.13%); teamwork (8 years; 34.61%); job satisfaction (11 years; 52.41%); recognition of the level of stress (8 years; 19.35%); and perception of the direction (22 years; 27.87%). The work environment dimension was unable to determine the behaviour of staff information, i.e. no information cultural roots were obtained. In general, it has been shown that there are weaknesses in the safety culture of the hospital, which is an opportunity to suggest changes to the mandatory policies in order to strengthen it. Copyright © 2016 SECA. Publicado por Elsevier España, S.L.U. All rights reserved.
MCMC-ODPR: Primer design optimization using Markov Chain Monte Carlo sampling
Directory of Open Access Journals (Sweden)
Kitchen James L
2012-11-01
Full Text Available Abstract Background Next generation sequencing technologies often require numerous primer designs that require good target coverage that can be financially costly. We aimed to develop a system that would implement primer reuse to design degenerate primers that could be designed around SNPs, thus find the fewest necessary primers and the lowest cost whilst maintaining an acceptable coverage and provide a cost effective solution. We have implemented Metropolis-Hastings Markov Chain Monte Carlo for optimizing primer reuse. We call it the Markov Chain Monte Carlo Optimized Degenerate Primer Reuse (MCMC-ODPR algorithm. Results After repeating the program 1020 times to assess the variance, an average of 17.14% fewer primers were found to be necessary using MCMC-ODPR for an equivalent coverage without implementing primer reuse. The algorithm was able to reuse primers up to five times. We compared MCMC-ODPR with single sequence primer design programs Primer3 and Primer-BLAST and achieved a lower primer cost per amplicon base covered of 0.21 and 0.19 and 0.18 primer nucleotides on three separate gene sequences, respectively. With multiple sequences, MCMC-ODPR achieved a lower cost per base covered of 0.19 than programs BatchPrimer3 and PAMPS, which achieved 0.25 and 0.64 primer nucleotides, respectively. Conclusions MCMC-ODPR is a useful tool for designing primers at various melting temperatures at good target coverage. By combining degeneracy with optimal primer reuse the user may increase coverage of sequences amplified by the designed primers at significantly lower costs. Our analyses showed that overall MCMC-ODPR outperformed the other primer-design programs in our study in terms of cost per covered base.
MCMC-ODPR: primer design optimization using Markov Chain Monte Carlo sampling.
Kitchen, James L; Moore, Jonathan D; Palmer, Sarah A; Allaby, Robin G
2012-11-05
Next generation sequencing technologies often require numerous primer designs that require good target coverage that can be financially costly. We aimed to develop a system that would implement primer reuse to design degenerate primers that could be designed around SNPs, thus find the fewest necessary primers and the lowest cost whilst maintaining an acceptable coverage and provide a cost effective solution. We have implemented Metropolis-Hastings Markov Chain Monte Carlo for optimizing primer reuse. We call it the Markov Chain Monte Carlo Optimized Degenerate Primer Reuse (MCMC-ODPR) algorithm. After repeating the program 1020 times to assess the variance, an average of 17.14% fewer primers were found to be necessary using MCMC-ODPR for an equivalent coverage without implementing primer reuse. The algorithm was able to reuse primers up to five times. We compared MCMC-ODPR with single sequence primer design programs Primer3 and Primer-BLAST and achieved a lower primer cost per amplicon base covered of 0.21 and 0.19 and 0.18 primer nucleotides on three separate gene sequences, respectively. With multiple sequences, MCMC-ODPR achieved a lower cost per base covered of 0.19 than programs BatchPrimer3 and PAMPS, which achieved 0.25 and 0.64 primer nucleotides, respectively. MCMC-ODPR is a useful tool for designing primers at various melting temperatures at good target coverage. By combining degeneracy with optimal primer reuse the user may increase coverage of sequences amplified by the designed primers at significantly lower costs. Our analyses showed that overall MCMC-ODPR outperformed the other primer-design programs in our study in terms of cost per covered base.
Markov Chain Monte Carlo Bayesian Learning for Neural Networks
Goodrich, Michael S.
2011-01-01
Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.
Kinetics and thermodynamics of first-order Markov chain copolymerization
Energy Technology Data Exchange (ETDEWEB)
Gaspard, P.; Andrieux, D. [Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels (Belgium)
2014-07-28
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer.
On the multi-level solution algorithm for Markov chains
Energy Technology Data Exchange (ETDEWEB)
Horton, G. [Univ. of Erlangen, Nuernberg (Germany)
1996-12-31
We discuss the recently introduced multi-level algorithm for the steady-state solution of Markov chains. The method is based on the aggregation principle, which is well established in the literature. Recursive application of the aggregation yields a multi-level method which has been shown experimentally to give results significantly faster than the methods currently in use. The algorithm can be reformulated as an algebraic multigrid scheme of Galerkin-full approximation type. The uniqueness of the scheme stems from its solution-dependent prolongation operator which permits significant computational savings in the evaluation of certain terms. This paper describes the modeling of computer systems to derive information on performance, measured typically as job throughput or component utilization, and availability, defined as the proportion of time a system is able to perform a certain function in the presence of component failures and possibly also repairs.
Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains.
Reich, W; Scheuermann, G
2012-12-01
Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In our paper we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov-Chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies.
Rate Reduction for State-labelled Markov Chains with Upper Time-bounded CSL Requirements
Directory of Open Access Journals (Sweden)
Bharath Siva Kumar Tati
2016-07-01
Full Text Available This paper presents algorithms for identifying and reducing a dedicated set of controllable transition rates of a state-labelled continuous-time Markov chain model. The purpose of the reduction is to make states to satisfy a given requirement, specified as a CSL upper time-bounded Until formula. We distinguish two different cases, depending on the type of probability bound. A natural partitioning of the state space allows us to develop possible solutions, leading to simple algorithms for both cases.
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.
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.
Potential-Decomposition Strategy in Markov Chain Monte Carlo Sampling Algorithms
International Nuclear Information System (INIS)
Shangguan Danhua; Bao Jingdong
2010-01-01
We introduce the potential-decomposition strategy (PDS), which can he used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in phase space, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner. Furthermore, if the accepted trial samples are insufficient, they can be recycled as initial states to form more unbiased samples. This strategy can greatly improve efficiency when the original potential has multiple metastable states separated by large barriers. We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating in these two representative examples that convergence is accelerated by orders of magnitude.
Energy Technology Data Exchange (ETDEWEB)
Adaro, Jorge; Cesari, Daniela; Lema, Alba; Galimberti, Pablo [Universidad Nacional de Rio Cuarto (Argentina). Facultad de Ingenieria]. E-mail: aadaro@ing.unrc.edu.ar
2000-07-01
The objective of the present work is to adopt a methodology that allows to generate sequences of values of global solar radiation. It is carried out a preliminary study on the generation of radiation sequence a concept of Chains of Markov. For it is analyzed it the readiness of data and it is investigated about the possibility of using such a methodology calculating values of indexes of clarity previously. With data of available radiation and provided the National Meteorological Service for Rio Cuarto, the preliminary study is carried out the preliminary study looking for to validated the pattern to the effects of being able to transfer the use of the methodology in other regions. (author)
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.
First and second order Markov chain models for synthetic generation of wind speed time series
International Nuclear Information System (INIS)
Shamshad, A.; Bawadi, M.A.; Wan Hussin, W.M.A.; Majid, T.A.; Sanusi, S.A.M.
2005-01-01
Hourly wind speed time series data of two meteorological stations in Malaysia have been used for stochastic generation of wind speed data using the transition matrix approach of the Markov chain process. The transition probability matrices have been formed using two different approaches: the first approach involves the use of the first order transition probability matrix of a Markov chain, and the second involves the use of a second order transition probability matrix that uses the current and preceding values to describe the next wind speed value. The algorithm to generate the wind speed time series from the transition probability matrices is described. Uniform random number generators have been used for transition between successive time states and within state wind speed values. The ability of each approach to retain the statistical properties of the generated speed is compared with the observed ones. The main statistical properties used for this purpose are mean, standard deviation, median, percentiles, Weibull distribution parameters, autocorrelations and spectral density of wind speed values. The comparison of the observed wind speed and the synthetically generated ones shows that the statistical characteristics are satisfactorily preserved
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.
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.)
Simulating reservoir lithologies by an actively conditioned Markov chain model
Feng, Runhai; Luthi, Stefan M.; Gisolf, Dries
2018-06-01
The coupled Markov chain model can be used to simulate reservoir lithologies between wells, by conditioning them on the observed data in the cored wells. However, with this method, only the state at the same depth as the current cell is going to be used for conditioning, which may be a problem if the geological layers are dipping. This will cause the simulated lithological layers to be broken or to become discontinuous across the reservoir. In order to address this problem, an actively conditioned process is proposed here, in which a tolerance angle is predefined. The states contained in the region constrained by the tolerance angle will be employed for conditioning in the horizontal chain first, after which a coupling concept with the vertical chain is implemented. In order to use the same horizontal transition matrix for different future states, the tolerance angle has to be small. This allows the method to work in reservoirs without complex structures caused by depositional processes or tectonic deformations. Directional artefacts in the modeling process are avoided through a careful choice of the simulation path. The tolerance angle and dipping direction of the strata can be obtained from a correlation between wells, or from seismic data, which are available in most hydrocarbon reservoirs, either by interpretation or by inversion that can also assist the construction of a horizontal probability matrix.
Steen Magnussen
2009-01-01
Areas burned annually in 29 Canadian forest fire regions show a patchy and irregular correlation structure that significantly influences the distribution of annual totals for Canada and for groups of regions. A binary Monte Carlo Markov Chain (MCMC) is constructed for the purpose of joint simulation of regional areas burned in forest fires. For each year the MCMC...
A Multistep Extending Truncation Method towards Model Construction of Infinite-State Markov Chains
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Kemin Wang
2014-01-01
Full Text Available The model checking of Infinite-State Continuous Time Markov Chains will inevitably encounter the state explosion problem when constructing the CTMCs model; our method is to get a truncated model of the infinite one; to get a sufficient truncated model to meet the model checking of Continuous Stochastic Logic based system properties, we propose a multistep extending advanced truncation method towards model construction of CTMCs and implement it in the INFAMY model checker; the experiment results show that our method is effective.
Schofield, Jeremy; Bayat, Hanif
2014-09-07
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the
International Nuclear Information System (INIS)
Schofield, Jeremy; Bayat, Hanif
2014-01-01
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the
Energy Technology Data Exchange (ETDEWEB)
Schofield, Jeremy, E-mail: jmschofi@chem.utoronto.ca; Bayat, Hanif, E-mail: hbayat@chem.utoronto.ca [Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)
2014-09-07
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the
Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution
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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
Travel Cost Inference from Sparse, Spatio-Temporally Correlated Time Series Using Markov Models
DEFF Research Database (Denmark)
Yang, Bin; Guo, Chenjuan; Jensen, Christian S.
2013-01-01
of such time series offers insight into the underlying system and enables prediction of system behavior. While the techniques presented in the paper apply more generally, we consider the case of transportation systems and aim to predict travel cost from GPS tracking data from probe vehicles. Specifically, each...... road segment has an associated travel-cost time series, which is derived from GPS data. We use spatio-temporal hidden Markov models (STHMM) to model correlations among different traffic time series. We provide algorithms that are able to learn the parameters of an STHMM while contending...... with the sparsity, spatio-temporal correlation, and heterogeneity of the time series. Using the resulting STHMM, near future travel costs in the transportation network, e.g., travel time or greenhouse gas emissions, can be inferred, enabling a variety of routing services, e.g., eco-routing. Empirical studies...
A new fuzzy Monte Carlo method for solving SLAE with ergodic fuzzy Markov chains
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Maryam Gharehdaghi
2015-05-01
Full Text Available In this paper we introduce a new fuzzy Monte Carlo method for solving system of linear algebraic equations (SLAE over the possibility theory and max-min algebra. To solve the SLAE, we first define a fuzzy estimator and prove that this is an unbiased estimator of the solution. To prove unbiasedness, we apply the ergodic fuzzy Markov chains. This new approach works even for cases with coefficients matrix with a norm greater than one.
Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue
2014-11-01
Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011)PLEEE81539-375510.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011)JMBLAJ0303-681210.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.
Dependability analysis of systems modeled by non-homogeneous Markov chains
Energy Technology Data Exchange (ETDEWEB)
Platis, Agapios; Limnios, Nikolaos; Le Du, Marc
1998-09-01
The case of time non-homogeneous Markov systems in discrete time is studied in this article. In order to have measures adapted to this kind of systems, some reliability and performability measures are formulated, such as reliability, availability, maintainability and different time variables including new indicators more dedicated to electrical systems like instantaneous expected load curtailed and the expected energy not supplied on a time interval. The previous indicators are also formulated in the case of cyclic chains where asymptotic results can be obtained. The interest of taking into account hazard rate time variation, is to get more accurate and more instructive indicators but also be able to access new performability indicators that cannot be obtained by classical methods. To illustrate this, an example from an Electricite De France electrical substation is solved.
Lu, Dan; Ricciuto, Daniel; Walker, Anthony; Safta, Cosmin; Munger, William
2017-09-01
Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.
Monte Carlo algorithms with absorbing Markov chains: Fast local algorithms for slow dynamics
International Nuclear Information System (INIS)
Novotny, M.A.
1995-01-01
A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest order of these algorithms reduces to the n-fold way algorithm. These algorithms are applied to study the escape from the metastable state in the two-dimensional square-lattice nearest-neighbor Ising ferromagnet in an unfavorable applied field, and the agreement with theoretical predictions is very good. It is demonstrated that the higher-order algorithms can be many orders of magnitude faster than either the traditional Monte Carlo or n-fold way algorithms
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.
Directory of Open Access Journals (Sweden)
Weimin Chen
2014-01-01
Full Text Available The standard approach to studying financial industrial agglomeration is to construct measures of the degree of agglomeration within financial industry. But such measures often fail to exploit the convergence or divergence of financial agglomeration. In this paper, we apply Markov chain approach to diagnose the convergence of financial agglomeration in China based on the location quotient coefficients across the provincial regions over 1993–2011. The estimation of Markov transition probability matrix offers more detailed insights into the mechanics of financial agglomeration evolution process in China during the research period. The results show that the spatial evolution of financial agglomeration changes faster in the period of 2003–2011 than that in the period of 1993–2002. Furthermore, there exists a very uneven financial development patterns, but there is regional convergence for financial agglomeration in China.
A stochastic Markov chain model to describe lung cancer growth and metastasis.
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Paul K Newton
Full Text Available A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold. Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.
A stochastic Markov chain model to describe lung cancer growth and metastasis.
Newton, Paul K; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila A; Nieva, Jorge; Kuhn, Peter
2012-01-01
A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.
Farr, W. M.; Mandel, I.; Stevens, D.
2015-01-01
Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient ‘global’ proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580
De Sanctis, Bianca; Krukov, Ivan; de Koning, A P Jason
2017-09-19
Determination of the age of an allele based on its population frequency is a well-studied problem in population genetics, for which a variety of approximations have been proposed. We present a new result that, surprisingly, allows the expectation and variance of allele age to be computed exactly (within machine precision) for any finite absorbing Markov chain model in a matter of seconds. This approach makes none of the classical assumptions (e.g., weak selection, reversibility, infinite sites), exploits modern sparse linear algebra techniques, integrates over all sample paths, and is rapidly computable for Wright-Fisher populations up to N e = 100,000. With this approach, we study the joint effect of recurrent mutation, dominance, and selection, and demonstrate new examples of "selective strolls" where the classical symmetry of allele age with respect to selection is violated by weakly selected alleles that are older than neutral alleles at the same frequency. We also show evidence for a strong age imbalance, where rare deleterious alleles are expected to be substantially older than advantageous alleles observed at the same frequency when population-scaled mutation rates are large. These results highlight the under-appreciated utility of computational methods for the direct analysis of Markov chain models in population genetics.
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.
Modeling and Computing of Stock Index Forecasting Based on Neural Network and Markov Chain
Dai, Yonghui; Han, Dongmei; Dai, Weihui
2014-01-01
The stock index reflects the fluctuation of the stock market. For a long time, there have been a lot of researches on the forecast of stock index. However, the traditional method is limited to achieving an ideal precision in the dynamic market due to the influences of many factors such as the economic situation, policy changes, and emergency events. Therefore, the approach based on adaptive modeling and conditional probability transfer causes the new attention of researchers. This paper presents a new forecast method by the combination of improved back-propagation (BP) neural network and Markov chain, as well as its modeling and computing technology. This method includes initial forecasting by improved BP neural network, division of Markov state region, computing of the state transition probability matrix, and the prediction adjustment. Results of the empirical study show that this method can achieve high accuracy in the stock index prediction, and it could provide a good reference for the investment in stock market. PMID:24782659
Modeling and Computing of Stock Index Forecasting Based on Neural Network and Markov Chain
Directory of Open Access Journals (Sweden)
Yonghui Dai
2014-01-01
Full Text Available The stock index reflects the fluctuation of the stock market. For a long time, there have been a lot of researches on the forecast of stock index. However, the traditional method is limited to achieving an ideal precision in the dynamic market due to the influences of many factors such as the economic situation, policy changes, and emergency events. Therefore, the approach based on adaptive modeling and conditional probability transfer causes the new attention of researchers. This paper presents a new forecast method by the combination of improved back-propagation (BP neural network and Markov chain, as well as its modeling and computing technology. This method includes initial forecasting by improved BP neural network, division of Markov state region, computing of the state transition probability matrix, and the prediction adjustment. Results of the empirical study show that this method can achieve high accuracy in the stock index prediction, and it could provide a good reference for the investment in stock market.
The use of Markov chains in forecasting wind speed: Matlab source code and applied case study
Directory of Open Access Journals (Sweden)
Ionuţ Alexandru Petre
2017-01-01
Full Text Available The ability to predict the wind speed has an important role for renewable energy industry which relies on wind speed forecasts in order to calculate the power a wind farm can produce in an area. There are several well-known methods to predict wind speed, but in this paper we focus on short-term wind forecasting using Markov chains. Often gaps can be found in the time series of the wind speed measurements and repeating the measurements is usually not a valid option. In this study it is shown that using Markov chains these gaps from the time series can be filled (they can be generated in an efficient way, but only when the missing data is for a short period of time. Also, the developed Matlab programms that are used in the case study, are included in the paper beeing presented and commented by the authors. In the case study data from a wind farm in Italy is used. The available data are as average wind speed at an interval of 10 minutes in the time period 11/23/2005 - 4/27/2006.
Kieftenbeld, Vincent; Natesan, Prathiba
2012-01-01
Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…
A general Bayes weibull inference model for accelerated life testing
International Nuclear Information System (INIS)
Dorp, J. Rene van; Mazzuchi, Thomas A.
2005-01-01
This article presents the development of a general Bayes inference model for accelerated life testing. The failure times at a constant stress level are assumed to belong to a Weibull distribution, but the specification of strict adherence to a parametric time-transformation function is not required. Rather, prior information is used to indirectly define a multivariate prior distribution for the scale parameters at the various stress levels and the common shape parameter. Using the approach, Bayes point estimates as well as probability statements for use-stress (and accelerated) life parameters may be inferred from a host of testing scenarios. The inference procedure accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The inference procedure uses the well-known MCMC (Markov Chain Monte Carlo) methods to derive posterior approximations. The approach is illustrated with an example
Fisher information and asymptotic normality in system identification for quantum Markov chains
International Nuclear Information System (INIS)
Guta, Madalin
2011-01-01
This paper deals with the problem of estimating the coupling constant θ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of θ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of θ=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.
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...
A Novel Method for Decoding Any High-Order Hidden Markov Model
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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.
System reliability analysis and introduction to modelisation by means of Markov chains
International Nuclear Information System (INIS)
Doyon, L.R.
1977-01-01
A new method to solve simultaneously all models of availability, reliability and maintenaibility for a complex system is described. This analysis is obtained more exactly by using time-intervals between failures and times to repare with probability laws and maintenance policies most adapted to the problem. The expression of this computation, using MARKOV chains corresponds perfectly to computer-language and results very short machine operation times. The procedure necessary for the use of APAFS program operationnal at the CISI (Compagnie Internationale de Services en Informatique) is also described. Thus, a very important tool is now available to designers without any requirement in programming knowledge [fr
Zhang, D.; Liao, Q.
2016-12-01
The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of
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....
International Nuclear Information System (INIS)
Kwon, Hyuk; Min, Byung Joo; Lee, Eui Jin; You, Byung Hoon
2006-01-01
According to the recent report by the OECD/NEA, there is a large imbalance between supply and demand of human resource in nuclear field. In the U.S., according to survey of Nuclear Engineering Department Heads Organization (NEDHO), 174 graduates in B.S or M.S degree were fed to nuclear industry in year 2004. Meanwhile, the total amount of demand in nuclear industry was about 642 engineers, which was approximately three times of the supply. In case of other developed western nations, the OECD/NEA report stated that the level of imbalance is similar to that of the U.S. However, nations having nuclear power development programs such as Korea, Japan and France seem to be in a different environment of supply and demand from that of the U.S. In this study, the difference of manpower status between the U.S and Korea has been investigated and the nuclear manpower required for the future in Korea is predicted. To investigate the factors making difference between the U.S. and NPP developing countries including Korea, a quantitative manpower planning model, Markov chains model, is applied. Since the Markov chains model has the strength of analyzing an inflow or push structure, the model fits the system governed by the inflow of manpower. A macroscopic status of manpower demand on nuclear industry is calculated up to 2015 using the Job coefficient (JC) and GDP, which are derived from the Survey for Roadmap of Electric Power Industry Manpower Planning. Furthermore, the total numbers of required manpower and supplied manpower up to 2030 were predicted by JC and Markov Chains model, respectively. Whereas the employee status of nuclear industries has been annually investigated by KAIF since 1995, the following data from the 10 th survey and nuclear energy yearbooks from 1998 to 2005 are applied; (a) the status of the manpower demand of industry, (b) number of students entering, graduating and getting job in nuclear engineering
Energy Technology Data Exchange (ETDEWEB)
Kwon, Hyuk; Min, Byung Joo; Lee, Eui Jin; You, Byung Hoon [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
2006-07-01
According to the recent report by the OECD/NEA, there is a large imbalance between supply and demand of human resource in nuclear field. In the U.S., according to survey of Nuclear Engineering Department Heads Organization (NEDHO), 174 graduates in B.S or M.S degree were fed to nuclear industry in year 2004. Meanwhile, the total amount of demand in nuclear industry was about 642 engineers, which was approximately three times of the supply. In case of other developed western nations, the OECD/NEA report stated that the level of imbalance is similar to that of the U.S. However, nations having nuclear power development programs such as Korea, Japan and France seem to be in a different environment of supply and demand from that of the U.S. In this study, the difference of manpower status between the U.S and Korea has been investigated and the nuclear manpower required for the future in Korea is predicted. To investigate the factors making difference between the U.S. and NPP developing countries including Korea, a quantitative manpower planning model, Markov chains model, is applied. Since the Markov chains model has the strength of analyzing an inflow or push structure, the model fits the system governed by the inflow of manpower. A macroscopic status of manpower demand on nuclear industry is calculated up to 2015 using the Job coefficient (JC) and GDP, which are derived from the Survey for Roadmap of Electric Power Industry Manpower Planning. Furthermore, the total numbers of required manpower and supplied manpower up to 2030 were predicted by JC and Markov Chains model, respectively. Whereas the employee status of nuclear industries has been annually investigated by KAIF since 1995, the following data from the 10{sup th} survey and nuclear energy yearbooks from 1998 to 2005 are applied; (a) the status of the manpower demand of industry, (b) number of students entering, graduating and getting job in nuclear engineering.
Solution of the Markov chain for the dead time problem
International Nuclear Information System (INIS)
Degweker, S.B.
1997-01-01
A method for solving the equation for the Markov chain, describing the effect of a non-extendible dead time on the statistics of time correlated pulses, is discussed. The equation, which was derived in an earlier paper, describes a non-linear process and is not amenable to exact solution. The present method consists of representing the probability generating function as a factorial cumulant expansion and neglecting factorial cumulants beyond the second. This results in a closed set of non-linear equations for the factorial moments. Stationary solutions of these equations, which are of interest for calculating the count rate, are obtained iteratively. The method is applied to the variable dead time counter technique for estimation of system parameters in passive neutron assay of Pu and reactor noise analysis. Comparisons of results by this method with Monte Carlo calculations are presented. (author)
BAYESIAN INFERENCE OF CMB GRAVITATIONAL LENSING
Energy Technology Data Exchange (ETDEWEB)
Anderes, Ethan [Department of Statistics, University of California, Davis, CA 95616 (United States); Wandelt, Benjamin D.; Lavaux, Guilhem [Sorbonne Universités, UPMC Univ Paris 06 and CNRS, UMR7095, Institut d’Astrophysique de Paris, F-75014, Paris (France)
2015-08-01
The Planck satellite, along with several ground-based telescopes, has mapped the cosmic microwave background (CMB) at sufficient resolution and signal-to-noise so as to allow a detection of the subtle distortions due to the gravitational influence of the intervening matter distribution. A natural modeling approach is to write a Bayesian hierarchical model for the lensed CMB in terms of the unlensed CMB and the lensing potential. So far there has been no feasible algorithm for inferring the posterior distribution of the lensing potential from the lensed CMB map. We propose a solution that allows efficient Markov Chain Monte Carlo sampling from the joint posterior of the lensing potential and the unlensed CMB map using the Hamiltonian Monte Carlo technique. The main conceptual step in the solution is a re-parameterization of CMB lensing in terms of the lensed CMB and the “inverse lensing” potential. We demonstrate a fast implementation on simulated data, including noise and a sky cut, that uses a further acceleration based on a very mild approximation of the inverse lensing potential. We find that the resulting Markov Chain has short correlation lengths and excellent convergence properties, making it promising for applications to high-resolution CMB data sets in the future.
Directory of Open Access Journals (Sweden)
Jean B. Lasserre
2000-01-01
Full Text Available We consider the class of Markov kernels for which the weak or strong Feller property fails to hold at some discontinuity set. We provide a simple necessary and sufficient condition for existence of an invariant probability measure as well as a Foster-Lyapunov sufficient condition. We also characterize a subclass, the quasi (weak or strong Feller kernels, for which the sequences of expected occupation measures share the same asymptotic properties as for (weak or strong Feller kernels. In particular, it is shown that the sequences of expected occupation measures of strong and quasi strong-Feller kernels with an invariant probability measure converge setwise to an invariant measure.
Hidden Markov models: the best models for forager movements?
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.
Hidden Markov modelling of movement data from fish
DEFF Research Database (Denmark)
Pedersen, Martin Wæver
Movement data from marine animals tagged with electronic tags are becoming increasingly diverse and plentiful. This trend entails a need for statistical methods that are able to filter the observations to extract the ecologically relevant content. This dissertation focuses on the development...... the behaviour of the animal. With the extended model can migratory and resident movement behaviour be related to geographical regions. For population inference multiple individual state-space analyses can be interconnected using mixed effects modelling. This framework provides parameter estimates...... approximated. This furthermore enables accurate probability densities of location to be computed. Finally, the performance of the HMM approach in analysing nonlinear state space models is compared with two alternatives: the AD Model Builder framework and BUGS, which relies on Markov chain Monte Carlo...
Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox
DEFF Research Database (Denmark)
Nonejad, Nima
This paper details Particle Markov chain Monte Carlo techniques for analysis of unobserved component time series models using several economic data sets. PMCMC combines the particle filter with the Metropolis-Hastings algorithm. Overall PMCMC provides a very compelling, computationally fast...... and efficient framework for estimation. These advantages are used to for instance estimate stochastic volatility models with leverage effect or with Student-t distributed errors. We also model changing time series characteristics of the US inflation rate by considering a heteroskedastic ARFIMA model where...
Energy Technology Data Exchange (ETDEWEB)
Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Bao, Jie; Swiler, Laura
2017-12-01
In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic amplitude versus angle (AVA) and controlled source electromagnetic (CSEM) data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo (MCMC) sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis (DREAM) and Adaptive Metropolis (AM) samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and CSEM data. The multi-chain MCMC is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic AVA and CSEM joint inversion provides better estimation of reservoir saturations than the seismic AVA-only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated – reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.
Markov-modulated and feedback fluid queues
Scheinhardt, Willem R.W.
1998-01-01
In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short
Prediction of annual precipitation on the territory of south Serbia using Markov chains
Directory of Open Access Journals (Sweden)
Lukić Predrag
2013-01-01
Full Text Available Prediction of precipitation is one of the important factors that affect the sectors such as industry, agriculture, environmental protection, and their related fields. The stochastic method based on a Markov chain model is used in the paper to predict the annual precipitation in the territory of South Serbia for the period 2009-2013. For this purpose, the precipitation data rainfall recorded on the four synoptic stations were used for the period 1980-2010. [Projekat Ministarstva nauke Republike Srbije, br. TR 37003: Razvoj hidroinformacionog sistema za praćenje i ranu najavu suša
Dorazio, R.M.; Johnson, F.A.
2003-01-01
Bayesian inference and decision theory may be used in the solution of relatively complex problems of natural resource management, owing to recent advances in statistical theory and computing. In particular, Markov chain Monte Carlo algorithms provide a computational framework for fitting models of adequate complexity and for evaluating the expected consequences of alternative management actions. We illustrate these features using an example based on management of waterfowl habitat.
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.
Detecting Violations of Unidimensionality by Order-Restricted Inference Methods
Directory of Open Access Journals (Sweden)
Moritz eHeene
2016-03-01
Full Text Available The assumption of unidimensionality and quantitative measurement represents one of the key concepts underlying most of the commonly applied of item response models. The assumption of unidimensionality is frequently tested although most commonly applied methods have been shown having low power against violations of unidimensionality whereas the assumption of quantitative measurement remains in most of the cases only an (implicit assumption. On the basis of a simulation study it is shown that order restricted inference methods within a Markov Chain Monte Carlo framework can successfully be used to test both assumptions.
Asteroid mass estimation using Markov-chain Monte Carlo
Siltala, Lauri; Granvik, Mikael
2017-11-01
Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to an inverse problem in at least 13 dimensions where the aim is to derive the mass of the perturbing asteroid(s) and six orbital elements for both the perturbing asteroid(s) and the test asteroid(s) based on astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations: the very rough 'marching' approximation, in which the asteroids' orbital elements are not fitted, thereby reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-chain Monte Carlo (MCMC) approach. We describe each of these algorithms with particular focus on the MCMC algorithm, and present example results using both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans.
Zhao, Chao; Jiang, Jingchi; Guan, Yi; Guo, Xitong; He, Bin
2018-05-01
Electronic medical records (EMRs) contain medical knowledge that can be used for clinical decision support (CDS). Our objective is to develop a general system that can extract and represent knowledge contained in EMRs to support three CDS tasks-test recommendation, initial diagnosis, and treatment plan recommendation-given the condition of a patient. We extracted four kinds of medical entities from records and constructed an EMR-based medical knowledge network (EMKN), in which nodes are entities and edges reflect their co-occurrence in a record. Three bipartite subgraphs (bigraphs) were extracted from the EMKN, one to support each task. One part of the bigraph was the given condition (e.g., symptoms), and the other was the condition to be inferred (e.g., diseases). Each bigraph was regarded as a Markov random field (MRF) to support the inference. We proposed three graph-based energy functions and three likelihood-based energy functions. Two of these functions are based on knowledge representation learning and can provide distributed representations of medical entities. Two EMR datasets and three metrics were utilized to evaluate the performance. As a whole, the evaluation results indicate that the proposed system outperformed the baseline methods. The distributed representation of medical entities does reflect similarity relationships with respect to knowledge level. Combining EMKN and MRF is an effective approach for general medical knowledge representation and inference. Different tasks, however, require individually designed energy functions. Copyright © 2018 Elsevier B.V. All rights reserved.
The Candy model revisited: Markov properties and inference
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
Directory of Open Access Journals (Sweden)
Adriana Pico
2003-01-01
Full Text Available Neoregelia 'Flandria'and N. 'Van Durme'are ornamental cultivars of Bromelia.Propagation by seeds is not viable and prunes constitutes the only way to propagateavoiding alterations. In this article the developmental floral pattern of 72 Bromeliastreated with ANA 190 ppm (T1, Ethrel: ANA + ETHREL,(T2 y ETHREL, (T3 anddivided into two age groups: E1 y E2 are shown. The treatments studied generated moreelongated plants and six new patterns. Using the Markov chain methodology theprobability to evolve to any pattern and the percentage of each were studied.
Gonthier, Peter L.; Koh, Yew-Meng; Kust Harding, Alice
2016-04-01
We present preliminary results of a new population synthesis of millisecond pulsars (MSP) from the Galactic disk using Markov Chain Monte Carlo techniques to better understand the model parameter space. We include empirical radio and gamma-ray luminosity models that are dependent on the pulsar period and period derivative with freely varying exponents. The magnitudes of the model luminosities are adjusted to reproduce the number of MSPs detected by a group of thirteen radio surveys as well as the MSP birth rate in the Galaxy and the number of MSPs detected by Fermi. We explore various high-energy emission geometries like the slot gap, outer gap, two pole caustic and pair starved polar cap models. The parameters associated with the birth distributions for the mass accretion rate, magnetic field, and period distributions are well constrained. With the set of four free parameters, we employ Markov Chain Monte Carlo simulations to explore the model parameter space. We present preliminary comparisons of the simulated and detected distributions of radio and gamma-ray pulsar characteristics. We estimate the contribution of MSPs to the diffuse gamma-ray background with a special focus on the Galactic Center.We express our gratitude for the generous support of the National Science Foundation (RUI: AST-1009731), Fermi Guest Investigator Program and the NASA Astrophysics Theory and Fundamental Program (NNX09AQ71G).
Energy Technology Data Exchange (ETDEWEB)
Cacuci, D. G. [Commiss Energy Atom, Direct Energy Nucl, Saclay, (France); Cacuci, D. G.; Balan, I. [Univ Karlsruhe, Inst Nucl Technol and Reactor Safetly, Karlsruhe, (Germany); Ionescu-Bujor, M. [Forschungszentrum Karlsruhe, Fus Program, D-76021 Karlsruhe, (Germany)
2008-07-01
In Part II of this work, the adjoint sensitivity analysis procedure developed in Part I is applied to perform sensitivity analysis of several dynamic reliability models of systems of increasing complexity, culminating with the consideration of the International Fusion Materials Irradiation Facility (IFMIF) accelerator system. Section II presents the main steps of a procedure for the automated generation of Markov chains for reliability analysis, including the abstraction of the physical system, construction of the Markov chain, and the generation and solution of the ensuing set of differential equations; all of these steps have been implemented in a stand-alone computer code system called QUEFT/MARKOMAG-S/MCADJSEN. This code system has been applied to sensitivity analysis of dynamic reliability measures for a paradigm '2-out-of-3' system comprising five components and also to a comprehensive dynamic reliability analysis of the IFMIF accelerator system facilities for the average availability and, respectively, the system's availability at the final mission time. The QUEFT/MARKOMAG-S/MCADJSEN has been used to efficiently compute sensitivities to 186 failure and repair rates characterizing components and subsystems of the first-level fault tree of the IFMIF accelerator system. (authors)
International Nuclear Information System (INIS)
Cacuci, D. G.; Cacuci, D. G.; Balan, I.; Ionescu-Bujor, M.
2008-01-01
In Part II of this work, the adjoint sensitivity analysis procedure developed in Part I is applied to perform sensitivity analysis of several dynamic reliability models of systems of increasing complexity, culminating with the consideration of the International Fusion Materials Irradiation Facility (IFMIF) accelerator system. Section II presents the main steps of a procedure for the automated generation of Markov chains for reliability analysis, including the abstraction of the physical system, construction of the Markov chain, and the generation and solution of the ensuing set of differential equations; all of these steps have been implemented in a stand-alone computer code system called QUEFT/MARKOMAG-S/MCADJSEN. This code system has been applied to sensitivity analysis of dynamic reliability measures for a paradigm '2-out-of-3' system comprising five components and also to a comprehensive dynamic reliability analysis of the IFMIF accelerator system facilities for the average availability and, respectively, the system's availability at the final mission time. The QUEFT/MARKOMAG-S/MCADJSEN has been used to efficiently compute sensitivities to 186 failure and repair rates characterizing components and subsystems of the first-level fault tree of the IFMIF accelerator system. (authors)
ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
Directory of Open Access Journals (Sweden)
Mohammad Mirabi
2012-01-01
Full Text Available
ENGLISH ABSTRACT: In this research, a Markov analysis of acceptance sampling plans in a single stage and in two stages is proposed, based on the quality of the items inspected. In a stage of this policy, if the number of defective items in a sample of inspected items is more than the upper threshold, the batch is rejected. However, the batch is accepted if the number of defective items is less than the lower threshold. Nonetheless, when the number of defective items falls between the upper and lower thresholds, the decision-making process continues to inspect the items and collect further samples. The primary objective is to determine the optimal values of the upper and lower thresholds using a Markov process to minimise the total cost associated with a batch acceptance policy. A solution method is presented, along with a numerical demonstration of the application of the proposed methodology.
AFRIKAANSE OPSOMMING: In hierdie navorsing word ’n Markov-ontleding gedoen van aannamemonsternemingsplanne wat plaasvind in ’n enkele stap of in twee stappe na gelang van die kwaliteit van die items wat geïnspekteer word. Indien die eerste monster toon dat die aantal defektiewe items ’n boonste grens oorskry, word die lot afgekeur. Indien die eerste monster toon dat die aantal defektiewe items minder is as ’n onderste grens, word die lot aanvaar. Indien die eerste monster toon dat die aantal defektiewe items in die gebied tussen die boonste en onderste grense lê, word die besluitnemingsproses voortgesit en verdere monsters word geneem. Die primêre doel is om die optimale waardes van die booonste en onderste grense te bepaal deur gebruik te maak van ’n Markov-proses sodat die totale koste verbonde aan die proses geminimiseer kan word. ’n Oplossing word daarna voorgehou tesame met ’n numeriese voorbeeld van die toepassing van die voorgestelde oplossing.
Perturbation approach to scaled type Markov renewal processes with infinite mean
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...
Directory of Open Access Journals (Sweden)
Antonio Vinicius Pimpão Gomes
2008-04-01
Full Text Available Nessa pesquisa é apresentada uma abordagem para gestão de estoques de peças de reposição com base em cadeias de Markov. É feita uma comparação com a simulação convencional, a fim de validar esta abordagem, bem como é apresentada uma heurística para determinação dos parâmetros da política (S, s de gestão de estoques, dado um conjunto de itens de custo (falta, excesso e ressuprimento e de demanda com distribuição Poisson. A análise dos gráficos desses itens de custo em função dos parâmetros da política (S, s fornece os trade-offs básicos para a formulação da heurística.In this study, we propose a model for a management stock system of spare parts using Markov chains. We compare this method with a conventional simulation showing that both methods are equivalent. In addition, we propose heuristics to find the system parameters based on the properties of Markov Chains and graphics related to the costs implied in the stock management of spare parts.
Using Markov Chains to predict the natural progression of diabetic retinopathy.
Srikanth, Priyanka
2015-01-01
To study the natural progression of diabetic retinopathy in patients with type 2 diabetes. This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy (NPDR) were treated. Markov Chains and Chi-square test were used for statistical analysis. We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the Markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference (P=0.70) which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07y in moderate NPDR, be in the severe NPDR state for 1.33y before moving into PDR for roughly 8y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29y. Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR. However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy (PDR) and stay in that state for long periods before transitioning into blindness.
A Bayesian inference approach to unveil supply curves in electricity markets
DEFF Research Database (Denmark)
Mitridati, Lesia Marie-Jeanne Mariane; Pinson, Pierre
2017-01-01
in the literature on modeling this uncertainty. In this study we introduce a Bayesian inference approach to reveal the aggregate supply curve in a day-ahead electricity market. The proposed algorithm relies on Markov Chain Monte Carlo and Sequential Monte Carlo methods. The major appeal of this approach......With increased competition in wholesale electricity markets, the need for new decision-making tools for strategic producers has arisen. Optimal bidding strategies have traditionally been modeled as stochastic profit maximization problems. However, for producers with non-negligible market power...
Bayesian inference for multivariate point processes observed at sparsely distributed times
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl; Møller, Jesper; Aukema, B.H.
We consider statistical and computational aspects of simulation-based Bayesian inference for a multivariate point process which is only observed at sparsely distributed times. For specicity we consider a particular data set which has earlier been analyzed by a discrete time model involving unknown...... normalizing constants. We discuss the advantages and disadvantages of using continuous time processes compared to discrete time processes in the setting of the present paper as well as other spatial-temporal situations. Keywords: Bark beetle, conditional intensity, forest entomology, Markov chain Monte Carlo...
a Probability Model for Drought Prediction Using Fusion of Markov Chain and SAX Methods
Jouybari-Moghaddam, Y.; Saradjian, M. R.; Forati, A. M.
2017-09-01
Drought is one of the most powerful natural disasters which are affected on different aspects of the environment. Most of the time this phenomenon is immense in the arid and semi-arid area. Monitoring and prediction the severity of the drought can be useful in the management of the natural disaster caused by drought. Many indices were used in predicting droughts such as SPI, VCI, and TVX. In this paper, based on three data sets (rainfall, NDVI, and land surface temperature) which are acquired from MODIS satellite imagery, time series of SPI, VCI, and TVX in time limited between winters 2000 to summer 2015 for the east region of Isfahan province were created. Using these indices and fusion of symbolic aggregation approximation and hidden Markov chain drought was predicted for fall 2015. For this purpose, at first, each time series was transformed into the set of quality data based on the state of drought (5 group) by using SAX algorithm then the probability matrix for the future state was created by using Markov hidden chain. The fall drought severity was predicted by fusion the probability matrix and state of drought severity in summer 2015. The prediction based on the likelihood for each state of drought includes severe drought, middle drought, normal drought, severe wet and middle wet. The analysis and experimental result from proposed algorithm show that the product of this algorithm is acceptable and the proposed algorithm is appropriate and efficient for predicting drought using remote sensor data.
Mitavskiy, Boris; Cannings, Chris
2009-01-01
The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When the mutation rate is positive, the Markov chain modeling of an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution. Rather little is known about the stationary distribution. In fact, the only quantitative facts established so far tell us that the stationary distributions of Markov chains modeling evolutionary algorithms concentrate on uniform populations (i.e., those populations consisting of a repeated copy of the same individual). At the same time, knowing the stationary distribution may provide some information about the expected time it takes for the algorithm to reach a certain solution, assessment of the biases due to recombination and selection, and is of importance in population genetics to assess what is called a "genetic load" (see the introduction for more details). In the recent joint works of the first author, some bounds have been established on the rates at which the stationary distribution concentrates on the uniform populations. The primary tool used in these papers is the "quotient construction" method. It turns out that the quotient construction method can be exploited to derive much more informative bounds on ratios of the stationary distribution values of various subsets of the state space. In fact, some of the bounds obtained in the current work are expressed in terms of the parameters involved in all the three main stages of an evolutionary algorithm: namely, selection, recombination, and mutation.
First Passage Probability Estimation of Wind Turbines by Markov Chain Monte Carlo
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
2013-01-01
Markov Chain Monte Carlo simulation has received considerable attention within the past decade as reportedly one of the most powerful techniques for the first passage probability estimation of dynamic systems. A very popular method in this direction capable of estimating probability of rare events...... of the method by modifying the conditional sampler. In this paper, applicability of the original SS is compared to the recently introduced modifications of the method on a wind turbine model. The model incorporates a PID pitch controller which aims at keeping the rotational speed of the wind turbine rotor equal...... to its nominal value. Finally Monte Carlo simulations are performed which allow assessment of the accuracy of the first passage probability estimation by the SS methods....
Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.
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.
International Nuclear Information System (INIS)
Kastner, S.O.
1980-01-01
Closed expressions are obtained for the conditional probabilities qsub(i)sub(j)sub(,)sub(k) required in evaluating particular ratios of atomic level populations, using a Markov-chain representation of the system of levels. The total transition probability between two arbitrary levels is also evaluated and its relation to population ratios is clarified. It is shown that Seaton's cascade matrix is a subset of the total transition probability matrix. (orig.)
Markov Chains For Testing Redundant Software
White, Allan L.; Sjogren, Jon A.
1990-01-01
Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
International Nuclear Information System (INIS)
Shrier, O; Khachan, J; Bosi, S
2006-01-01
A Markov chain method is presented as an alternative approach to Monte Carlo simulations of charge exchange collisions by an energetic hydrogen ion beam with a cold background hydrogen gas. This method was used to determine the average energy of the resulting energetic neutrals along the path of the beam. A comparison with Monte Carlo modelling showed a good agreement but with the advantage that it required much less computing time and produced no numerical noise. In particular, the Markov chain method works well for monotonically increasing or decreasing electrostatic potentials. Finally, a good agreement is obtained with experimental results from Doppler shift spectroscopy on energetic beams from a hollow cathode discharge. In particular, the average energy of ions that undergo charge exchange reaches a plateau that can be well below the full energy that might be expected from the applied voltage bias, depending on the background gas pressure. For example, pressures of ∼20 mTorr limit the ion energy to ∼20% of the applied voltage
International Nuclear Information System (INIS)
Raymond, V; Mandel, I; Kalogera, V; Van der Sluys, M V; Roever, C; Christensen, N
2010-01-01
Gravitational-wave signals from inspirals of binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave (GW) interferometers (LIGO, Virgo and GEO-600). We present parameter estimation results from our Markov-chain Monte Carlo code SPINspiral on signals from binaries with precessing spins. Two data sets are created by injecting simulated GW signals either into synthetic Gaussian noise or into LIGO detector data. We compute the 15-dimensional probability-density functions (PDFs) for both data sets, as well as for a data set containing LIGO data with a known, loud artefact ('glitch'). We show that the analysis of the signal in detector noise yields accuracies similar to those obtained using simulated Gaussian noise. We also find that while the Markov chains from the glitch do not converge, the PDFs would look consistent with a GW signal present in the data. While our parameter estimation results are encouraging, further investigations into how to differentiate an actual GW signal from noise are necessary.
Stochastic Dynamics through Hierarchically Embedded Markov Chains.
Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M
2017-02-03
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
Multi-site Stochastic Simulation of Daily Streamflow with Markov Chain and KNN Algorithm
Mathai, J.; Mujumdar, P.
2017-12-01
A key focus of this study is to develop a method which is physically consistent with the hydrologic processes that can capture short-term characteristics of daily hydrograph as well as the correlation of streamflow in temporal and spatial domains. In complex water resource systems, flow fluctuations at small time intervals require that discretisation be done at small time scales such as daily scales. Also, simultaneous generation of synthetic flows at different sites in the same basin are required. We propose a method to equip water managers with a streamflow generator within a stochastic streamflow simulation framework. The motivation for the proposed method is to generate sequences that extend beyond the variability represented in the historical record of streamflow time series. The method has two steps: In step 1, daily flow is generated independently at each station by a two-state Markov chain, with rising limb increments randomly sampled from a Gamma distribution and the falling limb modelled as exponential recession and in step 2, the streamflow generated in step 1 is input to a nonparametric K-nearest neighbor (KNN) time series bootstrap resampler. The KNN model, being data driven, does not require assumptions on the dependence structure of the time series. A major limitation of KNN based streamflow generators is that they do not produce new values, but merely reshuffle the historical data to generate realistic streamflow sequences. However, daily flow generated using the Markov chain approach is capable of generating a rich variety of streamflow sequences. Furthermore, the rising and falling limbs of daily hydrograph represent different physical processes, and hence they need to be modelled individually. Thus, our method combines the strengths of the two approaches. We show the utility of the method and improvement over the traditional KNN by simulating daily streamflow sequences at 7 locations in the Godavari River basin in India.
Zou, Yonghong; Christensen, Erik R; Zheng, Wei; Wei, Hua; Li, An
2014-11-01
A stochastic process was developed to simulate the stepwise debromination pathways for polybrominated diphenyl ethers (PBDEs). The stochastic process uses an analogue Markov Chain Monte Carlo (AMCMC) algorithm to generate PBDE debromination profiles. The acceptance or rejection of the randomly drawn stepwise debromination reactions was determined by a maximum likelihood function. The experimental observations at certain time points were used as target profiles; therefore, the stochastic processes are capable of presenting the effects of reaction conditions on the selection of debromination pathways. The application of the model is illustrated by adopting the experimental results of decabromodiphenyl ether (BDE209) in hexane exposed to sunlight. Inferences that were not obvious from experimental data were suggested by model simulations. For example, BDE206 has much higher accumulation at the first 30 min of sunlight exposure. By contrast, model simulation suggests that, BDE206 and BDE207 had comparable yields from BDE209. The reason for the higher BDE206 level is that BDE207 has the highest depletion in producing octa products. Compared to a previous version of the stochastic model based on stochastic reaction sequences (SRS), the AMCMC approach was determined to be more efficient and robust. Due to the feature of only requiring experimental observations as input, the AMCMC model is expected to be applicable to a wide range of PBDE debromination processes, e.g. microbial, photolytic, or joint effects in natural environments. Copyright © 2014 Elsevier Ltd. All rights reserved.
Model Checking Markov Reward Models with Impulse Rewards
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 Unified Framework for Complex Networks with Degree Trichotomy Based on Markov Chains.
Hui, David Shui Wing; Chen, Yi-Chao; Zhang, Gong; Wu, Weijie; Chen, Guanrong; Lui, John C S; Li, Yingtao
2017-06-16
This paper establishes a Markov chain model as a unified framework for describing the evolution processes in complex networks. The unique feature of the proposed model is its capability in addressing the formation mechanism that can reflect the "trichotomy" observed in degree distributions, based on which closed-form solutions can be derived. Important special cases of the proposed unified framework are those classical models, including Poisson, Exponential, Power-law distributed networks. Both simulation and experimental results demonstrate a good match of the proposed model with real datasets, showing its superiority over the classical models. Implications of the model to various applications including citation analysis, online social networks, and vehicular networks design, are also discussed in the paper.
Using Markov Chains to predict the natural progression of diabetic retinopathy
Directory of Open Access Journals (Sweden)
Priyanka Srikanth
2015-02-01
Full Text Available AIM: To study the natural progression of diabetic retinopathy in patients with type 2 diabetes. METHODS: This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy (NPDR were treated. Markov Chains and Chi-square test were used for statistical analysis. RESULTS: We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the Markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference (P=0.70 which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07y in moderate NPDR, be in the severe NPDR state for 1.33y before moving into PDR for roughly 8y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29y. CONCLUSION: Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR. However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy (PDR and stay in that state for long periods before transitioning into blindness.
Using Markov chains to predict the natural progression of diabetic retinopathy
Institute of Scientific and Technical Information of China (English)
Priyanka; Srikanth
2015-01-01
AIM: To study the natural progression of diabetic retinopathy in patients with type 2 diabetes.METHODS: This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy(NPDR) were treated.Markov Chains and Chi-square test were used for statistical analysis.RESULTS: We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the Markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference(P =0.70) which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07 y in moderate NPDR, be in the severe NPDR state for 1.33 y before moving into PDR for roughly8 y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29 y.CONCLUSION: Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR.However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy(PDR) and stay in that state for long periods before transitioning into blindness.
Energy Technology Data Exchange (ETDEWEB)
Kaflowski, Grzegorz; Kizilcay, Mustafa [Siegen Univ. (Germany). Lehrstuhl fuer Elektrische Energieversorgung
2010-02-15
In long-term planning of modernization measures in electric power supplies, forecasting of the future behaviour of the equipment is of great importance for its optimum utilization. Based on limited historical information on the technical condition of a collective of equipment, its future changes of condition can be modelled using Markov chains, which may support an assessment of the time of modernization or replacement. (orig.)
Carl Chiarella; Chih-Ying Hsiao
2005-01-01
This paper considers an asset allocation strategy over a finite period under investment uncertainty and short-sale constraints as a continuous time stochastic control problem. Investment uncertainty is characterised by a stochastic interest rate and inflation risk. If there are no short-sale constraints, the optimal asset allocation strategy can be solved analytically. We consider several kinds of short-sale constraints and employ the backward Markov chain approximation method to explore the ...
Fuzzy hidden Markov chains segmentation for volume determination and quantitation in PET
Energy Technology Data Exchange (ETDEWEB)
Hatt, M [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Lamare, F [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609, (France); Boussion, N [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Turzo, A [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Collet, C [Ecole Nationale Superieure de Physique de Strasbourg (ENSPS), ULP, Strasbourg, F-67000 (France); Salzenstein, F [Institut d' Electronique du Solide et des Systemes (InESS), ULP, Strasbourg, F-67000 (France); Roux, C [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Jarritt, P [Medical Physics Agency, Royal Victoria Hospital, Belfast (United Kingdom); Carson, K [Medical Physics Agency, Royal Victoria Hospital, Belfast (United Kingdom); Rest, C Cheze-Le [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Visvikis, D [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France)
2007-07-21
Accurate volume of interest (VOI) estimation in PET is crucial in different oncology applications such as response to therapy evaluation and radiotherapy treatment planning. The objective of our study was to evaluate the performance of the proposed algorithm for automatic lesion volume delineation; namely the fuzzy hidden Markov chains (FHMC), with that of current state of the art in clinical practice threshold based techniques. As the classical hidden Markov chain (HMC) algorithm, FHMC takes into account noise, voxel intensity and spatial correlation, in order to classify a voxel as background or functional VOI. However the novelty of the fuzzy model consists of the inclusion of an estimation of imprecision, which should subsequently lead to a better modelling of the 'fuzzy' nature of the object of interest boundaries in emission tomography data. The performance of the algorithms has been assessed on both simulated and acquired datasets of the IEC phantom, covering a large range of spherical lesion sizes (from 10 to 37 mm), contrast ratios (4:1 and 8:1) and image noise levels. Both lesion activity recovery and VOI determination tasks were assessed in reconstructed images using two different voxel sizes (8 mm{sup 3} and 64 mm{sup 3}). In order to account for both the functional volume location and its size, the concept of % classification errors was introduced in the evaluation of volume segmentation using the simulated datasets. Results reveal that FHMC performs substantially better than the threshold based methodology for functional volume determination or activity concentration recovery considering a contrast ratio of 4:1 and lesion sizes of <28 mm. Furthermore differences between classification and volume estimation errors evaluated were smaller for the segmented volumes provided by the FHMC algorithm. Finally, the performance of the automatic algorithms was less susceptible to image noise levels in comparison to the threshold based techniques. The
Context Tree Estimation in Variable Length Hidden Markov Models
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...
Supervised self-organization of homogeneous swarms using ergodic projections of Markov chains.
Chattopadhyay, Ishanu; Ray, Asok
2009-12-01
This paper formulates a self-organization algorithm to address the problem of global behavior supervision in engineered swarms of arbitrarily large population sizes. The swarms considered in this paper are assumed to be homogeneous collections of independent identical finite-state agents, each of which is modeled by an irreducible finite Markov chain. The proposed algorithm computes the necessary perturbations in the local agents' behavior, which guarantees convergence to the desired observed state of the swarm. The ergodicity property of the swarm, which is induced as a result of the irreducibility of the agent models, implies that while the local behavior of the agents converges to the desired behavior only in the time average, the overall swarm behavior converges to the specification and stays there at all times. A simulation example illustrates the underlying concept.
Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy
Sharma, Sanjib
2017-08-01
Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in the number of papers that employ Monte Carlo based Bayesian analysis. New, efficient Monte Carlo based methods are continuously being developed and explored. In this review, we first explain the basics of Bayesian theory and discuss how to set up data analysis problems within this framework. Next, we provide an overview of various Monte Carlo based methods for performing Bayesian data analysis. Finally, we discuss advanced ideas that enable us to tackle complex problems and thus hold great promise for the future. We also distribute downloadable computer software (available at https://github.com/sanjibs/bmcmc/ ) that implements some of the algorithms and examples discussed here.
Finding and testing network communities by lumped Markov chains.
Piccardi, Carlo
2011-01-01
Identifying communities (or clusters), namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov chain model of a random walker, a quality measure called "persistence probability" is associated to a cluster, which is then defined as an "α-community" if such a probability is not smaller than α. Consistently, a partition composed of α-communities is an "α-partition." These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired α-level allows one to immediately select the α-partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the quality of each single community. Given its ability in individually assessing each single cluster, this approach can also disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure.
Finding and testing network communities by lumped Markov chains.
Directory of Open Access Journals (Sweden)
Carlo Piccardi
Full Text Available Identifying communities (or clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov chain model of a random walker, a quality measure called "persistence probability" is associated to a cluster, which is then defined as an "α-community" if such a probability is not smaller than α. Consistently, a partition composed of α-communities is an "α-partition." These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired α-level allows one to immediately select the α-partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the quality of each single community. Given its ability in individually assessing each single cluster, this approach can also disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure.
Inference algorithms and learning theory for Bayesian sparse factor analysis
International Nuclear Information System (INIS)
Rattray, Magnus; Sharp, Kevin; Stegle, Oliver; Winn, John
2009-01-01
Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.
Inference algorithms and learning theory for Bayesian sparse factor analysis
Energy Technology Data Exchange (ETDEWEB)
Rattray, Magnus; Sharp, Kevin [School of Computer Science, University of Manchester, Manchester M13 9PL (United Kingdom); Stegle, Oliver [Max-Planck-Institute for Biological Cybernetics, Tuebingen (Germany); Winn, John, E-mail: magnus.rattray@manchester.ac.u [Microsoft Research Cambridge, Roger Needham Building, Cambridge, CB3 0FB (United Kingdom)
2009-12-01
Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.
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....
DEFF Research Database (Denmark)
Scholer, Marie; Irving, James; Zibar, Majken Caroline Looms
Geophysical methods have the potential to provide valuable information on hydrological properties in the unsaturated zone. In particular, time-lapse geophysical data, when coupled with a hydrological model and inverted stochastically, may allow for the effective estimation of subsurface hydraulic...... parameters and their corresponding uncertainties. In this study, we use a Bayesian Markov-chain-Monte-Carlo (MCMC) inversion approach to investigate how much information regarding vadose zone hydraulic properties can be retrieved from time-lapse crosshole GPR data collected at the Arrenaes field site...
Directory of Open Access Journals (Sweden)
Gerich M. S.
2012-12-01
Full Text Available Let ${xi(t, x(t}$ be a homogeneous semi-continuous lattice Poisson process on the Markov chain.The jumps of one sign are geometrically distributed, and jumps of the opposite sign are arbitrary latticed distribution. For a suchprocesses the relations for the components of two-sided matrix factorization are established.This relations define the moment genereting functions for extremumf of the process and their complements.
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Wintenberger, Olivier
2014-01-01
We introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of sequences. We illustrate the use of the cluster index by characterizing infinite variance stable...... limit distributions and precise large deviation results for sums of multivariate functions acting on a stationary Markov chain under a drift condition....
Unmixing hyperspectral images using Markov random fields
International Nuclear Information System (INIS)
Eches, Olivier; Dobigeon, Nicolas; Tourneret, Jean-Yves
2011-01-01
This paper proposes a new spectral unmixing strategy based on the normal compositional model that exploits the spatial correlations between the image pixels. The pure materials (referred to as endmembers) contained in the image are assumed to be available (they can be obtained by using an appropriate endmember extraction algorithm), while the corresponding fractions (referred to as abundances) are estimated by the proposed algorithm. Due to physical constraints, the abundances have to satisfy positivity and sum-to-one constraints. The image is divided into homogeneous distinct regions having the same statistical properties for the abundance coefficients. The spatial dependencies within each class are modeled thanks to Potts-Markov random fields. Within a Bayesian framework, prior distributions for the abundances and the associated hyperparameters are introduced. A reparametrization of the abundance coefficients is proposed to handle the physical constraints (positivity and sum-to-one) inherent to hyperspectral imagery. The parameters (abundances), hyperparameters (abundance mean and variance for each class) and the classification map indicating the classes of all pixels in the image are inferred from the resulting joint posterior distribution. To overcome the complexity of the joint posterior distribution, Markov chain Monte Carlo methods are used to generate samples asymptotically distributed according to the joint posterior of interest. Simulations conducted on synthetic and real data are presented to illustrate the performance of the proposed algorithm.
Ensemble bayesian model averaging using markov chain Monte Carlo sampling
Energy Technology Data Exchange (ETDEWEB)
Vrugt, Jasper A [Los Alamos National Laboratory; Diks, Cees G H [NON LANL; Clark, Martyn P [NON LANL
2008-01-01
Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery etal. Mon Weather Rev 133: 1155-1174, 2(05)) has recommended the Expectation-Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed Differential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model stream-flow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.
A reversible-jump Markov chain Monte Carlo algorithm for 1D inversion of magnetotelluric data
Mandolesi, Eric; Ogaya, Xenia; Campanyà, Joan; Piana Agostinetti, Nicola
2018-04-01
This paper presents a new computer code developed to solve the 1D magnetotelluric (MT) inverse problem using a Bayesian trans-dimensional Markov chain Monte Carlo algorithm. MT data are sensitive to the depth-distribution of rock electric conductivity (or its reciprocal, resistivity). The solution provided is a probability distribution - the so-called posterior probability distribution (PPD) for the conductivity at depth, together with the PPD of the interface depths. The PPD is sampled via a reversible-jump Markov Chain Monte Carlo (rjMcMC) algorithm, using a modified Metropolis-Hastings (MH) rule to accept or discard candidate models along the chains. As the optimal parameterization for the inversion process is generally unknown a trans-dimensional approach is used to allow the dataset itself to indicate the most probable number of parameters needed to sample the PPD. The algorithm is tested against two simulated datasets and a set of MT data acquired in the Clare Basin (County Clare, Ireland). For the simulated datasets the correct number of conductive layers at depth and the associated electrical conductivity values is retrieved, together with reasonable estimates of the uncertainties on the investigated parameters. Results from the inversion of field measurements are compared with results obtained using a deterministic method and with well-log data from a nearby borehole. The PPD is in good agreement with the well-log data, showing as a main structure a high conductive layer associated with the Clare Shale formation. In this study, we demonstrate that our new code go beyond algorithms developend using a linear inversion scheme, as it can be used: (1) to by-pass the subjective choices in the 1D parameterizations, i.e. the number of horizontal layers in the 1D parameterization, and (2) to estimate realistic uncertainties on the retrieved parameters. The algorithm is implemented using a simple MPI approach, where independent chains run on isolated CPU, to take
Energy Technology Data Exchange (ETDEWEB)
Nicoulaud-Gouin, V.; Giacalone, M.; Gonze, M.A. [Institut de Radioprotection et de Surete Nucleaire-PRP-ENV/SERIS/LM2E (France); Martin-Garin, A.; Garcia-Sanchez, L. [IRSN-PRP-ENV/SERIS/L2BT (France)
2014-07-01
Calibration of transfer models according to observation data is a challenge, especially if parameters uncertainty is required, and if competing models should be decided between them. Generally two main calibration methods are used: The frequentist approach in which the unknown parameter of interest is supposed fixed and its estimation is based on the data only. In this category, least squared method has many restrictions in nonlinear models and competing models need to be nested in order to be compared. The bayesian inference in which the unknown parameter of interest is supposed random and its estimation is based on the data and on prior information. Compared to frequentist method, it provides probability density functions and therefore pointwise estimation with credible intervals. However, in practical cases, Bayesian inference is a complex problem of numerical integration, which explains its low use in operational modeling including radioecology. This study aims to illustrate the interest and feasibility of Bayesian approach in radioecology particularly in the case of ordinary differential equations with non-constant coefficients models, which cover most radiological risk assessment models, notably those implemented in the Symbiose platform (Gonze et al, 2010). Markov Chain Monte Carlo (MCMC) method (Metropolis et al., 1953) was used because the posterior expectations are intractable integrals. The invariant distribution of the parameters was performed by the metropolis-Hasting algorithm (Hastings, 1970). GNU-MCSim software (Bois and Maszle, 2011) a bayesian hierarchical framework, was used to deal with nonlinear differential models. Two case studies including this type of model were investigated: An Equilibrium Kinetic sorption model (EK) (e.g. van Genuchten et al, 1974), with experimental data concerning {sup 137}Cs and {sup 85}Sr sorption and desorption in different soils studied in stirred flow-through reactors. This model, generalizing the K{sub d} approach
Evolutionary inference via the Poisson Indel Process.
Bouchard-Côté, Alexandre; Jordan, Michael I
2013-01-22
We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114-124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments.
Herrera, C.; Nava, F. A.; Lomnitz, C.
2006-08-01
A previous work introduced a new method for seismic hazard evaluation in a system (a geographic area with distinct, but related seismogenic regions) based on modeling the transition probabilities of states (patterns of presence or absence of seismicity, with magnitude greater or equal to a threshold magnitude Mr, in the regions of the system, during a time interval Δt) as a Markov chain. Application of this direct method to the Japan area gave very good results. Given that the most important limitation of the direct method is the relative scarcity of large magnitude events, we decided to explore the possibility that seismicity with magnitude M ≥ Mmr contains information about the future occurrence of earthquakes with M ≥ Mmr > Mmr. This mixed Markov chain method estimates the probabilities of occurrence of a system state for M ≥ MMr on the basis of the observed state for M ≥ Mmr in the previous Δt. Application of the mixed method to the area of Japan gives better hazard estimations than the direct method; in particular for large earthquakes. As part of this study, the problem of performance evaluation of hazard estimation methods is addressed, leading to the use of grading functions.
Markov chain of distances between parked cars
International Nuclear Information System (INIS)
Seba, Petr
2008-01-01
We describe the distribution of distances between parked cars as a solution of certain Markov processes and show that its solution is obtained with the help of a distributional fixed point equation. Under certain conditions the process is solved explicitly. The resulting probability density is compared with the actual parking data measured in the city. (fast track communication)
Minsley, Burke J.
2011-01-01
A meaningful interpretation of geophysical measurements requires an assessment of the space of models that are consistent with the data, rather than just a single, ‘best’ model which does not convey information about parameter uncertainty. For this purpose, a trans-dimensional Bayesian Markov chain Monte Carlo (MCMC) algorithm is developed for assessing frequencydomain electromagnetic (FDEM) data acquired from airborne or ground-based systems. By sampling the distribution of models that are consistent with measured data and any prior knowledge, valuable inferences can be made about parameter values such as the likely depth to an interface, the distribution of possible resistivity values as a function of depth and non-unique relationships between parameters. The trans-dimensional aspect of the algorithm allows the number of layers to be a free parameter that is controlled by the data, where models with fewer layers are inherently favoured, which provides a natural measure of parsimony and a signiﬁcant degree of ﬂexibility in parametrization. The MCMC algorithm is used with synthetic examples to illustrate how the distribution of acceptable models is affected by the choice of prior information, the system geometry and conﬁguration and the uncertainty in the measured system elevation. An airborne FDEM data set that was acquired for the purpose of hydrogeological characterization is also studied. The results compare favorably with traditional least-squares analysis, borehole resistivity and lithology logs from the site, and also provide new information about parameter uncertainty necessary for model assessment.
Markov chain algorithms: a template for building future robust low-power systems
Deka, Biplab; Birklykke, Alex A.; Duwe, Henry; Mansinghka, Vikash K.; Kumar, Rakesh
2014-01-01
Although computational systems are looking towards post CMOS devices in the pursuit of lower power, the expected inherent unreliability of such devices makes it difficult to design robust systems without additional power overheads for guaranteeing robustness. As such, algorithmic structures with inherent ability to tolerate computational errors are of significant interest. We propose to cast applications as stochastic algorithms based on Markov chains (MCs) as such algorithms are both sufficiently general and tolerant to transition errors. We show with four example applications—Boolean satisfiability, sorting, low-density parity-check decoding and clustering—how applications can be cast as MC algorithms. Using algorithmic fault injection techniques, we demonstrate the robustness of these implementations to transition errors with high error rates. Based on these results, we make a case for using MCs as an algorithmic template for future robust low-power systems. PMID:24842030
Using Markov Chains and Multi-Objective Optimization for Energy-Efficient Context Recognition
Directory of Open Access Journals (Sweden)
Vito Janko
2017-12-01
Full Text Available The recognition of the user’s context with wearable sensing systems is a common problem in ubiquitous computing. However, the typically small battery of such systems often makes continuous recognition impractical. The strain on the battery can be reduced if the sensor setting is adapted to each context. We propose a method that efficiently finds near-optimal sensor settings for each context. It uses Markov chains to simulate the behavior of the system in different configurations and the multi-objective genetic algorithm to find a set of good non-dominated configurations. The method was evaluated on three real-life datasets and found good trade-offs between the system’s energy expenditure and the system’s accuracy. One of the solutions, for example, consumed five-times less energy than the default one, while sacrificing only two percentage points of accuracy.
Using Markov Chains and Multi-Objective Optimization for Energy-Efficient Context Recognition.
Janko, Vito; Luštrek, Mitja
2017-12-29
The recognition of the user's context with wearable sensing systems is a common problem in ubiquitous computing. However, the typically small battery of such systems often makes continuous recognition impractical. The strain on the battery can be reduced if the sensor setting is adapted to each context. We propose a method that efficiently finds near-optimal sensor settings for each context. It uses Markov chains to simulate the behavior of the system in different configurations and the multi-objective genetic algorithm to find a set of good non-dominated configurations. The method was evaluated on three real-life datasets and found good trade-offs between the system's energy expenditure and the system's accuracy. One of the solutions, for example, consumed five-times less energy than the default one, while sacrificing only two percentage points of accuracy.
International Nuclear Information System (INIS)
Olivieri, E.; Scoppola, E.
1996-01-01
In this paper we consider aperiodic ergodic Markov chains with transition probabilities exponentially small in a large parameter β. We extend to the general, not necessarily reversible case the analysis, started in part I of this work, of the first exit problem from a general domain Q containing many stable equilibria (attracting equilibrium points for the β = ∞ dynamics). In particular we describe the tube of typical trajectories during the first excursion outside Q
Qingyou Yan; Chao Qin; Mingjian Nie; Le Yang
2018-01-01
Due to the deregulation of retail electricity market, consumers can choose retail electric suppliers freely, and market entities are facing fierce competition because of the increasing number of new entrants. Under these circumstances, forecasting the changes in all market entities, when market share stabilized, is important for suppliers making marketing decisions. In this paper, a market share forecasting model was established based on Markov chain, and a system dynamics model was construct...
Effects of tour boats on dolphin activity examined with sensitivity analysis of Markov chains.
Dans, Silvana Laura; Degrati, Mariana; Pedraza, Susana Noemí; Crespo, Enrique Alberto
2012-08-01
In Patagonia, Argentina, watching dolphins, especially dusky dolphins (Lagenorhynchus obscurus), is a new tourist activity. Feeding time decreases and time to return to feeding after feeding is abandoned and time it takes a group of dolphins to feed increase in the presence of boats. Such effects on feeding behavior may exert energetic costs on dolphins and thus reduce an individual's survival and reproductive capacity or maybe associated with shifts in distribution. We sought to predict which behavioral changes modify the activity pattern of dolphins the most. We modeled behavioral sequences of dusky dolphins with Markov chains. We calculated transition probabilities from one activity to another and arranged them in a stochastic matrix model. The proportion of time dolphins dedicated to a given activity (activity budget) and the time it took a dolphin to resume that activity after it had been abandoned (recurrence time) were calculated. We used a sensitivity analysis of Markov chains to calculate the sensitivity of the time budget and the activity-resumption time to changes in behavioral transition probabilities. Feeding-time budget was most sensitive to changes in the probability of dolphins switching from traveling to feeding behavior and of maintaining feeding behavior. Thus, an increase in these probabilities would be associated with the largest reduction in the time dedicated to feeding. A reduction in the probability of changing from traveling to feeding would also be associated with the largest increases in the time it takes dolphins to resume feeding. To approach dolphins when they are traveling would not affect behavior less because presence of the boat may keep dolphins from returning to feeding. Our results may help operators of dolphin-watching vessels minimize negative effects on dolphins. ©2012 Society for Conservation Biology.
THE DEVELOPMENT OF A MODEL INITIATION OF PROJECT IN A FORM OF MARKOV CHAIN
Directory of Open Access Journals (Sweden)
Катерина Вікторівна КОЛЕСНІКОВА
2017-03-01
Full Text Available The model of the initiation of projects which reproduces a fragment of the general scheme of interaction between the main entities in the project initiation phase is created. Determined that the project initiation through communication links between the four main entities: projects team, environment, the project itself and the customer. The result of the initiation of projects in the emerging communications referred to objects in the design phase through consistency requirements of stakeholders and the adoption of the basic concepts of projects, goal-projects, project planning, evaluation requirements of specialization and competence required for the formation of the project team. This Markov chain is part of the control circuit that includes elements such as the temporary organizational structure of the project design, project team, customer, and environment project. It is shown that the Markov model of interaction between project participants in their initiation phase, taking into account the role of a key player in the project ‑ the customer can determine changes of state and generate recommendations for initiating projects. Results of the study can serve as a basis for creating models of control objects that contain its organizational structure and reflect the parametric properties of the system to obtain information needed for decision making to initiate projects
Optimal choice of word length when comparing two Markov sequences using a χ 2-statistic.
Bai, Xin; Tang, Kujin; Ren, Jie; Waterman, Michael; Sun, Fengzhu
2017-10-03
Alignment-free sequence comparison using counts of word patterns (grams, k-tuples) has become an active research topic due to the large amount of sequence data from the new sequencing technologies. Genome sequences are frequently modelled by Markov chains and the likelihood ratio test or the corresponding approximate χ 2 -statistic has been suggested to compare two sequences. However, it is not known how to best choose the word length k in such studies. We develop an optimal strategy to choose k by maximizing the statistical power of detecting differences between two sequences. Let the orders of the Markov chains for the two sequences be r 1 and r 2 , respectively. We show through both simulations and theoretical studies that the optimal k= max(r 1 ,r 2 )+1 for both long sequences and next generation sequencing (NGS) read data. The orders of the Markov chains may be unknown and several methods have been developed to estimate the orders of Markov chains based on both long sequences and NGS reads. We study the power loss of the statistics when the estimated orders are used. It is shown that the power loss is minimal for some of the estimators of the orders of Markov chains. Our studies provide guidelines on choosing the optimal word length for the comparison of Markov sequences.