Sample records for absorbing markov chain

  1. Saliency Detection via Absorbing Markov Chain With Learnt Transition Probability.

    PubMed

    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.

  2. LECTURES ON GAME THEORY, MARKOV CHAINS, AND RELATED TOPICS

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Thompson, G L

    1958-03-01

    Notes on nine lectures delivered at Sandin Corporation in August 1957 are given. Part one contains the manuscript of a paper concerning a judging problem. Part two is concerned with finite Markov-chain theory amd discusses regular Markov chains, absorbing Markov chains, the classification of states, application to the Leontief input-output model, and semimartingales. Part three contains notes on game theory and covers matrix games, the effect of psychological attitudes on the outcomes of games, extensive games, amd matrix theory applied to mathematical economics. (auth)

  3. Assessing the Progress and the Underlying Nature of the Flows of Doctoral and Master Degree Candidates Using Absorbing Markov Chains

    ERIC Educational Resources Information Center

    Nicholls, Miles G.

    2007-01-01

    In this paper, absorbing markov chains are used to analyse the flows of higher degree by research candidates (doctoral and master) within an Australian faculty of business. The candidates are analysed according to whether they are full time or part time. The need for such analysis stemmed from what appeared to be a rather poor completion rate (as…

  4. Phasic Triplet Markov Chains.

    PubMed

    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.

  5. Noise can speed convergence in Markov chains.

    PubMed

    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.

  6. Quantum Markov chains

    NASA Astrophysics Data System (ADS)

    Gudder, Stanley

    2008-07-01

    A new approach to quantum Markov chains is presented. We first define a transition operation matrix (TOM) as a matrix whose entries are completely positive maps whose column sums form a quantum operation. A quantum Markov chain is defined to be a pair (G,E) where G is a directed graph and E =[Eij] is a TOM whose entry Eij labels the edge from vertex j to vertex i. We think of the vertices of G as sites that a quantum system can occupy and Eij is the transition operation from site j to site i in one time step. The discrete dynamics of the system is obtained by iterating the TOM E. We next consider a special type of TOM called a transition effect matrix. In this case, there are two types of dynamics, a state dynamics and an operator dynamics. Although these two types are not identical, they are statistically equivalent. We next give examples that illustrate various properties of quantum Markov chains. We conclude by showing that our formalism generalizes the usual framework for quantum random walks.

  7. On a Result for Finite Markov Chains

    ERIC Educational Resources Information Center

    Kulathinal, Sangita; Ghosh, Lagnojita

    2006-01-01

    In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…

  8. Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium.

    PubMed

    Kapfer, Sebastian C; Krauth, Werner

    2017-12-15

    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.

  9. Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium

    NASA Astrophysics Data System (ADS)

    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.

  10. Regenerative Simulation of Harris Recurrent Markov Chains.

    DTIC Science & Technology

    1982-07-01

    Sutijle) S. TYPE OF REPORT A PERIOD COVERED REGENERATIVE SIMULATION OF HARRIS RECURRENT Technical Report MARKOV CHAINS 14. PERFORMING ORG. REPORT NUMBER...7 AD-Ag 251 STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH /s i2/ REGENERATIVE SIMULATION OF HARRIS RECURRENT MARKOV CHAINS,(U) JUL 82 P W GLYNN N0001...76-C-0578 UNtLASSIFIED TR-62 NL EhhhIhEEEEEEI EEEEEIIIIIII REGENERATIVE SIMULATION OF HARRIS RECURRENT MARKOV CHAINS by Peter W. Glynn TECHNICAL

  11. Using Games to Teach Markov Chains

    ERIC Educational Resources Information Center

    Johnson, Roger W.

    2003-01-01

    Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…

  12. Probability distributions for Markov chain based quantum walks

    NASA Astrophysics Data System (ADS)

    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.

  13. Markov chains for testing redundant software

    NASA Technical Reports Server (NTRS)

    White, Allan L.; Sjogren, Jon A.

    1988-01-01

    A preliminary design for a validation experiment has been developed that addresses several problems unique to assuring the extremely high quality of multiple-version programs in process-control software. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process-control testing, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level using confidence intervals obtained for the transition probabilities during the experiment. An example demonstrating the method is provided.

  14. Handling target obscuration through Markov chain observations

    NASA Astrophysics Data System (ADS)

    Kouritzin, Michael A.; Wu, Biao

    2008-04-01

    Target Obscuration, including foliage or building obscuration of ground targets and landscape or horizon obscuration of airborne targets, plagues many real world filtering problems. In particular, ground moving target identification Doppler radar, mounted on a surveillance aircraft or unattended airborne vehicle, is used to detect motion consistent with targets of interest. However, these targets try to obscure themselves (at least partially) by, for example, traveling along the edge of a forest or around buildings. This has the effect of creating random blockages in the Doppler radar image that move dynamically and somewhat randomly through this image. Herein, we address tracking problems with target obscuration by building memory into the observations, eschewing the usual corrupted, distorted partial measurement assumptions of filtering in favor of dynamic Markov chain assumptions. In particular, we assume the observations are a Markov chain whose transition probabilities depend upon the signal. The state of the observation Markov chain attempts to depict the current obscuration and the Markov chain dynamics are used to handle the evolution of the partially obscured radar image. Modifications of the classical filtering equations that allow observation memory (in the form of a Markov chain) are given. We use particle filters to estimate the position of the moving targets. Moreover, positive proof-of-concept simulations are included.

  15. Assessing significance in a Markov chain without mixing

    PubMed Central

    Chikina, Maria; Frieze, Alan; Pegden, Wesley

    2017-01-01

    We present a statistical test to detect that a presented state of a reversible Markov chain was not chosen from a stationary distribution. In particular, given a value function for the states of the Markov chain, we would like to show rigorously that the presented state is an outlier with respect to the values, by establishing a p value under the null hypothesis that it was chosen from a stationary distribution of the chain. A simple heuristic used in practice is to sample ranks of states from long random trajectories on the Markov chain and compare these with the rank of the presented state; if the presented state is a 0.1% outlier compared with the sampled ranks (its rank is in the bottom 0.1% of sampled ranks), then this observation should correspond to a p value of 0.001. This significance is not rigorous, however, without good bounds on the mixing time of the Markov chain. Our test is the following: Given the presented state in the Markov chain, take a random walk from the presented state for any number of steps. We prove that observing that the presented state is an ε-outlier on the walk is significant at p=2ε under the null hypothesis that the state was chosen from a stationary distribution. We assume nothing about the Markov chain beyond reversibility and show that significance at p≈ε is best possible in general. We illustrate the use of our test with a potential application to the rigorous detection of gerrymandering in Congressional districting. PMID:28246331

  16. Sampling rare fluctuations of discrete-time Markov chains

    NASA Astrophysics Data System (ADS)

    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.

  17. Sampling rare fluctuations of discrete-time Markov chains.

    PubMed

    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.

  18. Assessing significance in a Markov chain without mixing.

    PubMed

    Chikina, Maria; Frieze, Alan; Pegden, Wesley

    2017-03-14

    We present a statistical test to detect that a presented state of a reversible Markov chain was not chosen from a stationary distribution. In particular, given a value function for the states of the Markov chain, we would like to show rigorously that the presented state is an outlier with respect to the values, by establishing a [Formula: see text] value under the null hypothesis that it was chosen from a stationary distribution of the chain. A simple heuristic used in practice is to sample ranks of states from long random trajectories on the Markov chain and compare these with the rank of the presented state; if the presented state is a [Formula: see text] outlier compared with the sampled ranks (its rank is in the bottom [Formula: see text] of sampled ranks), then this observation should correspond to a [Formula: see text] value of [Formula: see text] This significance is not rigorous, however, without good bounds on the mixing time of the Markov chain. Our test is the following: Given the presented state in the Markov chain, take a random walk from the presented state for any number of steps. We prove that observing that the presented state is an [Formula: see text]-outlier on the walk is significant at [Formula: see text] under the null hypothesis that the state was chosen from a stationary distribution. We assume nothing about the Markov chain beyond reversibility and show that significance at [Formula: see text] is best possible in general. We illustrate the use of our test with a potential application to the rigorous detection of gerrymandering in Congressional districting.

  19. Transition records of stationary Markov chains.

    PubMed

    Naudts, Jan; Van der Straeten, Erik

    2006-10-01

    In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary Markov chain is linear in the number of steps. Three applications are discussed. A known result about entropy production is reproduced. A thermodynamic relation is derived for equilibrium systems with Metropolis dynamics. Finally, a link is made with recent results concerning a one-dimensional polymer model.

  20. Markov Chain Ontology Analysis (MCOA)

    PubMed Central

    2012-01-01

    Background 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. Results 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. Conclusion 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

  1. Markov Chain Ontology Analysis (MCOA).

    PubMed

    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.

  2. Markov chains: computing limit existence and approximations with DNA.

    PubMed

    Cardona, M; Colomer, M A; Conde, J; Miret, J M; Miró, J; Zaragoza, A

    2005-09-01

    We present two algorithms to perform computations over Markov chains. The first one determines whether the sequence of powers of the transition matrix of a Markov chain converges or not to a limit matrix. If it does converge, the second algorithm enables us to estimate this limit. The combination of these algorithms allows the computation of a limit using DNA computing. In this sense, we have encoded the states and the transition probabilities using strands of DNA for generating paths of the Markov chain.

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

    PubMed

    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.

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

    PubMed Central

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

    2014-01-01

    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. PMID:24818062

  5. Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

    NASA Astrophysics Data System (ADS)

    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”.

  6. Temperature scaling method for Markov chains.

    PubMed

    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.

  7. Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains

    PubMed Central

    Meyer, Denny; Forbes, Don; Clarke, Stephen R.

    2006-01-01

    Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key Points A comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition. The Markov assumption appears to be valid. However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play. Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes. PMID:24357946

  8. Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains.

    PubMed

    Meyer, Denny; Forbes, Don; Clarke, Stephen R

    2006-01-01

    Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key PointsA comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition.The Markov assumption appears to be valid.However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play.Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes.

  9. Exact goodness-of-fit tests for Markov chains.

    PubMed

    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.

  10. Observation uncertainty in reversible Markov chains.

    PubMed

    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+) .

  11. Honest Importance Sampling with Multiple Markov Chains

    PubMed Central

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

    2017-01-01

    Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, 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 π1 is replaced by a Harris ergodic Markov chain with invariant density π1, 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, π1, …, πk, 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 selection in

  12. Honest Importance Sampling with Multiple Markov Chains.

    PubMed

    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

  13. Saccade selection when reward probability is dynamically manipulated using Markov chains

    PubMed Central

    Lovejoy, Lee P.; Krauzlis, Richard J.

    2012-01-01

    Markov chains (stochastic processes where probabilities are assigned based on the previous outcome) are commonly used to examine the transitions between behavioral states, such as those that occur during foraging or social interactions. However, relatively little is known about how well primates can incorporate knowledge about Markov chains into their behavior. Saccadic eye movements are an example of a simple behavior influenced by information about probability, and thus are good candidates for testing whether subjects can learn Markov chains. In addition, when investigating the influence of probability on saccade target selection, the use of Markov chains could provide an alternative method that avoids confounds present in other task designs. To investigate these possibilities, we evaluated human behavior on a task in which stimulus reward probabilities were assigned using a Markov chain. On each trial, the subject selected one of four identical stimuli by saccade; after selection, feedback indicated the rewarded stimulus. Each session consisted of 200–600 trials, and on some sessions, the reward magnitude varied. On sessions with a uniform reward, subjects (n = 6) learned to select stimuli at a frequency close to reward probability, which is similar to human behavior on matching or probability classification tasks. When informed that a Markov chain assigned reward probabilities, subjects (n = 3) learned to select the greatest reward probability more often, bringing them close to behavior that maximizes reward. On sessions where reward magnitude varied across stimuli, subjects (n = 6) demonstrated preferences for both greater reward probability and greater reward magnitude, resulting in a preference for greater expected value (the product of reward probability and magnitude). These results demonstrate that Markov chains can be used to dynamically assign probabilities that are rapidly exploited by human subjects during saccade target selection. PMID:18330552

  14. Saccade selection when reward probability is dynamically manipulated using Markov chains.

    PubMed

    Nummela, Samuel U; Lovejoy, Lee P; Krauzlis, Richard J

    2008-05-01

    Markov chains (stochastic processes where probabilities are assigned based on the previous outcome) are commonly used to examine the transitions between behavioral states, such as those that occur during foraging or social interactions. However, relatively little is known about how well primates can incorporate knowledge about Markov chains into their behavior. Saccadic eye movements are an example of a simple behavior influenced by information about probability, and thus are good candidates for testing whether subjects can learn Markov chains. In addition, when investigating the influence of probability on saccade target selection, the use of Markov chains could provide an alternative method that avoids confounds present in other task designs. To investigate these possibilities, we evaluated human behavior on a task in which stimulus reward probabilities were assigned using a Markov chain. On each trial, the subject selected one of four identical stimuli by saccade; after selection, feedback indicated the rewarded stimulus. Each session consisted of 200-600 trials, and on some sessions, the reward magnitude varied. On sessions with a uniform reward, subjects (n = 6) learned to select stimuli at a frequency close to reward probability, which is similar to human behavior on matching or probability classification tasks. When informed that a Markov chain assigned reward probabilities, subjects (n = 3) learned to select the greatest reward probability more often, bringing them close to behavior that maximizes reward. On sessions where reward magnitude varied across stimuli, subjects (n = 6) demonstrated preferences for both greater reward probability and greater reward magnitude, resulting in a preference for greater expected value (the product of reward probability and magnitude). These results demonstrate that Markov chains can be used to dynamically assign probabilities that are rapidly exploited by human subjects during saccade target selection.

  15. Diagonal couplings of quantum Markov chains

    NASA Astrophysics Data System (ADS)

    Kümmerer, Burkhard; Schwieger, Kay

    2016-05-01

    In this paper we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by analyzing couplings. For a given tensor dilation we construct a self-coupling of a Markov operator. It turns out that the coupling is a dual version of the extended dual transition operator studied by Gohm et al. We deduce that this coupling is successful if and only if the dilation is asymptotically complete.

  16. Operations and support cost modeling using Markov chains

    NASA Technical Reports Server (NTRS)

    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.

  17. Markov chain model for demersal fish catch analysis in Indonesia

    NASA Astrophysics Data System (ADS)

    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.

  18. Musical Markov Chains

    NASA Astrophysics Data System (ADS)

    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.

  19. Markov-modulated Markov chains and the covarion process of molecular evolution.

    PubMed

    Galtier, N; Jean-Marie, A

    2004-01-01

    The covarion (or site specific rate variation, SSRV) process of biological sequence evolution is a process by which the evolutionary rate of a nucleotide/amino acid/codon position can change in time. In this paper, we introduce time-continuous, space-discrete, Markov-modulated Markov chains as a model for representing SSRV processes, generalizing existing theory to any model of rate change. We propose a fast algorithm for diagonalizing the generator matrix of relevant Markov-modulated Markov processes. This algorithm makes phylogeny likelihood calculation tractable even for a large number of rate classes and a large number of states, so that SSRV models become applicable to amino acid or codon sequence datasets. Using this algorithm, we investigate the accuracy of the discrete approximation to the Gamma distribution of evolutionary rates, widely used in molecular phylogeny. We show that a relatively large number of classes is required to achieve accurate approximation of the exact likelihood when the number of analyzed sequences exceeds 20, both under the SSRV and among site rate variation (ASRV) models.

  20. First and second order semi-Markov chains for wind speed modeling

    NASA Astrophysics Data System (ADS)

    Prattico, F.; Petroni, F.; D'Amico, G.

    2012-04-01

    The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [3] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [1], by using two models, first

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  3. Document Ranking Based upon Markov Chains.

    ERIC Educational Resources Information Center

    Danilowicz, Czeslaw; Balinski, Jaroslaw

    2001-01-01

    Considers how the order of documents in information retrieval responses are determined and introduces a method that uses a probabilistic model of a document set where documents are regarded as states of a Markov chain and where transition probabilities are directly proportional to similarities between documents. (Author/LRW)

  4. Modeling haplotype block variation using Markov chains.

    PubMed

    Greenspan, G; Geiger, D

    2006-04-01

    Models of background variation in genomic regions form the basis of linkage disequilibrium mapping methods. In this work we analyze a background model that groups SNPs into haplotype blocks and represents the dependencies between blocks by a Markov chain. We develop an error measure to compare the performance of this model against the common model that assumes that blocks are independent. By examining data from the International Haplotype Mapping project, we show how the Markov model over haplotype blocks is most accurate when representing blocks in strong linkage disequilibrium. This contrasts with the independent model, which is rendered less accurate by linkage disequilibrium. We provide a theoretical explanation for this surprising property of the Markov model and relate its behavior to allele diversity.

  5. Modeling Haplotype Block Variation Using Markov Chains

    PubMed Central

    Greenspan, G.; Geiger, D.

    2006-01-01

    Models of background variation in genomic regions form the basis of linkage disequilibrium mapping methods. In this work we analyze a background model that groups SNPs into haplotype blocks and represents the dependencies between blocks by a Markov chain. We develop an error measure to compare the performance of this model against the common model that assumes that blocks are independent. By examining data from the International Haplotype Mapping project, we show how the Markov model over haplotype blocks is most accurate when representing blocks in strong linkage disequilibrium. This contrasts with the independent model, which is rendered less accurate by linkage disequilibrium. We provide a theoretical explanation for this surprising property of the Markov model and relate its behavior to allele diversity. PMID:16361244

  6. Analysing grouping of nucleotides in DNA sequences using lumped processes constructed from Markov chains.

    PubMed

    Guédon, Yann; d'Aubenton-Carafa, Yves; Thermes, Claude

    2006-03-01

    The most commonly used models for analysing local dependencies in DNA sequences are (high-order) Markov chains. Incorporating knowledge relative to the possible grouping of the nucleotides enables to define dedicated sub-classes of Markov chains. The problem of formulating lumpability hypotheses for a Markov chain is therefore addressed. In the classical approach to lumpability, this problem can be formulated as the determination of an appropriate state space (smaller than the original state space) such that the lumped chain defined on this state space retains the Markov property. We propose a different perspective on lumpability where the state space is fixed and the partitioning of this state space is represented by a one-to-many probabilistic function within a two-level stochastic process. Three nested classes of lumped processes can be defined in this way as sub-classes of first-order Markov chains. These lumped processes enable parsimonious reparameterizations of Markov chains that help to reveal relevant partitions of the state space. Characterizations of the lumped processes on the original transition probability matrix are derived. Different model selection methods relying either on hypothesis testing or on penalized log-likelihood criteria are presented as well as extensions to lumped processes constructed from high-order Markov chains. The relevance of the proposed approach to lumpability is illustrated by the analysis of DNA sequences. In particular, the use of lumped processes enables to highlight differences between intronic sequences and gene untranslated region sequences.

  7. Markov chain decision model for urinary incontinence procedures.

    PubMed

    Kumar, Sameer; Ghildayal, Nidhi; Ghildayal, Neha

    2017-03-13

    Purpose Urinary incontinence (UI) is a common chronic health condition, a problem specifically among elderly women that impacts quality of life negatively. However, UI is usually viewed as likely result of old age, and as such is generally not evaluated or even managed appropriately. Many treatments are available to manage incontinence, such as bladder training and numerous surgical procedures such as Burch colposuspension and Sling for UI which have high success rates. The purpose of this paper is to analyze which of these popular surgical procedures for UI is effective. Design/methodology/approach This research employs randomized, prospective studies to obtain robust cost and utility data used in the Markov chain decision model for examining which of these surgical interventions is more effective in treating women with stress UI based on two measures: number of quality adjusted life years (QALY) and cost per QALY. Treeage Pro Healthcare software was employed in Markov decision analysis. Findings Results showed the Sling procedure is a more effective surgical intervention than the Burch. However, if a utility greater than certain utility value, for which both procedures are equally effective, is assigned to persistent incontinence, the Burch procedure is more effective than the Sling procedure. Originality/value This paper demonstrates the efficacy of a Markov chain decision modeling approach to study the comparative effectiveness analysis of available treatments for patients with UI, an important public health issue, widely prevalent among elderly women in developed and developing countries. This research also improves upon other analyses using a Markov chain decision modeling process to analyze various strategies for treating UI.

  8. Fuzzy Markov random fields versus chains for multispectral image segmentation.

    PubMed

    Salzenstein, Fabien; Collet, Christophe

    2006-11-01

    This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data.

  9. MC3: Multi-core Markov-chain Monte Carlo code

    NASA Astrophysics Data System (ADS)

    Cubillos, Patricio; Harrington, Joseph; Lust, Nate; Foster, AJ; Stemm, Madison; Loredo, Tom; Stevenson, Kevin; Campo, Chris; Hardin, Matt; Hardy, Ryan

    2016-10-01

    MC3 (Multi-core Markov-chain Monte Carlo) is a Bayesian statistics tool that can be executed from the shell prompt or interactively through the Python interpreter with single- or multiple-CPU parallel computing. It offers Markov-chain Monte Carlo (MCMC) posterior-distribution sampling for several algorithms, Levenberg-Marquardt least-squares optimization, and uniform non-informative, Jeffreys non-informative, or Gaussian-informative priors. MC3 can share the same value among multiple parameters and fix the value of parameters to constant values, and offers Gelman-Rubin convergence testing and correlated-noise estimation with time-averaging or wavelet-based likelihood estimation methods.

  10. Extreme event statistics in a drifting Markov chain

    NASA Astrophysics Data System (ADS)

    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.

  11. Influence of credit scoring on the dynamics of Markov chain

    NASA Astrophysics Data System (ADS)

    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.

  12. Metastable Distributions of Markov Chains with Rare Transitions

    NASA Astrophysics Data System (ADS)

    Freidlin, M.; Koralov, L.

    2017-06-01

    In this paper we consider Markov chains X^\\varepsilon _t with transition rates that depend on a small parameter \\varepsilon . We are interested in the long time behavior of X^\\varepsilon _t at various \\varepsilon -dependent time scales t = t(\\varepsilon ). The asymptotic behavior depends on how the point (1/\\varepsilon , t(\\varepsilon )) approaches infinity. We introduce a general notion of complete asymptotic regularity (a certain asymptotic relation between the ratios of transition rates), which ensures the existence of the metastable distribution for each initial point and a given time scale t(\\varepsilon ). The technique of i-graphs allows one to describe the metastable distribution explicitly. The result may be viewed as a generalization of the ergodic theorem to the case of parameter-dependent Markov chains.

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

    NASA Astrophysics Data System (ADS)

    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.

  14. Markov Chain Estimation of Avian Seasonal Fecundity

    EPA Science Inventory

    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...

  15. Bayesian tomography by interacting Markov chains

    NASA Astrophysics Data System (ADS)

    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.

  16. The spectral method and the central limit theorem for general Markov chains

    NASA Astrophysics Data System (ADS)

    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.

  17. The cutoff phenomenon in finite Markov chains.

    PubMed Central

    Diaconis, P

    1996-01-01

    Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to symmetry) is explored. Examples are given where the symmetry is broken but the cutoff phenomenon persists. PMID:11607633

  18. Bayesian analysis of non-homogeneous Markov chains: application to mental health data.

    PubMed

    Sung, Minje; Soyer, Refik; Nhan, Nguyen

    2007-07-10

    In this paper we present a formal treatment of non-homogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the non-homogeneity of transition patterns. In doing so, we introduce a logistic regression set-up for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study. Copyright 2006 John Wiley & Sons, Ltd.

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

    NASA Astrophysics Data System (ADS)

    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.

  20. Markov chain Monte Carlo estimation of quantum states

    NASA Astrophysics Data System (ADS)

    Diguglielmo, James; Messenger, Chris; Fiurášek, Jaromír; Hage, Boris; Samblowski, Aiko; Schmidt, Tabea; Schnabel, Roman

    2009-03-01

    We apply a Bayesian data analysis scheme known as the Markov chain Monte Carlo to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical information concerning all reconstruction parameters including their statistical correlations with no a priori assumptions as to the form of the distribution from which it has been obtained. From this vector we can derive, e.g., the marginal distributions and uncertainties of all model parameters, and also of other quantities such as the purity of the reconstructed state. We demonstrate the utility of this scheme by reconstructing the Wigner function of phase-diffused squeezed states. These states possess non-Gaussian statistics and therefore represent a nontrivial case of tomographic reconstruction. We compare our results to those obtained through pure maximum-likelihood and Fisher information approaches.

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

    PubMed

    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.

  2. A simplified parsimonious higher order multivariate Markov chain model

    NASA Astrophysics Data System (ADS)

    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.

  3. Investigation of reliability indicators of information analysis systems based on Markov’s absorbing chain model

    NASA Astrophysics Data System (ADS)

    Gilmanshin, I. R.; Kirpichnikov, A. P.

    2017-09-01

    In the result of study of the algorithm of the functioning of the early detection module of excessive losses, it is proven the ability to model it by using absorbing Markov chains. The particular interest is in the study of probability characteristics of early detection module functioning algorithm of losses in order to identify the relationship of indicators of reliability of individual elements, or the probability of occurrence of certain events and the likelihood of transmission of reliable information. The identified relations during the analysis allow to set thresholds reliability characteristics of the system components.

  4. Multi-chain Markov chain Monte Carlo methods for computationally expensive models

    NASA Astrophysics Data System (ADS)

    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.

  5. An Overview of Markov Chain Methods for the Study of Stage-Sequential Developmental Processes

    ERIC Educational Resources Information Center

    Kapland, David

    2008-01-01

    This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model.…

  6. Allele Age Under Non-Classical Assumptions is Clarified by an Exact Computational Markov Chain Approach.

    PubMed

    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.

  7. A tridiagonal parsimonious higher order multivariate Markov chain model

    NASA Astrophysics Data System (ADS)

    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.

  8. Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

    NASA Astrophysics Data System (ADS)

    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.

  9. Numerical methods in Markov chain modeling

    NASA Technical Reports Server (NTRS)

    Philippe, Bernard; Saad, Youcef; Stewart, William J.

    1989-01-01

    Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

  10. Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

    NASA Astrophysics Data System (ADS)

    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.

  11. Classification of customer lifetime value models using Markov chain

    NASA Astrophysics Data System (ADS)

    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.

  12. Using Markov Chain Analyses in Counselor Education Research

    ERIC Educational Resources Information Center

    Duys, David K.; Headrick, Todd C.

    2004-01-01

    This study examined the efficacy of an infrequently used statistical analysis in counselor education research. A Markov chain analysis was used to examine hypothesized differences between students' use of counseling skills in an introductory course. Thirty graduate students participated in the study. Independent raters identified the microskills…

  13. Constructing 1/omegaalpha noise from reversible Markov chains.

    PubMed

    Erland, Sveinung; Greenwood, Priscilla E

    2007-09-01

    This paper gives sufficient conditions for the output of 1/omegaalpha noise from reversible Markov chains on finite state spaces. We construct several examples exhibiting this behavior in a specified range of frequencies. We apply simple representations of the covariance function and the spectral density in terms of the eigendecomposition of the probability transition matrix. The results extend to hidden Markov chains. We generalize the results for aggregations of AR1-processes of C. W. J. Granger [J. Econometrics 14, 227 (1980)]. Given the eigenvalue function, there is a variety of ways to assign values to the states such that the 1/omegaalpha condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of 1/omega noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct 1/omegaalpha noise which also has a long memory.

  14. Exploring Mass Perception with Markov Chain Monte Carlo

    ERIC Educational Resources Information Center

    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…

  15. Variable context Markov chains for HIV protease cleavage site prediction.

    PubMed

    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.

  16. Limiting Distributions of Functionals of Markov Chains.

    DTIC Science & Technology

    1984-08-01

    limiting distributions; periodic * nonhomoger.,!ous Poisson processes . 19 ANS? MACY IConuui oe nonoe’ee if necorglooy and edern thty by block numbers...homogeneous Poisson processes is of interest in itself. The problem considered in this paper is of interest in the theory of partially observable...where we obtain the limiting distribution of the interevent times. Key Words: Markov Chains, Limiting Distributions, Periodic Nonhomogeneous Poisson

  17. Simplification of irreversible Markov chains by removal of states with fast leaving rates.

    PubMed

    Jia, Chen

    2016-07-07

    In the recent work of Ullah et al. (2012a), the authors developed an effective method to simplify reversible Markov chains by removal of states with low equilibrium occupancies. In this paper, we extend this result to irreversible Markov chains. We show that an irreversible chain can be simplified by removal of states with fast leaving rates. Moreover, we reveal that the irreversibility of the chain will always decrease after model simplification. This suggests that although model simplification can retain almost all the dynamic information of the chain, it will lose some thermodynamic information as a trade-off. Examples from biology are also given to illustrate the main results of this paper. Copyright © 2016 Elsevier Ltd. All rights reserved.

  18. Asteroid mass estimation with Markov-chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    Siltala, L.; Granvik, M.

    2017-09-01

    We have developed a new Markov-chain Monte Carlo-based algorithm for asteroid mass estimation based on mutual encounters and tested it for several different asteroids. Our results are in line with previous literature values but suggest that uncertainties of prior estimates may be misleading as a consequence of using linearized methods.

  19. Building Higher-Order Markov Chain Models with EXCEL

    ERIC Educational Resources Information Center

    Ching, Wai-Ki; Fung, Eric S.; Ng, Michael K.

    2004-01-01

    Categorical data sequences occur in many applications such as forecasting, data mining and bioinformatics. In this note, we present higher-order Markov chain models for modelling categorical data sequences with an efficient algorithm for solving the model parameters. The algorithm can be implemented easily in a Microsoft EXCEL worksheet. We give a…

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

    PubMed

    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.

  1. SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.

    PubMed

    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.

  2. Enhancement of Markov chain model by integrating exponential smoothing: A case study on Muslims marriage and divorce

    NASA Astrophysics Data System (ADS)

    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.

  3. Radiative transfer calculated from a Markov chain formalism

    NASA Technical Reports Server (NTRS)

    Esposito, L. W.; House, L. L.

    1978-01-01

    The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

  4. Generation of intervention strategy for a genetic regulatory network represented by a family of Markov Chains.

    PubMed

    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.

  5. Constructing 1/ωα noise from reversible Markov chains

    NASA Astrophysics Data System (ADS)

    Erland, Sveinung; Greenwood, Priscilla E.

    2007-09-01

    This paper gives sufficient conditions for the output of 1/ωα noise from reversible Markov chains on finite state spaces. We construct several examples exhibiting this behavior in a specified range of frequencies. We apply simple representations of the covariance function and the spectral density in terms of the eigendecomposition of the probability transition matrix. The results extend to hidden Markov chains. We generalize the results for aggregations of AR1-processes of C. W. J. Granger [J. Econometrics 14, 227 (1980)]. Given the eigenvalue function, there is a variety of ways to assign values to the states such that the 1/ωα condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of 1/ω noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct 1/ωα noise which also has a long memory.

  6. DNA motif alignment by evolving a population of Markov chains.

    PubMed

    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.

  7. Quantitative risk stratification in Markov chains with limiting conditional distributions.

    PubMed

    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.

  8. Statistical significance test for transition matrices of atmospheric Markov chains

    NASA Technical Reports Server (NTRS)

    Vautard, Robert; Mo, Kingtse C.; Ghil, Michael

    1990-01-01

    Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.

  9. Density Control of Multi-Agent Systems with Safety Constraints: A Markov Chain Approach

    NASA Astrophysics Data System (ADS)

    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

  10. Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains

    NASA Astrophysics Data System (ADS)

    Formentin, M.; Külske, C.; Reichenbachs, A.

    2012-01-01

    We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.

  11. An 'adding' algorithm for the Markov chain formalism for radiation transfer

    NASA Technical Reports Server (NTRS)

    Esposito, L. W.

    1979-01-01

    An adding algorithm is presented, that extends the Markov chain method and considers a preceding calculation as a single state of a new Markov chain. This method takes advantage of the description of the radiation transport as a stochastic process. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. It is determined that the time required for the algorithm is comparable to that for a doubling calculation for homogeneous atmospheres. For an inhomogeneous atmosphere the new method is considerably faster than the standard adding routine. It is concluded that the algorithm is efficient, accurate, and suitable for smaller computers in calculating the diffuse intensity scattered by an inhomogeneous planetary atmosphere.

  12. On the utility of the multi-level algorithm for the solution of nearly completely decomposable Markov chains

    NASA Technical Reports Server (NTRS)

    Leutenegger, Scott T.; Horton, Graham

    1994-01-01

    Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper, we consider the performance of the Multi-Level algorithm for solving Nearly Completely Decomposable (NCD) Markov chains, for which special-purpose iteractive aggregation/disaggregation algorithms such as the Koury-McAllister-Stewart (KMS) method have been developed that can exploit the decomposability of the the Markov chain. We present experimental results indicating that the general-purpose Multi-Level algorithm is competitive, and can be significantly faster than the special-purpose KMS algorithm when Gauss-Seidel and Gaussian Elimination are used for solving the individual blocks.

  13. Network Security Risk Assessment System Based on Attack Graph and Markov Chain

    NASA Astrophysics Data System (ADS)

    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.

  14. Students' Progress throughout Examination Process as a Markov Chain

    ERIC Educational Resources Information Center

    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…

  15. Marathon: An Open Source Software Library for the Analysis of Markov-Chain Monte Carlo Algorithms

    PubMed Central

    Rechner, Steffen; Berger, Annabell

    2016-01-01

    We present the software library marathon, which is designed to support the analysis of sampling algorithms that are based on the Markov-Chain Monte Carlo principle. The main application of this library is the computation of properties of so-called state graphs, which represent the structure of Markov chains. We demonstrate applications and the usefulness of marathon by investigating the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graphs. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is often several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time. PMID:26824442

  16. Monte Carlo estimation of total variation distance of Markov chains on large spaces, with application to phylogenetics.

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    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

  18. Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics.

    PubMed

    Wu, Xiao-Lin; Sun, Chuanyu; Beissinger, Timothy M; Rosa, Guilherme Jm; Weigel, Kent A; Gatti, Natalia de Leon; Gianola, Daniel

    2012-09-25

    Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.

  19. Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

    PubMed Central

    2012-01-01

    Background Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Results Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Conclusions Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs. PMID:23009363

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  2. A Markov chain model for reliability growth and decay

    NASA Technical Reports Server (NTRS)

    Siegrist, K.

    1982-01-01

    A mathematical model is developed to describe a complex system undergoing a sequence of trials in which there is interaction between the internal states of the system and the outcomes of the trials. For example, the model might describe a system undergoing testing that is redesigned after each failure. The basic assumptions for the model are that the state of the system after a trial depends probabilistically only on the state before the trial and on the outcome of the trial and that the outcome of a trial depends probabilistically only on the state of the system before the trial. It is shown that under these basic assumptions, the successive states form a Markov chain and the successive states and outcomes jointly form a Markov chain. General results are obtained for the transition probabilities, steady-state distributions, etc. A special case studied in detail describes a system that has two possible state ('repaired' and 'unrepaired') undergoing trials that have three possible outcomes ('inherent failure', 'assignable-cause' 'failure' and 'success'). For this model, the reliability function is computed explicitly and an optimal repair policy is obtained.

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

    PubMed

    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.

  4. Covariate adjustment of event histories estimated from Markov chains: the additive approach.

    PubMed

    Aalen, O O; Borgan, O; Fekjaer, H

    2001-12-01

    Markov chain models are frequently used for studying event histories that include transitions between several states. An empirical transition matrix for nonhomogeneous Markov chains has previously been developed, including a detailed statistical theory based on counting processes and martingales. In this article, we show how to estimate transition probabilities dependent on covariates. This technique may, e.g., be used for making estimates of individual prognosis in epidemiological or clinical studies. The covariates are included through nonparametric additive models on the transition intensities of the Markov chain. The additive model allows for estimation of covariate-dependent transition intensities, and again a detailed theory exists based on counting processes. The martingale setting now allows for a very natural combination of the empirical transition matrix and the additive model, resulting in estimates that can be expressed as stochastic integrals, and hence their properties are easily evaluated. Two medical examples will be given. In the first example, we study how the lung cancer mortality of uranium miners depends on smoking and radon exposure. In the second example, we study how the probability of being in response depends on patient group and prophylactic treatment for leukemia patients who have had a bone marrow transplantation. A program in R and S-PLUS that can carry out the analyses described here has been developed and is freely available on the Internet.

  5. Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China☆

    PubMed Central

    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

  6. Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China.

    PubMed

    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.

  7. User's Manual MCnest - Markov Chain Nest Productivity Model Version 2.0

    EPA Science Inventory

    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...

  8. Generating intrinsically disordered protein conformational ensembles from a Markov chain

    NASA Astrophysics Data System (ADS)

    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.

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

    PubMed

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

    2014-02-01

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

  10. Parallel algorithms for simulating continuous time Markov chains

    NASA Technical Reports Server (NTRS)

    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.

  11. Markov Chain Analysis of Musical Dice Games

    NASA Astrophysics Data System (ADS)

    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.

  12. Irreversible Markov chains in spin models: Topological excitations

    NASA Astrophysics Data System (ADS)

    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.

  13. Markov Chain Model with Catastrophe to Determine Mean Time to Default of Credit Risky Assets

    NASA Astrophysics Data System (ADS)

    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.

  14. Medical imaging feasibility in body fluids using Markov chains

    NASA Astrophysics Data System (ADS)

    Kavehrad, M.; Armstrong, A. D.

    2017-02-01

    A relatively wide field-of-view and high resolution imaging is necessary for navigating the scope within the body, inspecting tissue, diagnosing disease, and guiding surgical interventions. As the large number of modes available in the multimode fibers (MMF) provides higher resolution, MMFs could replace the millimeters-thick bundles of fibers and lenses currently used in endoscopes. However, attributes of body fluids and obscurants such as blood, impose perennial limitations on resolution and reliability of optical imaging inside human body. To design and evaluate optimum imaging techniques that operate under realistic body fluids conditions, a good understanding of the channel (medium) behavior is necessary. In most prior works, Monte-Carlo Ray Tracing (MCRT) algorithm has been used to analyze the channel behavior. This task is quite numerically intensive. The focus of this paper is on investigating the possibility of simplifying this task by a direct extraction of state transition matrices associated with standard Markov modeling from the MCRT computer simulations programs. We show that by tracing a photon's trajectory in the body fluids via a Markov chain model, the angular distribution can be calculated by simple matrix multiplications. We also demonstrate that the new approach produces result that are close to those obtained by MCRT and other known methods. Furthermore, considering the fact that angular, spatial, and temporal distributions of energy are inter-related, mixing time of Monte- Carlo Markov Chain (MCMC) for different types of liquid concentrations is calculated based on Eigen-analysis of the state transition matrix and possibility of imaging in scattering media are investigated. To this end, we have started to characterize the body fluids that reduce the resolution of imaging [1].

  15. Detecting memory and structure in human navigation patterns using Markov chain models of varying order.

    PubMed

    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.

  16. Detecting Memory and Structure in Human Navigation Patterns Using Markov Chain Models of Varying Order

    PubMed Central

    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. PMID:25013937

  17. Time-patterns of antibiotic exposure in poultry production--a Markov chains exploratory study of nature and consequences.

    PubMed

    Chauvin, C; Clement, C; Bruneau, M; Pommeret, D

    2007-07-16

    This article describes the use of Markov chains to explore the time-patterns of antimicrobial exposure in broiler poultry. The transition in antimicrobial exposure status (exposed/not exposed to an antimicrobial, with a distinction between exposures to the different antimicrobial classes) in extensive data collected in broiler chicken flocks from November 2003 onwards, was investigated. All Markov chains were first-order chains. Mortality rate, geographical location and slaughter semester were sources of heterogeneity between transition matrices. Transitions towards a 'no antimicrobial' exposure state were highly predominant, whatever the initial state. From a 'no antimicrobial' exposure state, the transition to beta-lactams was predominant among transitions to an antimicrobial exposure state. Transitions between antimicrobial classes were rare and variable. Switches between antimicrobial classes and repeats of a particular class were both observed. Application of Markov chains analysis to the database of the nation-wide antimicrobial resistance monitoring programme pointed out that transition probabilities between antimicrobial exposure states increased with the number of resistances in Escherichia coli strains.

  18. Predicting hepatitis B monthly incidence rates using weighted Markov chains and time series methods.

    PubMed

    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.

  19. Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

    NASA Astrophysics Data System (ADS)

    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.

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

    PubMed

    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.

  1. Animal vocal sequences: not the Markov chains we thought they were

    PubMed Central

    Kershenbaum, Arik; Bowles, Ann E.; Freeberg, Todd M.; Jin, Dezhe Z.; Lameira, Adriano R.; Bohn, Kirsten

    2014-01-01

    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. PMID:25143037

  2. Animal vocal sequences: not the Markov chains we thought they were.

    PubMed

    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.

  3. Vulnerability of networks of interacting Markov chains.

    PubMed

    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.

  4. Markov chains at the interface of combinatorics, computing, and statistical physics

    NASA Astrophysics Data System (ADS)

    Streib, Amanda Pascoe

    The fields of statistical physics, discrete probability, combinatorics, and theoretical computer science have converged around efforts to understand random structures and algorithms. Recent activity in the interface of these fields has enabled tremendous breakthroughs in each domain and has supplied a new set of techniques for researchers approaching related problems. This thesis makes progress on several problems in this interface whose solutions all build on insights from multiple disciplinary perspectives. First, we consider a dynamic growth process arising in the context of DNA-based self-assembly. The assembly process can be modeled as a simple Markov chain. We prove that the chain is rapidly mixing for large enough bias in regions of Zd. The proof uses a geometric distance function and a variant of path coupling in order to handle distances that can be exponentially large. We also provide the first results in the case of fluctuating bias, where the bias can vary depending on the location of the tile, which arises in the nanotechnology application. Moreover, we use intuition from statistical physics to construct a choice of the biases for which the Markov chain Mmon requires exponential time to converge. Second, we consider a related problem regarding the convergence rate of biased permutations that arises in the context of self-organizing lists. The Markov chain Mnn in this case is a nearest-neighbor chain that allows adjacent transpositions, and the rate of these exchanges is governed by various input parameters. It was conjectured that the chain is always rapidly mixing when the inversion probabilities are positively biased, i.e., we put nearest neighbor pair x < y in order with bias 1/2 ≤ pxy ≤ 1 and out of order with bias 1 - pxy. The Markov chain Mmon was known to have connections to a simplified version of this biased card-shuffling. We provide new connections between Mnn and Mmon by using simple combinatorial bijections, and we prove that Mnn is

  5. LD-SPatt: large deviations statistics for patterns on Markov chains.

    PubMed

    Nuel, G

    2004-01-01

    Statistics on Markov chains are widely used for the study of patterns in biological sequences. Statistics on these models can be done through several approaches. Central limit theorem (CLT) producing Gaussian approximations are one of the most popular ones. Unfortunately, in order to find a pattern of interest, these methods have to deal with tail distribution events where CLT is especially bad. In this paper, we propose a new approach based on the large deviations theory to assess pattern statistics. We first recall theoretical results for empiric mean (level 1) as well as empiric distribution (level 2) large deviations on Markov chains. Then, we present the applications of these results focusing on numerical issues. LD-SPatt is the name of GPL software implementing these algorithms. We compare this approach to several existing ones in terms of complexity and reliability and show that the large deviations are more reliable than the Gaussian approximations in absolute values as well as in terms of ranking and are at least as reliable as compound Poisson approximations. We then finally discuss some further possible improvements and applications of this new method.

  6. Markov chain aggregation and its applications to combinatorial reaction networks.

    PubMed

    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.

  7. Markov Chain Models for Stochastic Behavior in Resonance Overlap Regions

    NASA Astrophysics Data System (ADS)

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

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

    DOE PAGES

    Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; ...

    2017-10-17

    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 ismore » 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.« less

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan

    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 ismore » 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.« less

  11. Data Analysis Recipes: Using Markov Chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    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. .

  12. A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis

    ERIC Educational Resources Information Center

    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…

  13. Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

    PubMed

    Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W

    2007-07-01

    Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

  14. Overshoot in biological systems modelled by Markov chains: a non-equilibrium dynamic phenomenon.

    PubMed

    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.

  15. Bayesian seismic tomography by parallel interacting Markov chains

    NASA Astrophysics Data System (ADS)

    Gesret, Alexandrine; Bottero, Alexis; Romary, Thomas; Noble, Mark; Desassis, Nicolas

    2014-05-01

    The velocity field estimated by first arrival traveltime tomography is commonly used as a starting point for further seismological, mineralogical, tectonic or similar analysis. In order to interpret quantitatively the results, the tomography uncertainty values as well as their spatial distribution are required. The estimated velocity model is obtained through inverse modeling by minimizing an objective function that compares observed and computed traveltimes. This step is often performed by gradient-based optimization algorithms. The major drawback of such local optimization schemes, beyond the possibility of being trapped in a local minimum, is that they do not account for the multiple possible solutions of the inverse problem. They are therefore unable to assess the uncertainties linked to the solution. Within a Bayesian (probabilistic) framework, solving the tomography inverse problem aims at estimating the posterior probability density function of velocity model using a global sampling algorithm. Markov chains Monte-Carlo (MCMC) methods are known to produce samples of virtually any distribution. In such a Bayesian inversion, the total number of simulations we can afford is highly related to the computational cost of the forward model. Although fast algorithms have been recently developed for computing first arrival traveltimes of seismic waves, the complete browsing of the posterior distribution of velocity model is hardly performed, especially when it is high dimensional and/or multimodal. In the latter case, the chain may even stay stuck in one of the modes. In order to improve the mixing properties of classical single MCMC, we propose to make interact several Markov chains at different temperatures. This method can make efficient use of large CPU clusters, without increasing the global computational cost with respect to classical MCMC and is therefore particularly suited for Bayesian inversion. The exchanges between the chains allow a precise sampling of the

  16. A simplified parsimonious higher order multivariate Markov chain model with new convergence condition

    NASA Astrophysics Data System (ADS)

    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.

  17. Modelling Faculty Replacement Strategies Using a Time-Dependent Finite Markov-Chain Process.

    ERIC Educational Resources Information Center

    Hackett, E. Raymond; Magg, Alexander A.; Carrigan, Sarah D.

    1999-01-01

    Describes the use of a time-dependent Markov-chain model to develop faculty-replacement strategies within a college at a research university. The study suggests that a stochastic modelling approach can provide valuable insight when planning for personnel needs in the immediate (five-to-ten year) future. (MSE)

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

    ERIC Educational Resources Information Center

    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…

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

    PubMed

    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.

  20. A Graph-Algorithmic Approach for the Study of Metastability in Markov Chains

    NASA Astrophysics Data System (ADS)

    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.

  1. Technical manual for basic version of the Markov chain nest productivity model (MCnest)

    EPA Science Inventory

    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...

  2. User’s manual for basic version of MCnest Markov chain nest productivity model

    EPA Science Inventory

    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...

  3. Alignment-free Transcriptomic and Metatranscriptomic Comparison Using Sequencing Signatures with Variable Length Markov Chains.

    PubMed

    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.

  4. Multivariate Markov chain modeling for stock markets

    NASA Astrophysics Data System (ADS)

    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.

  5. Adaptive relaxation for the steady-state analysis of Markov chains

    NASA Technical Reports Server (NTRS)

    Horton, Graham

    1994-01-01

    We consider a variant of the well-known Gauss-Seidel method for the solution of Markov chains in steady state. Whereas the standard algorithm visits each state exactly once per iteration in a predetermined order, the alternative approach uses a dynamic strategy. A set of states to be visited is maintained which can grow and shrink as the computation progresses. In this manner, we hope to concentrate the computational work in those areas of the chain in which maximum improvement in the solution can be achieved. We consider the adaptive approach both as a solver in its own right and as a relaxation method within the multi-level algorithm. Experimental results show significant computational savings in both cases.

  6. Experiences with Markov Chain Monte Carlo Convergence Assessment in Two Psychometric Examples

    ERIC Educational Resources Information Center

    Sinharay, Sandip

    2004-01-01

    There is an increasing use of Markov chain Monte Carlo (MCMC) algorithms for fitting statistical models in psychometrics, especially in situations where the traditional estimation techniques are very difficult to apply. One of the disadvantages of using an MCMC algorithm is that it is not straightforward to determine the convergence of the…

  7. Utilization of two web-based continuing education courses evaluated by Markov chain model.

    PubMed

    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.

  8. Utilization of two web-based continuing education courses evaluated by Markov chain model

    PubMed Central

    Lin, Jin-Mann S; Reeves, William C

    2011-01-01

    Objectives To evaluate the web structure of two web-based continuing education courses, identify problems and assess the effects of web site modifications. Design 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. Measurements Web navigation paths were collected between 2008 and 2010. The probability of navigating from one web page to another was analyzed. Results 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. Conclusions 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. PMID:21976027

  9. Geometry and Dynamics for Markov Chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    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.

  10. Optimized nested Markov chain Monte Carlo sampling: theory

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Coe, Joshua D; Shaw, M Sam; Sewell, Thomas D

    2009-01-01

    Metropolis Monte Carlo sampling of a reference potential is used to build a Markov chain in the isothermal-isobaric ensemble. At the endpoints of the chain, the energy is reevaluated at a different level of approximation (the 'full' energy) and a composite move encompassing all of the intervening steps is accepted on the basis of a modified Metropolis criterion. By manipulating the thermodynamic variables characterizing the reference system we maximize the average acceptance probability of composite moves, lengthening significantly the random walk made between consecutive evaluations of the full energy at a fixed acceptance probability. This provides maximally decorrelated samples ofmore » the full potential, thereby lowering the total number required to build ensemble averages of a given variance. The efficiency of the method is illustrated using model potentials appropriate to molecular fluids at high pressure. Implications for ab initio or density functional theory (DFT) treatment are discussed.« less

  11. Space system operations and support cost analysis using Markov chains

    NASA Technical Reports Server (NTRS)

    Unal, Resit; Dean, Edwin B.; Moore, Arlene A.; Fairbairn, Robert E.

    1990-01-01

    This paper evaluates the use of Markov chain process in probabilistic life cycle cost analysis and suggests further uses of the process as a design aid tool. A methodology is developed for estimating operations and support cost and expected life for reusable space transportation systems. Application of the methodology is demonstrated for the case of a hypothetical space transportation vehicle. A sensitivity analysis is carried out to explore the effects of uncertainty in key model inputs.

  12. Characterization of the rat exploratory behavior in the elevated plus-maze with Markov chains.

    PubMed

    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.

  13. A Markov Chain-based quantitative study of angular distribution of photons through turbid slabs via isotropic light scattering

    NASA Astrophysics Data System (ADS)

    Li, Xuesong; Northrop, William F.

    2016-04-01

    This paper describes a quantitative approach to approximate multiple scattering through an isotropic turbid slab based on Markov Chain theorem. There is an increasing need to utilize multiple scattering for optical diagnostic purposes; however, existing methods are either inaccurate or computationally expensive. Here, we develop a novel Markov Chain approximation approach to solve multiple scattering angular distribution (AD) that can accurately calculate AD while significantly reducing computational cost compared to Monte Carlo simulation. We expect this work to stimulate ongoing multiple scattering research and deterministic reconstruction algorithm development with AD measurements.

  14. Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry-Mather Theory

    NASA Astrophysics Data System (ADS)

    Lopes, Artur O.; Neumann, Adriana

    2015-05-01

    In the present paper, we consider a family of continuous time symmetric random walks indexed by , . For each the matching random walk take values in the finite set of states ; notice that is a subset of , where is the unitary circle. The infinitesimal generator of such chain is denoted by . The stationary probability for such process converges to the uniform distribution on the circle, when . Here we want to study other natural measures, obtained via a limit on , that are concentrated on some points of . We will disturb this process by a potential and study for each the perturbed stationary measures of this new process when . We disturb the system considering a fixed potential and we will denote by the restriction of to . Then, we define a non-stochastic semigroup generated by the matrix , where is the infinifesimal generator of . From the continuous time Perron's Theorem one can normalized such semigroup, and, then we get another stochastic semigroup which generates a continuous time Markov Chain taking values on . This new chain is called the continuous time Gibbs state associated to the potential , see (Lopes et al. in J Stat Phys 152:894-933, 2013). The stationary probability vector for such Markov Chain is denoted by . We assume that the maximum of is attained in a unique point of , and from this will follow that . Thus, here, our main goal is to analyze the large deviation principle for the family , when . The deviation function , which is defined on , will be obtained from a procedure based on fixed points of the Lax-Oleinik operator and Aubry-Mather theory. In order to obtain the associated Lax-Oleinik operator we use the Varadhan's Lemma for the process . For a careful analysis of the problem we present full details of the proof of the Large Deviation Principle, in the Skorohod space, for such family of Markov Chains, when . Finally, we compute the entropy of the invariant probabilities on the Skorohod space associated to the Markov Chains we analyze.

  15. On the Multilevel Solution Algorithm for Markov Chains

    NASA Technical Reports Server (NTRS)

    Horton, Graham

    1997-01-01

    We discuss the recently introduced multilevel algorithm for the steady-state solution of Markov chains. The method is based on an aggregation principle which is well established in the literature and features a multiplicative coarse-level correction. Recursive application of the aggregation principle, which uses an operator-dependent coarsening, yields a multi-level method which has been shown experimentally to give results significantly faster than the typical methods currently in use. When cast as a multigrid-like method, the algorithm is seen to be a Galerkin-Full Approximation Scheme with a solution-dependent prolongation operator. Special properties of this prolongation lead to the cancellation of the computationally intensive terms of the coarse-level equations.

  16. Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics

    PubMed Central

    Hey, Jody; Nielsen, Rasmus

    2007-01-01

    In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided. PMID:17301231

  17. Avian life history profiles for use in the Markov chain nest productivity model (MCnest)

    EPA Science Inventory

    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...

  18. Metrics for Labeled Markov Systems

    NASA Technical Reports Server (NTRS)

    Desharnais, Josee; Jagadeesan, Radha; Gupta, Vineet; Panangaden, Prakash

    1999-01-01

    Partial Labeled Markov Chains are simultaneously generalizations of process algebra and of traditional Markov chains. They provide a foundation for interacting discrete probabilistic systems, the interaction being synchronization on labels as in process algebra. Existing notions of process equivalence are too sensitive to the exact probabilities of various transitions. This paper addresses contextual reasoning principles for reasoning about more robust notions of "approximate" equivalence between concurrent interacting probabilistic systems. The present results indicate that:We develop a family of metrics between partial labeled Markov chains to formalize the notion of distance between processes. We show that processes at distance zero are bisimilar. We describe a decision procedure to compute the distance between two processes. We show that reasoning about approximate equivalence can be done compositionally by showing that process combinators do not increase distance. We introduce an asymptotic metric to capture asymptotic properties of Markov chains; and show that parallel composition does not increase asymptotic distance.

  19. Block-accelerated aggregation multigrid for Markov chains with application to PageRank problems

    NASA Astrophysics Data System (ADS)

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  1. Motif finding in DNA sequences based on skipping nonconserved positions in background Markov chains.

    PubMed

    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.

  2. Under-reported data analysis with INAR-hidden Markov chains.

    PubMed

    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.

  3. Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model

    ERIC Educational Resources Information Center

    de la Torre, Jimmy; Stark, Stephen; Chernyshenko, Oleksandr S.

    2006-01-01

    The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…

  4. H2-control and the separation principle for discrete-time jump systems with the Markov chain in a general state space

    NASA Astrophysics Data System (ADS)

    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.

  5. Nonequilibrium thermodynamic potentials for continuous-time Markov chains.

    PubMed

    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.

  6. Multilocus association mapping using variable-length Markov chains.

    PubMed

    Browning, Sharon R

    2006-06-01

    I propose a new method for association-based gene mapping that makes powerful use of multilocus data, is computationally efficient, and is straightforward to apply over large genomic regions. The approach is based on the fitting of variable-length Markov chain models, which automatically adapt to the degree of linkage disequilibrium (LD) between markers to create a parsimonious model for the LD structure. Edges of the fitted graph are tested for association with trait status. This approach can be thought of as haplotype testing with sophisticated windowing that accounts for extent of LD to reduce degrees of freedom and number of tests while maximizing information. I present analyses of two published data sets that show that this approach can have better power than single-marker tests or sliding-window haplotypic tests.

  7. Multilocus Association Mapping Using Variable-Length Markov Chains

    PubMed Central

    Browning, Sharon R.

    2006-01-01

    I propose a new method for association-based gene mapping that makes powerful use of multilocus data, is computationally efficient, and is straightforward to apply over large genomic regions. The approach is based on the fitting of variable-length Markov chain models, which automatically adapt to the degree of linkage disequilibrium (LD) between markers to create a parsimonious model for the LD structure. Edges of the fitted graph are tested for association with trait status. This approach can be thought of as haplotype testing with sophisticated windowing that accounts for extent of LD to reduce degrees of freedom and number of tests while maximizing information. I present analyses of two published data sets that show that this approach can have better power than single-marker tests or sliding-window haplotypic tests. PMID:16685642

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bates, Cameron Russell; Mckigney, Edward Allen

    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.

  9. Fracture overprinting history using Markov chain analysis: Windsor-Kennetcook subbasin, Maritimes Basin, Canada

    NASA Astrophysics Data System (ADS)

    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.

  10. Maximally reliable Markov chains under energy constraints.

    PubMed

    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.

  11. Modeling long correlation times using additive binary Markov chains: Applications to wind generation time series.

    PubMed

    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.

  12. Modeling long correlation times using additive binary Markov chains: Applications to wind generation time series

    NASA Astrophysics Data System (ADS)

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  14. Short-term droughts forecast using Markov chain model in Victoria, Australia

    NASA Astrophysics Data System (ADS)

    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.

  15. A multi-level solution algorithm for steady-state Markov chains

    NASA Technical Reports Server (NTRS)

    Horton, Graham; Leutenegger, Scott T.

    1993-01-01

    A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

  16. A descriptive model of resting-state networks using Markov chains.

    PubMed

    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.

  17. Quantum Markov chains, sufficiency of quantum channels, and Rényi information measures

    NASA Astrophysics Data System (ADS)

    Datta, Nilanjana; Wilde, Mark M.

    2015-12-01

    A short quantum Markov chain is a tripartite state {ρ }{ABC} such that system A can be recovered perfectly by acting on system C of the reduced state {ρ }{BC}. Such states have conditional mutual information I(A;B| C) equal to zero and are the only states with this property. A quantum channel {N} is sufficient for two states ρ and σ if there exists a recovery channel using which one can perfectly recover ρ from {N}(ρ ) and σ from {N}(σ ). The relative entropy difference D(ρ \\parallel σ )-D({N}(ρ )\\parallel {N}(σ )) is equal to zero if and only if {N} is sufficient for ρ and σ. In this paper, we show that these properties extend to Rényi generalizations of these information measures which were proposed in (Berta et al 2015 J. Math. Phys. 56 022205; Seshadreesan et al 2015 J. Phys. A: Math. Theor. 48 395303), thus providing an alternate characterization of short quantum Markov chains and sufficient quantum channels. These results give further support to these quantities as being legitimate Rényi generalizations of the conditional mutual information and the relative entropy difference. Along the way, we solve some open questions of Ruskai and Zhang, regarding the trace of particular matrices that arise in the study of monotonicity of relative entropy under quantum operations and strong subadditivity of the von Neumann entropy.

  18. Markov Chain Monte Carlo Inference of Parametric Dictionaries for Sparse Bayesian Approximations

    PubMed Central

    Chaspari, Theodora; Tsiartas, Andreas; Tsilifis, Panagiotis; Narayanan, Shrikanth

    2016-01-01

    Parametric dictionaries can increase the ability of sparse representations to meaningfully capture and interpret the underlying signal information, such as encountered in biomedical problems. Given a mapping function from the atom parameter space to the actual atoms, we propose a sparse Bayesian framework for learning the atom parameters, because of its ability to provide full posterior estimates, take uncertainty into account and generalize on unseen data. Inference is performed with Markov Chain Monte Carlo, that uses block sampling to generate the variables of the Bayesian problem. Since the parameterization of dictionary atoms results in posteriors that cannot be analytically computed, we use a Metropolis-Hastings-within-Gibbs framework, according to which variables with closed-form posteriors are generated with the Gibbs sampler, while the remaining ones with the Metropolis Hastings from appropriate candidate-generating densities. We further show that the corresponding Markov Chain is uniformly ergodic ensuring its convergence to a stationary distribution independently of the initial state. Results on synthetic data and real biomedical signals indicate that our approach offers advantages in terms of signal reconstruction compared to previously proposed Steepest Descent and Equiangular Tight Frame methods. This paper demonstrates the ability of Bayesian learning to generate parametric dictionaries that can reliably represent the exemplar data and provides the foundation towards inferring the entire variable set of the sparse approximation problem for signal denoising, adaptation and other applications. PMID:28649173

  19. Distance between configurations in Markov chain Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    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.

  20. Strong diffusion formulation of Markov chain ensembles and its optimal weaker reductions

    NASA Astrophysics Data System (ADS)

    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.

  1. Respondent-driven sampling as Markov chain Monte Carlo.

    PubMed

    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.

  2. Population Synthesis of Radio and Y-ray Millisecond Pulsars Using Markov Chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    Gonthier, Peter L.; Billman, C.; Harding, A. K.

    2013-04-01

    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 γ-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 ten radio surveys and by Fermi, predicting the MSP birth rate in the Galaxy. We follow a similar set of assumptions that we have used in previous, more constrained Monte Carlo simulations. The parameters associated with the birth distributions such as those for the accretion rate, magnetic field and period distributions are also free to vary. With the large set of free parameters, we employ Markov Chain Monte Carlo simulations to explore the large and small worlds of the parameter space. We present preliminary comparisons of the simulated and detected distributions of radio and γ-ray pulsar characteristics. We express our gratitude for the generous support of the National Science Foundation (REU and RUI), Fermi Guest Investigator Program and the NASA Astrophysics Theory and Fundamental Program.

  3. Trans-dimensional matched-field geoacoustic inversion with hierarchical error models and interacting Markov chains.

    PubMed

    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.

  4. Physical time scale in kinetic Monte Carlo simulations of continuous-time Markov chains.

    PubMed

    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.

  5. An Evaluation of a Markov Chain Monte Carlo Method for the Two-Parameter Logistic Model.

    ERIC Educational Resources Information Center

    Kim, Seock-Ho; Cohen, Allan S.

    The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…

  6. Predicting Urban Medical Services Demand in China: An Improved Grey Markov Chain Model by Taylor Approximation.

    PubMed

    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.

  7. Zipf exponent of trajectory distribution in the hidden Markov model

    NASA Astrophysics Data System (ADS)

    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.

  8. Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.

    PubMed

    Steven Ernest, C; Nyberg, Joakim; Karlsson, Mats O; Hooker, Andrew C

    2014-12-01

    D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase

  9. Open Markov Processes and Reaction Networks

    ERIC Educational Resources Information Center

    Swistock Pollard, Blake Stephen

    2017-01-01

    We begin by defining the concept of "open" Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain "boundary" states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow…

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  14. Bayesian posterior distributions without Markov chains.

    PubMed

    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.

  15. Manpower planning using Markov Chain model

    NASA Astrophysics Data System (ADS)

    Saad, Syafawati Ab; Adnan, Farah Adibah; Ibrahim, Haslinda; Rahim, Rahela

    2014-07-01

    Manpower planning is a planning model which understands the flow of manpower based on the policies changes. For such purpose, numerous attempts have been made by researchers to develop a model to investigate the track of movements of lecturers for various universities. As huge number of lecturers in a university, it is difficult to track the movement of lecturers and also there is no quantitative way used in tracking the movement of lecturers. This research is aimed to determine the appropriate manpower model to understand the flow of lecturers in a university in Malaysia by determine the probability and mean time of lecturers remain in the same status rank. In addition, this research also intended to estimate the number of lecturers in different status rank (lecturer, senior lecturer and associate professor). From the previous studies, there are several methods applied in manpower planning model and appropriate method used in this research is Markov Chain model. Results obtained from this study indicate that the appropriate manpower planning model used is validated by compare to the actual data. The smaller margin of error gives a better result which means that the projection is closer to actual data. These results would give some suggestions for the university to plan the hiring lecturers and budgetary for university in future.

  16. Characterizing Quality Factor of Niobium Resonators Using a Markov Chain Monte Carlo Approach

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Basu Thakur, Ritoban; Tang, Qing Yang; McGeehan, Ryan

    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.

  17. A Linear Regression and Markov Chain Model for the Arabian Horse Registry

    DTIC Science & Technology

    1993-04-01

    as a tax deduction? Yes No T-4367 68 26. Regardless of previous equine tax deductions, do you consider your current horse activities to be... (Mark one...E L T-4367 A Linear Regression and Markov Chain Model For the Arabian Horse Registry Accesion For NTIS CRA&I UT 7 4:iC=D 5 D-IC JA" LI J:13tjlC,3 lO...the Arabian Horse Registry, which needed to forecast its future registration of purebred Arabian horses . A linear regression model was utilized to

  18. RESPONDENT-DRIVEN SAMPLING AS MARKOV CHAIN MONTE CARLO

    PubMed Central

    GOEL, SHARAD; SALGANIK, MATTHEW J.

    2013-01-01

    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 respondent-driven sampling as Markov chain Monte Carlo (MCMC) 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 sample members are encouraged to recruit multiple future sample members. The paper concludes with suggestions for implementing and evaluating respondent-driven sampling studies. PMID:19572381

  19. [Analysis and modelling of safety culture in a Mexican hospital by Markov chains].

    PubMed

    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.

  20. MCMC-ODPR: primer design optimization using Markov Chain Monte Carlo sampling.

    PubMed

    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.

  1. MCMC-ODPR: Primer design optimization using Markov Chain Monte Carlo sampling

    PubMed Central

    2012-01-01

    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. PMID:23126469

  2. An NCME Instructional Module on Estimating Item Response Theory Models Using Markov Chain Monte Carlo Methods

    ERIC Educational Resources Information Center

    Kim, Jee-Seon; Bolt, Daniel M.

    2007-01-01

    The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…

  3. Markov Chain Monte Carlo in the Analysis of Single-Molecule Experimental Data

    NASA Astrophysics Data System (ADS)

    Kou, S. C.; Xie, X. Sunney; Liu, Jun S.

    2003-11-01

    This article provides a Bayesian analysis of the single-molecule fluorescence lifetime experiment designed to probe the conformational dynamics of a single DNA hairpin molecule. The DNA hairpin's conformational change is initially modeled as a two-state Markov chain, which is not observable and has to be indirectly inferred. The Brownian diffusion of the single molecule, in addition to the hidden Markov structure, further complicates the matter. We show that the analytical form of the likelihood function can be obtained in the simplest case and a Metropolis-Hastings algorithm can be designed to sample from the posterior distribution of the parameters of interest and to compute desired estiamtes. To cope with the molecular diffusion process and the potentially oscillating energy barrier between the two states of the DNA hairpin, we introduce a data augmentation technique to handle both the Brownian diffusion and the hidden Ornstein-Uhlenbeck process associated with the fluctuating energy barrier, and design a more sophisticated Metropolis-type algorithm. Our method not only increases the estimating resolution by several folds but also proves to be successful for model discrimination.

  4. Markov Chain Monte Carlo Bayesian Learning for Neural Networks

    NASA Technical Reports Server (NTRS)

    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.

  5. Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

    PubMed Central

    Golightly, Andrew; Wilkinson, Darren J.

    2011-01-01

    Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

  6. Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains.

    PubMed

    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.

  7. Markov-chain model of classified atomistic transition states for discrete kinetic Monte Carlo simulations.

    PubMed

    Numazawa, Satoshi; Smith, Roger

    2011-10-01

    Classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The scheme is then used to determine transitions that can be applied in a lattice-based kinetic Monte Carlo (KMC) atomistic simulation model. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multidimensional Boolean valued functions in three-dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology-dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion. Excellent agreement with observed experimental results is obtained.

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

    NASA Astrophysics Data System (ADS)

    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.

  9. Projection methods for the numerical solution of Markov chain models

    NASA Technical Reports Server (NTRS)

    Saad, Youcef

    1989-01-01

    Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

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

    PubMed

    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.

  11. Simulating reservoir lithologies by an actively conditioned Markov chain model

    NASA Astrophysics Data System (ADS)

    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.

  12. Indexed semi-Markov process for wind speed modeling.

    NASA Astrophysics Data System (ADS)

    Petroni, F.; D'Amico, G.; Prattico, F.

    2012-04-01

    The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [1] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [3], by using two models, first

  13. Joint simulation of regional areas burned in Canadian forest fires: A Markov Chain Monte Carlo approach

    Treesearch

    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...

  14. Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hock, Kiel; Earle, Keith

    2016-02-06

    In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. In conclusion, the posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.

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

    PubMed

    Djordjevic, Ivan B

    2015-08-24

    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 are mutually

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

    PubMed Central

    Djordjevic, Ivan B.

    2015-01-01

    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 are mutually

  17. The distribution of genome shared identical by descent for a pair of full sibs by means of the continuous time Markov chain

    NASA Astrophysics Data System (ADS)

    Julie, Hongki; Pasaribu, Udjianna S.; Pancoro, Adi

    2015-12-01

    This paper will allow Markov Chain's application in genome shared identical by descent by two individual at full sibs model. The full sibs model was a continuous time Markov Chain with three state. In the full sibs model, we look for the cumulative distribution function of the number of sub segment which have 2 IBD haplotypes from a segment of the chromosome which the length is t Morgan and the cumulative distribution function of the number of sub segment which have at least 1 IBD haplotypes from a segment of the chromosome which the length is t Morgan. This cumulative distribution function will be developed by the moment generating function.

  18. Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks.

    PubMed

    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.

  19. Markov Chain Monte Carlo: an introduction for epidemiologists

    PubMed Central

    Hamra, Ghassan; MacLehose, Richard; Richardson, David

    2013-01-01

    Markov Chain Monte Carlo (MCMC) methods are increasingly popular among epidemiologists. The reason for this may in part be that MCMC offers an appealing approach to handling some difficult types of analyses. Additionally, MCMC methods are those most commonly used for Bayesian analysis. However, epidemiologists are still largely unfamiliar with MCMC. They may lack familiarity either with he implementation of MCMC or with interpretation of the resultant output. As with tutorials outlining the calculus behind maximum likelihood in previous decades, a simple description of the machinery of MCMC is needed. We provide an introduction to conducting analyses with MCMC, and show that, given the same data and under certain model specifications, the results of an MCMC simulation match those of methods based on standard maximum-likelihood estimation (MLE). In addition, we highlight examples of instances in which MCMC approaches to data analysis provide a clear advantage over MLE. We hope that this brief tutorial will encourage epidemiologists to consider MCMC approaches as part of their analytic tool-kit. PMID:23569196

  20. Variance-reduced simulation of lattice discrete-time Markov chains with applications in reaction networks

    NASA Astrophysics Data System (ADS)

    Maginnis, P. A.; West, M.; Dullerud, G. E.

    2016-10-01

    We propose an algorithm to accelerate Monte Carlo simulation for a broad class of stochastic processes. Specifically, the class of countable-state, discrete-time Markov chains driven by additive Poisson noise, or lattice discrete-time Markov chains. In particular, this class includes simulation of reaction networks via the tau-leaping algorithm. To produce the speedup, we simulate pairs of fair-draw trajectories that are negatively correlated. Thus, when averaged, these paths produce an unbiased Monte Carlo estimator that has reduced variance and, therefore, reduced error. Numerical results for three example systems included in this work demonstrate two to four orders of magnitude reduction of mean-square error. The numerical examples were chosen to illustrate different application areas and levels of system complexity. The areas are: gene expression (affine state-dependent rates), aerosol particle coagulation with emission and human immunodeficiency virus infection (both with nonlinear state-dependent rates). Our algorithm views the system dynamics as a ;black-box;, i.e., we only require control of pseudorandom number generator inputs. As a result, typical codes can be retrofitted with our algorithm using only minor changes. We prove several analytical results. Among these, we characterize the relationship of covariances between paths in the general nonlinear state-dependent intensity rates case, and we prove variance reduction of mean estimators in the special case of affine intensity rates.

  1. A stochastic Markov chain model to describe lung cancer growth and metastasis.

    PubMed

    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.

  2. An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations

    PubMed Central

    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

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

    NASA Astrophysics Data System (ADS)

    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.

  4. Modeling and Computing of Stock Index Forecasting Based on Neural Network and Markov Chain

    PubMed Central

    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

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

    ERIC Educational Resources Information Center

    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…

  6. Fisher information and asymptotic normality in system identification for quantum Markov chains

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Guta, Madalin

    2011-06-15

    This paper deals with the problem of estimating the coupling constant {theta} 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 {theta} 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 absolutemore » bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of {theta}=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.« less

  7. Markov chains of infinite order and asymptotic satisfaction of balance: application to the adaptive integration method.

    PubMed

    Earl, David J; Deem, Michael W

    2005-04-14

    Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated density distribution. In convergent cases, our result implies that the balance condition need only be satisfied asymptotically. As an example, we show that the adaptive integration method converges.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan

    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,more » 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.« less

  9. A Markov Chain Model for Changes in Users' Assessment of Search Results.

    PubMed

    Zhitomirsky-Geffet, Maayan; Bar-Ilan, Judit; Levene, Mark

    2016-01-01

    Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same"coarse" relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users' judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results.

  10. A Markov Chain Model for Changes in Users’ Assessment of Search Results

    PubMed Central

    Zhitomirsky-Geffet, Maayan; Bar-Ilan, Judit; Levene, Mark

    2016-01-01

    Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same”coarse” relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users’ judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results. PMID:27171426

  11. Asteroid mass estimation using Markov-chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    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.

  12. A Markov chain technique for determining the acquisition behavior of a digital tracking loop

    NASA Technical Reports Server (NTRS)

    Chadwick, H. D.

    1972-01-01

    An iterative procedure is presented for determining the acquisition behavior of discrete or digital implementations of a tracking loop. The technique is based on the theory of Markov chains and provides the cumulative probability of acquisition in the loop as a function of time in the presence of noise and a given set of initial condition probabilities. A digital second-order tracking loop to be used in the Viking command receiver for continuous tracking of the command subcarrier phase was analyzed using this technique, and the results agree closely with experimental data.

  13. Population synthesis of radio and gamma-ray millisecond pulsars using Markov Chain Monte Carlo techniques

    NASA Astrophysics Data System (ADS)

    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).

  14. Estimates and Standard Errors for Ratios of Normalizing Constants from Multiple Markov Chains via Regeneration

    PubMed Central

    Doss, Hani; Tan, Aixin

    2017-01-01

    In the classical biased sampling problem, we have k densities π1(·), …, πk(·), each known up to a normalizing constant, i.e. for l = 1, …, k, πl(·) = νl(·)/ml, where νl(·) is a known function and ml is an unknown constant. For each l, we have an iid sample from πl,·and the problem is to estimate the ratios ml/ms 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 πl’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. PMID:28706463

  15. Estimates and Standard Errors for Ratios of Normalizing Constants from Multiple Markov Chains via Regeneration.

    PubMed

    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.

  16. Spreaders and Sponges define metastasis in lung cancer: A Markov chain Monte Carlo Mathematical Model

    PubMed Central

    Newton, Paul K.; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Norton, Larry; Kuhn, Peter

    2013-01-01

    The classic view of metastatic cancer progression is that it is a unidirectional process initiated at the primary tumor site, progressing to variably distant metastatic sites in a fairly predictable, though not perfectly understood, fashion. A Markov chain Monte Carlo mathematical approach can determine a pathway diagram that classifies metastatic tumors as ‘spreaders’ or ‘sponges’ and orders the timescales of progression from site to site. In light of recent experimental evidence highlighting the potential significance of self-seeding of primary tumors, we use a Markov chain Monte Carlo (MCMC) approach, based on large autopsy data sets, to quantify the stochastic, systemic, and often multi-directional aspects of cancer progression. We quantify three types of multi-directional mechanisms of progression: (i) self-seeding of the primary tumor; (ii) re-seeding of the primary tumor from a metastatic site (primary re-seeding); and (iii) re-seeding of metastatic tumors (metastasis re-seeding). The model shows that the combined characteristics of the primary and the first metastatic site to which it spreads largely determine the future pathways and timescales of systemic disease. For lung cancer, the main ‘spreaders’ of systemic disease are the adrenal gland and kidney, whereas the main ‘sponges’ are regional lymph nodes, liver, and bone. Lung is a significant self-seeder, although it is a ‘sponge’ site with respect to progression characteristics. PMID:23447576

  17. A Markov chain model for studying suicide dynamics: an illustration of the Rose theorem

    PubMed Central

    2014-01-01

    Background High-risk strategies would only have a modest effect on suicide prevention within a population. It is best to incorporate both high-risk and population-based strategies to prevent suicide. This study aims to compare the effectiveness of suicide prevention between high-risk and population-based strategies. Methods A Markov chain illness and death model is proposed to determine suicide dynamic in a population and examine its effectiveness for reducing the number of suicides by modifying certain parameters of the model. Assuming a population with replacement, the suicide risk of the population was estimated by determining the final state of the Markov model. Results The model shows that targeting the whole population for suicide prevention is more effective than reducing risk in the high-risk tail of the distribution of psychological distress (i.e. the mentally ill). Conclusions The results of this model reinforce the essence of the Rose theorem that lowering the suicidal risk in the population at large may be more effective than reducing the high risk in a small population. PMID:24948330

  18. Decentralized learning in Markov games.

    PubMed

    Vrancx, Peter; Verbeeck, Katja; Nowé, Ann

    2008-08-01

    Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies.

  19. Searching for efficient Markov chain Monte Carlo proposal kernels

    PubMed Central

    Yang, Ziheng; Rodríguez, Carlos E.

    2013-01-01

    Markov chain Monte Carlo (MCMC) or the Metropolis–Hastings algorithm is a simulation algorithm that has made modern Bayesian statistical inference possible. Nevertheless, the efficiency of different Metropolis–Hastings proposal kernels has rarely been studied except for the Gaussian proposal. Here we propose a unique class of Bactrian kernels, which avoid proposing values that are very close to the current value, and compare their efficiency with a number of proposals for simulating different target distributions, with efficiency measured by the asymptotic variance of a parameter estimate. The uniform kernel is found to be more efficient than the Gaussian kernel, whereas the Bactrian kernel is even better. When optimal scales are used for both, the Bactrian kernel is at least 50% more efficient than the Gaussian. Implementation in a Bayesian program for molecular clock dating confirms the general applicability of our results to generic MCMC algorithms. Our results refute a previous claim that all proposals had nearly identical performance and will prompt further research into efficient MCMC proposals. PMID:24218600

  20. Using Markov Chains to predict the natural progression of diabetic retinopathy.

    PubMed

    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.

  1. Conditional rate derivation in the presence of intervening variables using a Markov chain.

    PubMed

    Shachtman, R H; Schoenfelder, J R; Hogue, C J

    1982-01-01

    When conducting inferential and epidemiologic studies, researchers are often interested in the distribution of time until the occurrence of some specified event, a form of incidence calculation. Furthermore, this interest often extends to the effects of intervening factors on this distribution. In this paper we impose the assumption that the phenomena being investigated are governed by a stationary Markov chain and review how one may estimate the above distribution. We then introduce and relate two different methods of investigating the effects of intervening factors. In particular, we show how an investigator may evaluate the effect of potential intervention programs. Finally, we demonstrate the proposed methodology using data from a population study.

  2. Estimating the ratios of the stationary distribution values for Markov chains modeling evolutionary algorithms.

    PubMed

    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.

  3. a Probability Model for Drought Prediction Using Fusion of Markov Chain and SAX Methods

    NASA Astrophysics Data System (ADS)

    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.

  4. Building Simple Hidden Markov Models. Classroom Notes

    ERIC Educational Resources Information Center

    Ching, Wai-Ki; Ng, Michael K.

    2004-01-01

    Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.

  5. Model-Averaged ℓ1 Regularization using Markov Chain Monte Carlo Model Composition

    PubMed Central

    Fraley, Chris; Percival, Daniel

    2014-01-01

    Bayesian Model Averaging (BMA) is an effective technique for addressing model uncertainty in variable selection problems. However, current BMA approaches have computational difficulty dealing with data in which there are many more measurements (variables) than samples. This paper presents a method for combining ℓ1 regularization and Markov chain Monte Carlo model composition techniques for BMA. By treating the ℓ1 regularization path as a model space, we propose a method to resolve the model uncertainty issues arising in model averaging from solution path point selection. We show that this method is computationally and empirically effective for regression and classification in high-dimensional datasets. We apply our technique in simulations, as well as to some applications that arise in genomics. PMID:25642001

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

    NASA Astrophysics Data System (ADS)

    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.

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

    PubMed

    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.

  8. Markov Chains For Testing Redundant Software

    NASA Technical Reports Server (NTRS)

    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.

  9. MBMC: An Effective Markov Chain Approach for Binning Metagenomic Reads from Environmental Shotgun Sequencing Projects.

    PubMed

    Wang, Ying; Hu, Haiyan; Li, Xiaoman

    2016-08-01

    Metagenomics is a next-generation omics field currently impacting postgenomic life sciences and medicine. Binning metagenomic reads is essential for the understanding of microbial function, compositions, and interactions in given environments. Despite the existence of dozens of computational methods for metagenomic read binning, it is still very challenging to bin reads. This is especially true for reads from unknown species, from species with similar abundance, and/or from low-abundance species in environmental samples. In this study, we developed a novel taxonomy-dependent and alignment-free approach called MBMC (Metagenomic Binning by Markov Chains). Different from all existing methods, MBMC bins reads by measuring the similarity of reads to the trained Markov chains for different taxa instead of directly comparing reads with known genomic sequences. By testing on more than 24 simulated and experimental datasets with species of similar abundance, species of low abundance, and/or unknown species, we report here that MBMC reliably grouped reads from different species into separate bins. Compared with four existing approaches, we demonstrated that the performance of MBMC was comparable with existing approaches when binning reads from sequenced species, and superior to existing approaches when binning reads from unknown species. MBMC is a pivotal tool for binning metagenomic reads in the current era of Big Data and postgenomic integrative biology. The MBMC software can be freely downloaded at http://hulab.ucf.edu/research/projects/metagenomics/MBMC.html .

  10. Stochastic Dynamics through Hierarchically Embedded Markov Chains.

    PubMed

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

    2017-02-03

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

  11. Stochastic Dynamics through Hierarchically Embedded Markov Chains

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

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

  12. Multi-site Stochastic Simulation of Daily Streamflow with Markov Chain and KNN Algorithm

    NASA Astrophysics Data System (ADS)

    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.

  13. A Unified Framework for Complex Networks with Degree Trichotomy Based on Markov Chains.

    PubMed

    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.

  14. Using Markov Chains to predict the natural progression of diabetic retinopathy

    PubMed Central

    Srikanth, Priyanka

    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 1.07y 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. PMID:25709923

  15. Fuzzy hidden Markov chains segmentation for volume determination and quantitation in PET.

    PubMed

    Hatt, M; Lamare, F; Boussion, N; Turzo, A; Collet, C; Salzenstein, F; Roux, C; Jarritt, P; Carson, K; Cheze-Le Rest, C; Visvikis, D

    2007-06-21

    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 mm3 and 64 mm3). 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 analysis of both

  16. Estimating the Earthquake Source Time Function by Markov Chain Monte Carlo Sampling

    NASA Astrophysics Data System (ADS)

    Dȩbski, Wojciech

    2008-07-01

    Many aspects of earthquake source dynamics like dynamic stress drop, rupture velocity and directivity, etc. are currently inferred from the source time functions obtained by a deconvolution of the propagation and recording effects from seismograms. The question of the accuracy of obtained results remains open. In this paper we address this issue by considering two aspects of the source time function deconvolution. First, we propose a new pseudo-spectral parameterization of the sought function which explicitly takes into account the physical constraints imposed on the sought functions. Such parameterization automatically excludes non-physical solutions and so improves the stability and uniqueness of the deconvolution. Secondly, we demonstrate that the Bayesian approach to the inverse problem at hand, combined with an efficient Markov Chain Monte Carlo sampling technique, is a method which allows efficient estimation of the source time function uncertainties. The key point of the approach is the description of the solution of the inverse problem by the a posteriori probability density function constructed according to the Bayesian (probabilistic) theory. Next, the Markov Chain Monte Carlo sampling technique is used to sample this function so the statistical estimator of a posteriori errors can be easily obtained with minimal additional computational effort with respect to modern inversion (optimization) algorithms. The methodological considerations are illustrated by a case study of the mining-induced seismic event of the magnitude M L ≈3.1 that occurred at Rudna (Poland) copper mine. The seismic P-wave records were inverted for the source time functions, using the proposed algorithm and the empirical Green function technique to approximate Green functions. The obtained solutions seem to suggest some complexity of the rupture process with double pulses of energy release. However, the error analysis shows that the hypothesis of source complexity is not justified at

  17. Supervised self-organization of homogeneous swarms using ergodic projections of Markov chains.

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  19. Finding and testing network communities by lumped Markov chains.

    PubMed

    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.

  20. Comprehensive cosmographic analysis by Markov chain method

    NASA Astrophysics Data System (ADS)

    Capozziello, S.; Lazkoz, R.; Salzano, V.

    2011-12-01

    We study the possibility of extracting model independent information about the dynamics of the Universe by using cosmography. We intend to explore it systematically, to learn about its limitations and its real possibilities. Here we are sticking to the series expansion approach on which cosmography is based. We apply it to different data sets: Supernovae type Ia (SNeIa), Hubble parameter extracted from differential galaxy ages, gamma ray bursts, and the baryon acoustic oscillations data. We go beyond past results in the literature extending the series expansion up to the fourth order in the scale factor, which implies the analysis of the deceleration q0, the jerk j0, and the snap s0. We use the Markov chain Monte Carlo method (MCMC) to analyze the data statistically. We also try to relate direct results from cosmography to dark energy (DE) dynamical models parametrized by the Chevallier-Polarski-Linder model, extracting clues about the matter content and the dark energy parameters. The main results are: (a) even if relying on a mathematical approximate assumption such as the scale factor series expansion in terms of time, cosmography can be extremely useful in assessing dynamical properties of the Universe; (b) the deceleration parameter clearly confirms the present acceleration phase; (c) the MCMC method can help giving narrower constraints in parameter estimation, in particular for higher order cosmographic parameters (the jerk and the snap), with respect to the literature; and (d) both the estimation of the jerk and the DE parameters reflect the possibility of a deviation from the ΛCDM cosmological model.

  1. A reversible-jump Markov chain Monte Carlo algorithm for 1D inversion of magnetotelluric data

    NASA Astrophysics Data System (ADS)

    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

  2. A compositional framework for Markov processes

    NASA Astrophysics Data System (ADS)

    Baez, John C.; Fong, Brendan; Pollard, Blake S.

    2016-03-01

    We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs." One can build up a Markov process from smaller open pieces. This process is formalized by making open Markov processes into the morphisms of a dagger compact category. We show that the behavior of a detailed balanced open Markov process is determined by a principle of minimum dissipation, closely related to Prigogine's principle of minimum entropy production. Using this fact, we set up a functor mapping open detailed balanced Markov processes to open circuits made of linear resistors. We also describe how to "black box" an open Markov process, obtaining the linear relation between input and output data that holds in any steady state, including nonequilibrium steady states with a nonzero flow of probability through the system. We prove that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to Lagrangian relations between symplectic vector spaces. This allows us to compute the steady state behavior of an open detailed balanced Markov process from the behaviors of smaller pieces from which it is built. We relate this black box functor to a previously constructed black box functor for circuits.

  3. Using Markov Chains and Multi-Objective Optimization for Energy-Efficient Context Recognition.

    PubMed

    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.

  4. Markov chain algorithms: a template for building future robust low-power systems

    PubMed Central

    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

  5. Recovery of Item Parameters in the Nominal Response Model: A Comparison of Marginal Maximum Likelihood Estimation and Markov Chain Monte Carlo Estimation.

    ERIC Educational Resources Information Center

    Wollack, James A.; Bolt, Daniel M.; Cohen, Allan S.; Lee, Young-Sun

    2002-01-01

    Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)

  6. Effects of tour boats on dolphin activity examined with sensitivity analysis of Markov chains.

    PubMed

    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.

  7. Optimal choice of word length when comparing two Markov sequences using a χ 2-statistic.

    PubMed

    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.

  8. Asteroid mass estimation using Markov-Chain Monte Carlo techniques

    NASA Astrophysics Data System (ADS)

    Siltala, Lauri; Granvik, Mikael

    2016-10-01

    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 a 13-dimensional inverse problem where the aim is to derive the mass of the perturbing asteroid and six orbital elements for both the perturbing asteroid and the test asteroid using astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations into the OpenOrb asteroid-orbit-computation software: the very rough 'marching' approximation, in which the asteroid orbits are fixed at a given epoch, 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 will introduce each of these algorithms with particular focus on the MCMC algorithm, and present example results for 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, particularly in connection with ESA's Gaia mission.

  9. A Markov Random Field Framework for Protein Side-Chain Resonance Assignment

    NASA Astrophysics Data System (ADS)

    Zeng, Jianyang; Zhou, Pei; Donald, Bruce Randall

    Nuclear magnetic resonance (NMR) spectroscopy plays a critical role in structural genomics, and serves as a primary tool for determining protein structures, dynamics and interactions in physiologically-relevant solution conditions. The current speed of protein structure determination via NMR is limited by the lengthy time required in resonance assignment, which maps spectral peaks to specific atoms and residues in the primary sequence. Although numerous algorithms have been developed to address the backbone resonance assignment problem [68,2,10,37,14,64,1,31,60], little work has been done to automate side-chain resonance assignment [43, 48, 5]. Most previous attempts in assigning side-chain resonances depend on a set of NMR experiments that record through-bond interactions with side-chain protons for each residue. Unfortunately, these NMR experiments have low sensitivity and limited performance on large proteins, which makes it difficult to obtain enough side-chain resonance assignments. On the other hand, it is essential to obtain almost all of the side-chain resonance assignments as a prerequisite for high-resolution structure determination. To overcome this deficiency, we present a novel side-chain resonance assignment algorithm based on alternative NMR experiments measuring through-space interactions between protons in the protein, which also provide crucial distance restraints and are normally required in high-resolution structure determination. We cast the side-chain resonance assignment problem into a Markov Random Field (MRF) framework, and extend and apply combinatorial protein design algorithms to compute the optimal solution that best interprets the NMR data. Our MRF framework captures the contact map information of the protein derived from NMR spectra, and exploits the structural information available from the backbone conformations determined by orientational restraints and a set of discretized side-chain conformations (i.e., rotamers). A Hausdorff

  10. A reward semi-Markov process with memory for wind speed modeling

    NASA Astrophysics Data System (ADS)

    Petroni, F.; D'Amico, G.; Prattico, F.

    2012-04-01

    The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [1] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [3], by using two models, first

  11. A brief history of the introduction of generalized ensembles to Markov chain Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Berg, Bernd A.

    2017-03-01

    The most efficient weights for Markov chain Monte Carlo calculations of physical observables are not necessarily those of the canonical ensemble. Generalized ensembles, which do not exist in nature but can be simulated on computers, lead often to a much faster convergence. In particular, they have been used for simulations of first order phase transitions and for simulations of complex systems in which conflicting constraints lead to a rugged free energy landscape. Starting off with the Metropolis algorithm and Hastings' extension, I present a minireview which focuses on the explosive use of generalized ensembles in the early 1990s. Illustrations are given, which range from spin models to peptides.

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

    NASA Astrophysics Data System (ADS)

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

    2017-12-01

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

  13. Markov Chain-Based Acute Effect Estimation of Air Pollution on Elder Asthma Hospitalization

    PubMed Central

    Luo, Li; Zhang, Fengyi; Sun, Lin; Li, Chunyang; Huang, Debin; Han, Gao; Wang, Bin

    2017-01-01

    Background Asthma caused substantial economic and health care burden and is susceptible to air pollution. Particularly, when it comes to elder asthma patient (older than 65), the phenomenon is more significant. The aim of this study is to investigate the Markov-based acute effects of air pollution on elder asthma hospitalizations, in forms of transition probabilities. Methods A retrospective, population-based study design was used to assess temporal patterns in hospitalizations for asthma in a region of Sichuan province, China. Approximately 12 million residents were covered during this period. Relative risk analysis and Markov chain model were employed on daily hospitalization state estimation. Results Among PM2.5, PM10, NO2, and SO2, only SO2 was significant. When air pollution is severe, the transition probability from a low-admission state (previous day) to high-admission state (next day) is 35.46%, while it is 20.08% when air pollution is mild. In particular, for female-cold subgroup, the counterparts are 30.06% and 0.01%, respectively. Conclusions SO2 was a significant risk factor for elder asthma hospitalization. When air pollution worsened, the transition probabilities from each state to high admission states increase dramatically. This phenomenon appeared more evidently, especially in female-cold subgroup (which is in cold season for female admissions). Based on our work, admission amount forecast, asthma intervention, and corresponding healthcare allocation can be done. PMID:29147496

  14. Markov reward processes

    NASA Technical Reports Server (NTRS)

    Smith, R. M.

    1991-01-01

    Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.

  15. Transition probabilities of health states for workers in Malaysia using a Markov chain model

    NASA Astrophysics Data System (ADS)

    Samsuddin, Shamshimah; Ismail, Noriszura

    2017-04-01

    The aim of our study is to estimate the transition probabilities of health states for workers in Malaysia who contribute to the Employment Injury Scheme under the Social Security Organization Malaysia using the Markov chain model. Our study uses four states of health (active, temporary disability, permanent disability and death) based on the data collected from the longitudinal studies of workers in Malaysia for 5 years. The transition probabilities vary by health state, age and gender. The results show that men employees are more likely to have higher transition probabilities to any health state compared to women employees. The transition probabilities can be used to predict the future health of workers in terms of a function of current age, gender and health state.

  16. A toolbox for safety instrumented system evaluation based on improved continuous-time Markov chain

    NASA Astrophysics Data System (ADS)

    Wardana, Awang N. I.; Kurniady, Rahman; Pambudi, Galih; Purnama, Jaka; Suryopratomo, Kutut

    2017-08-01

    Safety instrumented system (SIS) is designed to restore a plant into a safe condition when pre-hazardous event is occur. It has a vital role especially in process industries. A SIS shall be meet with safety requirement specifications. To confirm it, SIS shall be evaluated. Typically, the evaluation is calculated by hand. This paper presents a toolbox for SIS evaluation. It is developed based on improved continuous-time Markov chain. The toolbox supports to detailed approach of evaluation. This paper also illustrates an industrial application of the toolbox to evaluate arch burner safety system of primary reformer. The results of the case study demonstrates that the toolbox can be used to evaluate industrial SIS in detail and to plan the maintenance strategy.

  17. Using Markov Chains and Multi-Objective Optimization for Energy-Efficient Context Recognition †

    PubMed Central

    Janko, Vito

    2017-01-01

    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. PMID:29286301

  18. Dynamics of a discrete chain of bi-stable elements: A biomimetic shock absorbing mechanism

    NASA Astrophysics Data System (ADS)

    Cohen, T.; Givli, S.

    2014-03-01

    A biomimetic shock absorbing mechanism, inspired by the bi-stable elongation behavior of the giant protein titin, is examined. A bi-stable element, composed of three mass particles with monotonous interaction forces, is suggested to facilitate an internal degree of freedom of finite mass which contributes significantly to dissipation upon unlocking of an internal link. An essential feature of the suggested element is that it undergoes reversible rapture and therefore retrieves its initial configuration once unloaded. The quasistatic and dynamic behaviors are investigated showing similarity to the common tri-linear bi-stable response, with two steady phases separated by a spinodal region. The dynamic behavior of a chain of elements is also examined, for several loading scenarios, showing that the suggested mechanism serves as an efficient shock absorber in a sub-critical dampening environment, as compared with a simple mass on spring system. Propagation of shock waves and refraction waves in an element chain is observed and the effect of natural imperfections is considered.

  19. Coupling of Markov chains and cellular automata spatial models to predict land cover changes (case study: upper Ci Leungsi catchment area)

    NASA Astrophysics Data System (ADS)

    Marko, K.; Zulkarnain, F.; Kusratmoko, E.

    2016-11-01

    Land cover changes particular in urban catchment area has been rapidly occur. Land cover changes occur as a result of increasing demand for built-up area. Various kinds of environmental and hydrological problems e.g. floods and urban heat island can happen if the changes are uncontrolled. This study aims to predict land cover changes using coupling of Markov chains and cellular automata. One of the most rapid land cover changes is occurs at upper Ci Leungsi catchment area that located near Bekasi City and Jakarta Metropolitan Area. Markov chains has a good ability to predict the probability of change statistically while cellular automata believed as a powerful method in reading the spatial patterns of change. Temporal land cover data was obtained by remote sensing satellite imageries. In addition, this study also used multi-criteria analysis to determine which driving factor that could stimulate the changes such as proximity, elevation, and slope. Coupling of these two methods could give better prediction model rather than just using it separately. The prediction model was validated using existing 2015 land cover data and shown a satisfactory kappa coefficient. The most significant increasing land cover is built-up area from 24% to 53%.

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

    NASA Astrophysics Data System (ADS)

    Graham, Eleanor; Cuore Collaboration

    2017-09-01

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

  1. Measuring and partitioning the high-order linkage disequilibrium by multiple order Markov chains.

    PubMed

    Kim, Yunjung; Feng, Sheng; Zeng, Zhao-Bang

    2008-05-01

    A map of the background levels of disequilibrium between nearby markers can be useful for association mapping studies. In order to assess the background levels of linkage disequilibrium (LD), multilocus LD measures are more advantageous than pairwise LD measures because the combined analysis of pairwise LD measures is not adequate to detect simultaneous allele associations among multiple markers. Various multilocus LD measures based on haplotypes have been proposed. However, most of these measures provide a single index of association among multiple markers and does not reveal the complex patterns and different levels of LD structure. In this paper, we employ non-homogeneous, multiple order Markov Chain models as a statistical framework to measure and partition the LD among multiple markers into components due to different orders of marker associations. Using a sliding window of multiple markers on phased haplotype data, we compute corresponding likelihoods for different Markov Chain (MC) orders in each window. The log-likelihood difference between the lowest MC order model (MC0) and the highest MC order model in each window is used as a measure of the total LD or the overall deviation from the gametic equilibrium for the window. Then, we partition the total LD into lower order disequilibria and estimate the effects from two-, three-, and higher order disequilibria. The relationship between different orders of LD and the log-likelihood difference involving two different orders of MC models are explored. By applying our method to the phased haplotype data in the ENCODE regions of the HapMap project, we are able to identify high/low multilocus LD regions. Our results reveal that the most LD in the HapMap data is attributed to the LD between adjacent pairs of markers across the whole region. LD between adjacent pairs of markers appears to be more significant in high multilocus LD regions than in low multilocus LD regions. We also find that as the multilocus total LD

  2. Markov chain sampling of the O(n) loop models on the infinite plane

    NASA Astrophysics Data System (ADS)

    Herdeiro, Victor

    2017-07-01

    A numerical method was recently proposed in Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] showing a precise sampling of the infinite plane two-dimensional critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the O(n) loop gas models for n ∈(1 ,2 ] . We argue that even though the Gibbs measure is nonlocal, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the O(n) models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.

  3. Simplification of reversible Markov chains by removal of states with low equilibrium occupancy.

    PubMed

    Ullah, Ghanim; Bruno, William J; Pearson, John E

    2012-10-21

    We present a practical method for simplifying Markov chains on a potentially large state space when detailed balance holds. A simple and transparent technique is introduced to remove states with low equilibrium occupancy. The resulting system has fewer parameters. The resulting effective rates between the remaining nodes give dynamics identical to the original system's except on very fast timescales. This procedure amounts to using separation of timescales to neglect small capacitance nodes in a network of resistors and capacitors. We illustrate the technique by simplifying various reaction networks, including transforming an acyclic four-node network to a three-node cyclic network. For a reaction step in which a ligand binds, the law of mass action implies a forward rate proportional to ligand concentration. The effective rates in the simplified network are found to be rational functions of ligand concentration. Copyright © 2012 Elsevier Ltd. All rights reserved.

  4. Recombination Processes and Nonlinear Markov Chains.

    PubMed

    Pirogov, Sergey; Rybko, Alexander; Kalinina, Anastasia; Gelfand, Mikhail

    2016-09-01

    Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity between the recombining segments, several studies examined whether this could lead to the emergence of subspecies. Most of them simulated fixed-size Wright-Fisher populations, in which the genetic drift should be taken into account. Here, we use nonlinear Markov processes to describe a bacterial population evolving under mutation and recombination. We consider a population structure as a probability measure on the space of genomes. This approach implies the infinite population size limit, and thus, the genetic drift is not assumed. We prove that under these conditions, the emergence of subspecies is impossible.

  5. Free flowing and cohesive powders agitation in a cylindrical convective blender- kinetics experiments and Markov chain modelling

    NASA Astrophysics Data System (ADS)

    Legoix, Léonard; Milhé, Mathieu; Gatumel, Cendrine; Berthiaux, Henri

    2017-06-01

    An original methodology for studying powder flow in a cylindrical convective blender has been developed. A free-flowing and a cohesive powder were studied, at a fixed stirring speed, in rolling regime. For both powders, three apparent flow mechanisms were evidenced: convection in the volume swept by the blades, diffusion/shearing between the agitated zone and the stagnant one, as well as in the stagnant zone itself, and avalanches at the powder bed surface between agitated and stagnant zones. After defining six zones in the blender, tracing experiments were carried out by placing appropriate tracers in different starting zones and sampling the whole bed at different stirring times, which lead to mixing kinetics of the powders into themselves. A Markov chains model of the blender allowed the quantification of the three mechanisms respective magnitude by fitting the experimental data. This simple model has a good agreement with the free-flowing powder data, but is not able to represent well the observations for the cohesive powder. Bed consolidation should probably be taken into account for this kind of powders and thus a linear Markov model is not sufficient.

  6. Study of behavior and determination of customer lifetime value(CLV) using Markov chain model

    NASA Astrophysics Data System (ADS)

    Permana, Dony; Indratno, Sapto Wahyu; Pasaribu, Udjianna S.

    2014-03-01

    Customer Lifetime Value or CLV is a restriction on interactive marketing to help a company in arranging financial for the marketing of new customer acquisition and customer retention. Additionally CLV can be able to segment customers for financial arrangements. Stochastic models for the fairly new CLV used a Markov chain. In this model customer retention probability and new customer acquisition probability play an important role. This model is originally introduced by Pfeifer and Carraway in 2000 [1]. They introduced several CLV models, one of them only involves customer and former customer. In this paper we expand the model by adding the assumption of the transition from former customer to customer. In the proposed model, the CLV value is higher than the CLV value obtained by Pfeifer and Caraway model. But our model still requires a longer convergence time.

  7. A methodology for stochastic analysis of share prices as Markov chains with finite states.

    PubMed

    Mettle, Felix Okoe; Quaye, Enoch Nii Boi; Laryea, Ravenhill Adjetey

    2014-01-01

    Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data.

  8. Projection of postgraduate students flow with a smoothing matrix transition diagram of Markov chain

    NASA Astrophysics Data System (ADS)

    Rahim, Rahela; Ibrahim, Haslinda; Adnan, Farah Adibah

    2013-04-01

    This paper presents a case study of modeling postgraduate students flow at the College of Art and Sciences, Universiti Utara Malaysia. First, full time postgraduate students and the semester they were in are identified. Then administrative data were used to estimate the transitions between these semesters for the year 2001-2005 periods. Markov chain model is developed to calculate the -5 and -10 years projection of postgraduate students flow at the college. The optimization question addressed in this study is 'Which transitions would sustain the desired structure in the dynamic situation such as trend towards graduation?' The smoothed transition probabilities are proposed to estimate the transition probabilities matrix of 16 × 16. The results shows that using smoothed transition probabilities, the projection number of postgraduate students enrolled in the respective semesters are closer to actual than using the conventional steady states transition probabilities.

  9. Study of behavior and determination of customer lifetime value(CLV) using Markov chain model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Permana, Dony, E-mail: donypermana@students.itb.ac.id; Indratno, Sapto Wahyu; Pasaribu, Udjianna S.

    Customer Lifetime Value or CLV is a restriction on interactive marketing to help a company in arranging financial for the marketing of new customer acquisition and customer retention. Additionally CLV can be able to segment customers for financial arrangements. Stochastic models for the fairly new CLV used a Markov chain. In this model customer retention probability and new customer acquisition probability play an important role. This model is originally introduced by Pfeifer and Carraway in 2000 [1]. They introduced several CLV models, one of them only involves customer and former customer. In this paper we expand the model by addingmore » the assumption of the transition from former customer to customer. In the proposed model, the CLV value is higher than the CLV value obtained by Pfeifer and Caraway model. But our model still requires a longer convergence time.« less

  10. Educational Aspirations: Markov and Poisson Models. Rural Industrial Development Project Working Paper Number 14, August 1971.

    ERIC Educational Resources Information Center

    Kayser, Brian D.

    The fit of educational aspirations of Illinois rural high school youths to 3 related one-parameter mathematical models was investigated. The models used were the continuous-time Markov chain model, the discrete-time Markov chain, and the Poisson distribution. The sample of 635 students responded to questionnaires from 1966 to 1969 as part of an…

  11. Sanov and central limit theorems for output statistics of quantum Markov chains

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Horssen, Merlijn van, E-mail: merlijn.vanhorssen@nottingham.ac.uk; Guţă, Mădălin, E-mail: madalin.guta@nottingham.ac.uk

    2015-02-15

    In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Suchmore » higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.« less

  12. Finding exact constants in a Markov model of Zipfs law generation

    NASA Astrophysics Data System (ADS)

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

    2017-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Bozhalkina, Yana

    2017-12-01

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

  14. Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains.

    PubMed

    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.

  15. Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches.

    PubMed

    Li, Michael; Dushoff, Jonathan; Bolker, Benjamin M

    2018-07-01

    Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

  16. An example of complex modelling in dentistry using Markov chain Monte Carlo (MCMC) simulation.

    PubMed

    Helfenstein, Ulrich; Menghini, Giorgio; Steiner, Marcel; Murati, Francesca

    2002-09-01

    In the usual regression setting one regression line is computed for a whole data set. In a more complex situation, each person may be observed for example at several points in time and thus a regression line might be calculated for each person. Additional complexities, such as various forms of errors in covariables may make a straightforward statistical evaluation difficult or even impossible. During recent years methods have been developed allowing convenient analysis of problems where the data and the corresponding models show these and many other forms of complexity. The methodology makes use of a Bayesian approach and Markov chain Monte Carlo (MCMC) simulations. The methods allow the construction of increasingly elaborate models by building them up from local sub-models. The essential structure of the models can be represented visually by directed acyclic graphs (DAG). This attractive property allows communication and discussion of the essential structure and the substantial meaning of a complex model without needing algebra. After presentation of the statistical methods an example from dentistry is presented in order to demonstrate their application and use. The dataset of the example had a complex structure; each of a set of children was followed up over several years. The number of new fillings in permanent teeth had been recorded at several ages. The dependent variables were markedly different from the normal distribution and could not be transformed to normality. In addition, explanatory variables were assumed to be measured with different forms of error. Illustration of how the corresponding models can be estimated conveniently via MCMC simulation, in particular, 'Gibbs sampling', using the freely available software BUGS is presented. In addition, how the measurement error may influence the estimates of the corresponding coefficients is explored. It is demonstrated that the effect of the independent variable on the dependent variable may be markedly

  17. Nonpoint Source Solute Transport Normal to Aquifer Bedding in Heterogeneous, Markov Chain Random Fields

    NASA Astrophysics Data System (ADS)

    Zhang, H.; Harter, T.; Sivakumar, B.

    2005-12-01

    Facies-based geostatistical models have become important tools for the stochastic analysis of flow and transport processes in heterogeneous aquifers. However, little is known about the dependency of these processes on the parameters of facies- based geostatistical models. This study examines the nonpoint source solute transport normal to the major bedding plane in the presence of interconnected high conductivity (coarse- textured) facies in the aquifer medium and the dependence of the transport behavior upon the parameters of the constitutive facies model. A facies-based Markov chain geostatistical model is used to quantify the spatial variability of the aquifer system hydrostratigraphy. It is integrated with a groundwater flow model and a random walk particle transport model to estimate the solute travel time probability distribution functions (pdfs) for solute flux from the water table to the bottom boundary (production horizon) of the aquifer. The cases examined include, two-, three-, and four-facies models with horizontal to vertical facies mean length anisotropy ratios, ek, from 25:1 to 300:1, and with a wide range of facies volume proportions (e.g, from 5% to 95% coarse textured facies). Predictions of travel time pdfs are found to be significantly affected by the number of hydrostratigraphic facies identified in the aquifer, the proportions of coarse-textured sediments, the mean length of the facies (particularly the ratio of length to thickness of coarse materials), and - to a lesser degree - the juxtapositional preference among the hydrostratigraphic facies. In transport normal to the sedimentary bedding plane, travel time pdfs are not log- normally distributed as is often assumed. Also, macrodispersive behavior (variance of the travel time pdf) was found to not be a unique function of the conductivity variance. The skewness of the travel time pdf varied from negatively skewed to strongly positively skewed within the parameter range examined. We also show

  18. Asteroid mass estimation with Markov-chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    Siltala, Lauri; Granvik, Mikael

    2017-10-01

    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 a 13-dimensional inverse problem at minimum where the aim is to derive the mass of the perturbing asteroid and six orbital elements for both the perturbing asteroid and the test asteroid by fitting their trajectories to their observed positions. The fitting has typically been carried out with linearized methods such as the least-squares method. These methods need to make certain assumptions regarding the shape of the probability distributions of the model parameters. This is problematic as these assumptions have not been validated. We have developed a new Markov-chain Monte Carlo method for mass estimation which does not require an assumption regarding the shape of the parameter distribution. Recently, we have implemented several upgrades to our MCMC method including improved schemes for handling observational errors and outlier data alongside the option to consider multiple perturbers and/or test asteroids simultaneously. These upgrades promise significantly improved results: based on two separate results for (19) Fortuna with different test asteroids we previously hypothesized that simultaneous use of both test asteroids would lead to an improved result similar to the average literature value for (19) Fortuna with substantially reduced uncertainties. Our upgraded algorithm indeed finds a result essentially equal to the literature value for this asteroid, confirming our previous hypothesis. Here we show these new results for (19) Fortuna and other example cases, and compare our results to previous estimates. Finally, we discuss our plans to improve our algorithm further, particularly in connection with Gaia.

  19. Regression without truth with Markov chain Monte-Carlo

    NASA Astrophysics Data System (ADS)

    Madan, Hennadii; Pernuš, Franjo; Likar, Boštjan; Å piclin, Žiga

    2017-03-01

    Regression without truth (RWT) is a statistical technique for estimating error model parameters of each method in a group of methods used for measurement of a certain quantity. A very attractive aspect of RWT is that it does not rely on a reference method or "gold standard" data, which is otherwise difficult RWT was used for a reference-free performance comparison of several methods for measuring left ventricular ejection fraction (EF), i.e. a percentage of blood leaving the ventricle each time the heart contracts, and has since been applied for various other quantitative imaging biomarkerss (QIBs). Herein, we show how Markov chain Monte-Carlo (MCMC), a computational technique for drawing samples from a statistical distribution with probability density function known only up to a normalizing coefficient, can be used to augment RWT to gain a number of important benefits compared to the original approach based on iterative optimization. For instance, the proposed MCMC-based RWT enables the estimation of joint posterior distribution of the parameters of the error model, straightforward quantification of uncertainty of the estimates, estimation of true value of the measurand and corresponding credible intervals (CIs), does not require a finite support for prior distribution of the measureand generally has a much improved robustness against convergence to non-global maxima. The proposed approach is validated using synthetic data that emulate the EF data for 45 patients measured with 8 different methods. The obtained results show that 90% CI of the corresponding parameter estimates contain the true values of all error model parameters and the measurand. A potential real-world application is to take measurements of a certain QIB several different methods and then use the proposed framework to compute the estimates of the true values and their uncertainty, a vital information for diagnosis based on QIB.

  20. Of bugs and birds: Markov Chain Monte Carlo for hierarchical modeling in wildlife research

    USGS Publications Warehouse

    Link, W.A.; Cam, E.; Nichols, J.D.; Cooch, E.G.

    2002-01-01

    Markov chain Monte Carlo (MCMC) is a statistical innovation that allows researchers to fit far more complex models to data than is feasible using conventional methods. Despite its widespread use in a variety of scientific fields, MCMC appears to be underutilized in wildlife applications. This may be due to a misconception that MCMC requires the adoption of a subjective Bayesian analysis, or perhaps simply to its lack of familiarity among wildlife researchers. We introduce the basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling), stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathematical sophistication. We illustrate the use of MCMC with an analysis of the association between latent factors governing individual heterogeneity in breeding and survival rates of kittiwakes (Rissa tridactyla). We conclude with a discussion of the importance of individual heterogeneity for understanding population dynamics and designing management plans.

  1. Bayesian calibration of terrestrial ecosystem models: A study of advanced Markov chain Monte Carlo methods

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lu, Dan; Ricciuto, Daniel; Walker, Anthony

    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 study, a Differential Evolution Adaptive Metropolis (DREAM) algorithm was 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 DREAM is a multi-chainmore » method and uses differential evolution technique for chain movement, allowing it to be efficiently applied to high-dimensional problems, and can reliably estimate heavy-tailed and multimodal distributions that are difficult for single-chain schemes using a Gaussian proposal distribution. The results were evaluated against the popular Adaptive Metropolis (AM) scheme. DREAM indicated that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identified one mode. The calibration of DREAM resulted in a better model fit and predictive performance compared to the AM. DREAM provides means for a good exploration of the posterior distributions of model parameters. Lastly, it reduces the risk of false convergence to a local optimum and potentially improves the predictive performance of the calibrated model.« less

  2. Bayesian calibration of terrestrial ecosystem models: A study of advanced Markov chain Monte Carlo methods

    DOE PAGES

    Lu, Dan; Ricciuto, Daniel; Walker, Anthony; ...

    2017-02-22

    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 study, a Differential Evolution Adaptive Metropolis (DREAM) algorithm was 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 DREAM is a multi-chainmore » method and uses differential evolution technique for chain movement, allowing it to be efficiently applied to high-dimensional problems, and can reliably estimate heavy-tailed and multimodal distributions that are difficult for single-chain schemes using a Gaussian proposal distribution. The results were evaluated against the popular Adaptive Metropolis (AM) scheme. DREAM indicated that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identified one mode. The calibration of DREAM resulted in a better model fit and predictive performance compared to the AM. DREAM provides means for a good exploration of the posterior distributions of model parameters. Lastly, it reduces the risk of false convergence to a local optimum and potentially improves the predictive performance of the calibrated model.« less

  3. Two-state Markov-chain Poisson nature of individual cellphone call statistics

    NASA Astrophysics Data System (ADS)

    Jiang, Zhi-Qiang; Xie, Wen-Jie; Li, Ming-Xia; Zhou, Wei-Xing; Sornette, Didier

    2016-07-01

    Unfolding the burst patterns in human activities and social interactions is a very important issue especially for understanding the spreading of disease and information and the formation of groups and organizations. Here, we conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73 339 anonymous cellphone users, whose inter-call durations are Weibull distributed. We find that the individual call events exhibit a pattern of bursts, that high activity periods are alternated with low activity periods. In both periods, the number of calls are exponentially distributed for individuals, but power-law distributed for the population. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain, giving significant fits for nearly half of the individuals. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we purport the existence of power-law distributions, via the ‘superposition of distributions’ mechanism. Our findings shed light on the origins of bursty patterns in other human activities.

  4. A Markov chain model for image ranking system in social networks

    NASA Astrophysics Data System (ADS)

    Zin, Thi Thi; Tin, Pyke; Toriu, Takashi; Hama, Hiromitsu

    2014-03-01

    In today world, different kinds of networks such as social, technological, business and etc. exist. All of the networks are similar in terms of distributions, continuously growing and expanding in large scale. Among them, many social networks such as Facebook, Twitter, Flickr and many others provides a powerful abstraction of the structure and dynamics of diverse kinds of inter personal connection and interaction. Generally, the social network contents are created and consumed by the influences of all different social navigation paths that lead to the contents. Therefore, identifying important and user relevant refined structures such as visual information or communities become major factors in modern decision making world. Moreover, the traditional method of information ranking systems cannot be successful due to their lack of taking into account the properties of navigation paths driven by social connections. In this paper, we propose a novel image ranking system in social networks by using the social data relational graphs from social media platform jointly with visual data to improve the relevance between returned images and user intentions (i.e., social relevance). Specifically, we propose a Markov chain based Social-Visual Ranking algorithm by taking social relevance into account. By using some extensive experiments, we demonstrated the significant and effectiveness of the proposed social-visual ranking method.

  5. DIM SUM: demography and individual migration simulated using a Markov chain.

    PubMed

    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.

  6. A Markov chain analysis of the movements of juvenile salmonids in the forebay of McNary Dam, Washington and Oregon, 2006-09

    USGS Publications Warehouse

    Adams, Noah S.; Hatton, Tyson W.

    2012-01-01

    Passage and survival data for yearling and subyearling Chinook salmon and juvenile steelhead were collected at McNary Dam between 2006 and 2009. These data have provided critical information for resource managers to implement structural and operational changes designed to improve the survival of juvenile salmonids as they migrate past the dam. Much of the information collected at McNary Dam was in the form of three-dimensional tracks of fish movements in the forebay. These data depicted the behavior of multiple species (in three dimensions) during different diel periods, spill conditions, powerhouse operations, and test configurations of the surface bypass structures (temporary spillway weirs; TSWs). One of the challenges in reporting three-dimensional results is presenting the information in a manner that allows interested parties to summarize the behavior of many fish over many different conditions across multiple years. To accomplish this, we investigated the feasibility of using a Markov chain analysis to characterize fish movement patterns in the forebay of McNary Dam. The Markov chain analysis is one way that can be used to summarize numerically the behavior of fish in the forebay. Numerically summarizing the behavior of juvenile salmonids in the forebay of McNary Dam using the Markov chain analysis allowed us to confirm what had been previously summarized using visualization software. For example, proportions of yearling and subyearling Chinook salmon passing the three powerhouse areas was often greater in the southern and middle areas, compared to the northern area. The opposite generally was observed for steelhead. Results of this analysis also allowed us to confirm and quantify the extent of milling behavior that had been observed for steelhead. For fish that were first detected in the powerhouse region, less than 0.10 of the steelhead, on average, passed within each of the powerhouse areas. Instead, steelhead transitioned to adjoining areas in the

  7. Quantum Enhanced Inference in Markov Logic Networks

    NASA Astrophysics Data System (ADS)

    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.

  8. Quantum Enhanced Inference in Markov Logic Networks.

    PubMed

    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.

  9. Quantum Enhanced Inference in Markov Logic Networks

    PubMed Central

    Wittek, Peter; Gogolin, Christian

    2017-01-01

    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. PMID:28422093

  10. Enhancing Data Assimilation by Evolutionary Particle Filter and Markov Chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    Moradkhani, H.; Abbaszadeh, P.; Yan, H.

    2016-12-01

    Particle Filters (PFs) have received increasing attention by the researchers from different disciplines in hydro-geosciences as an effective method to improve model predictions in nonlinear and non-Gaussian dynamical systems. The implication of dual state and parameter estimation by means of data assimilation in hydrology and geoscience has evolved since 2005 from SIR-PF to PF-MCMC and now to the most effective and robust framework through evolutionary PF approach based on Genetic Algorithm (GA) and Markov Chain Monte Carlo (MCMC), the so-called EPF-MCMC. In this framework, the posterior distribution undergoes an evolutionary process to update an ensemble of prior states that more closely resemble realistic posterior probability distribution. The premise of this approach is that the particles move to optimal position using the GA optimization coupled with MCMC increasing the number of effective particles, hence the particle degeneracy is avoided while the particle diversity is improved. The proposed algorithm is applied on a conceptual and highly nonlinear hydrologic model and the effectiveness, robustness and reliability of the method in jointly estimating the states and parameters and also reducing the uncertainty is demonstrated for few river basins across the United States.

  11. Pattern statistics on Markov chains and sensitivity to parameter estimation.

    PubMed

    Nuel, Grégory

    2006-10-17

    In order to compute pattern statistics in computational biology a Markov model is commonly used to take into account the sequence composition. Usually its parameter must be estimated. The aim of this paper is to determine how sensitive these statistics are to parameter estimation, and what are the consequences of this variability on pattern studies (finding the most over-represented words in a genome, the most significant common words to a set of sequences,...). In the particular case where pattern statistics (overlap counting only) computed through binomial approximations we use the delta-method to give an explicit expression of sigma, the standard deviation of a pattern statistic. This result is validated using simulations and a simple pattern study is also considered. We establish that the use of high order Markov model could easily lead to major mistakes due to the high sensitivity of pattern statistics to parameter estimation.

  12. Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis-Hastings Markov Chain Monte Carlo algorithm

    NASA Astrophysics Data System (ADS)

    Wang, Hongrui; Wang, Cheng; Wang, Ying; Gao, Xiong; Yu, Chen

    2017-06-01

    This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLE confidence interval and thus more precise estimation by using the related information from regional gage stations. The Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.

  13. A nonstationary Markov transition model for computing the relative risk of dementia before death

    PubMed Central

    Yu, Lei; Griffith, William S.; Tyas, Suzanne L.; Snowdon, David A.; Kryscio, Richard J.

    2010-01-01

    This paper investigates the long-term behavior of the k-step transition probability matrix for a nonstationary discrete time Markov chain in the context of modeling transitions from intact cognition to dementia with mild cognitive impairment (MCI) and global impairment (GI) as intervening cognitive states. The authors derive formulas for the following absorption statistics: (1) the relative risk of absorption between competing absorbing states, and (2) the mean and variance of the number of visits among the transient states before absorption. Since absorption is not guaranteed, sufficient conditions are discussed to ensure that the substochastic matrix associated with transitions among transient states converges to zero in limit. Results are illustrated with an application to the Nun Study, a cohort of 678 participants, 75 to 107 years of age, followed longitudinally with up to ten cognitive assessments over a fifteen-year period. PMID:20087848

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

    PubMed

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

    2015-03-01

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

  15. Open Markov Processes and Reaction Networks

    NASA Astrophysics Data System (ADS)

    Swistock Pollard, Blake Stephen

    We begin by defining the concept of `open' Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain `boundary' states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow of probability vanishes between all pairs of states. External couplings which fix the probabilities of boundary states can maintain such systems in non-equilibrium steady states in which non-zero probability currents flow. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. Tensoring in this category corresponds to placing two such systems side by side. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where

  16. Dynamic Bandwidth Provisioning Using Markov Chain Based on RSVP

    DTIC Science & Technology

    2013-09-01

    AUTHOR(S) Yavuz Sagir 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS (ES) Naval Postgraduate School Monterey, CA 93943-5000 8. PERFORMING...ORGANIZATION REPORT NUMBER 9. SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS (ES) N/A 10. SPONSORING/MONITORING AGENCY REPORT NUMBER 11...is finite or countable. A Markov process is basically a stochastic process in which the past history of the process is irrelevant if the current

  17. Pattern statistics on Markov chains and sensitivity to parameter estimation

    PubMed Central

    Nuel, Grégory

    2006-01-01

    Background: In order to compute pattern statistics in computational biology a Markov model is commonly used to take into account the sequence composition. Usually its parameter must be estimated. The aim of this paper is to determine how sensitive these statistics are to parameter estimation, and what are the consequences of this variability on pattern studies (finding the most over-represented words in a genome, the most significant common words to a set of sequences,...). Results: In the particular case where pattern statistics (overlap counting only) computed through binomial approximations we use the delta-method to give an explicit expression of σ, the standard deviation of a pattern statistic. This result is validated using simulations and a simple pattern study is also considered. Conclusion: We establish that the use of high order Markov model could easily lead to major mistakes due to the high sensitivity of pattern statistics to parameter estimation. PMID:17044916

  18. Numerical solutions for patterns statistics on Markov chains.

    PubMed

    Nuel, Gregory

    2006-01-01

    We propose here a review of the methods available to compute pattern statistics on text generated by a Markov source. Theoretical, but also numerical aspects are detailed for a wide range of techniques (exact, Gaussian, large deviations, binomial and compound Poisson). The SPatt package (Statistics for Pattern, free software available at http://stat.genopole.cnrs.fr/spatt) implementing all these methods is then used to compare all these approaches in terms of computational time and reliability in the most complete pattern statistics benchmark available at the present time.

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

    NASA Astrophysics Data System (ADS)

    Zhang, Hua; Harter, Thomas; Sivakumar, Bellie

    2006-06-01

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

  20. Assessment of parameter uncertainty in hydrological model using a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis method

    NASA Astrophysics Data System (ADS)

    Zhang, Junlong; Li, Yongping; Huang, Guohe; Chen, Xi; Bao, Anming

    2016-07-01

    Without a realistic assessment of parameter uncertainty, decision makers may encounter difficulties in accurately describing hydrologic processes and assessing relationships between model parameters and watershed characteristics. In this study, a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis (MCMC-MFA) method is developed, which can not only generate samples of parameters from a well constructed Markov chain and assess parameter uncertainties with straightforward Bayesian inference, but also investigate the individual and interactive effects of multiple parameters on model output through measuring the specific variations of hydrological responses. A case study is conducted for addressing parameter uncertainties in the Kaidu watershed of northwest China. Effects of multiple parameters and their interactions are quantitatively investigated using the MCMC-MFA with a three-level factorial experiment (totally 81 runs). A variance-based sensitivity analysis method is used to validate the results of parameters' effects. Results disclose that (i) soil conservation service runoff curve number for moisture condition II (CN2) and fraction of snow volume corresponding to 50% snow cover (SNO50COV) are the most significant factors to hydrological responses, implying that infiltration-excess overland flow and snow water equivalent represent important water input to the hydrological system of the Kaidu watershed; (ii) saturate hydraulic conductivity (SOL_K) and soil evaporation compensation factor (ESCO) have obvious effects on hydrological responses; this implies that the processes of percolation and evaporation would impact hydrological process in this watershed; (iii) the interactions of ESCO and SNO50COV as well as CN2 and SNO50COV have an obvious effect, implying that snow cover can impact the generation of runoff on land surface and the extraction of soil evaporative demand in lower soil layers. These findings can help enhance the hydrological model

  1. UMAP Modules-Units 105, 107-109, 111-112, 158-162.

    ERIC Educational Resources Information Center

    Keller, Mary K.; And Others

    This collection of materials includes six units dealing with applications of matrix methods. These are: 105-Food Service Management; 107-Markov Chains; 108-Electrical Circuits; 109-Food Service and Dietary Requirements; 111-Fixed Point and Absorbing Markov Chains; and 112-Analysis of Linear Circuits. The units contain exercises and model exams,…

  2. A Monte-Carlo method which is not based on Markov chain algorithm, used to study electrostatic screening of ion potential

    NASA Astrophysics Data System (ADS)

    Šantić, Branko; Gracin, Davor

    2017-12-01

    A new simple Monte Carlo method is introduced for the study of electrostatic screening by surrounding ions. The proposed method is not based on the generally used Markov chain method for sample generation. Each sample is pristine and there is no correlation with other samples. As the main novelty, the pairs of ions are gradually added to a sample provided that the energy of each ion is within the boundaries determined by the temperature and the size of ions. The proposed method provides reliable results, as demonstrated by the screening of ion in plasma and in water.

  3. Estimating Model Probabilities using Thermodynamic Markov Chain Monte Carlo Methods

    NASA Astrophysics Data System (ADS)

    Ye, M.; Liu, P.; Beerli, P.; Lu, D.; Hill, M. C.

    2014-12-01

    Markov chain Monte Carlo (MCMC) methods are widely used to evaluate model probability for quantifying model uncertainty. In a general procedure, MCMC simulations are first conducted for each individual model, and MCMC parameter samples are then used to approximate marginal likelihood of the model by calculating the geometric mean of the joint likelihood of the model and its parameters. It has been found the method of evaluating geometric mean suffers from the numerical problem of low convergence rate. A simple test case shows that even millions of MCMC samples are insufficient to yield accurate estimation of the marginal likelihood. To resolve this problem, a thermodynamic method is used to have multiple MCMC runs with different values of a heating coefficient between zero and one. When the heating coefficient is zero, the MCMC run is equivalent to a random walk MC in the prior parameter space; when the heating coefficient is one, the MCMC run is the conventional one. For a simple case with analytical form of the marginal likelihood, the thermodynamic method yields more accurate estimate than the method of using geometric mean. This is also demonstrated for a case of groundwater modeling with consideration of four alternative models postulated based on different conceptualization of a confining layer. This groundwater example shows that model probabilities estimated using the thermodynamic method are more reasonable than those obtained using the geometric method. The thermodynamic method is general, and can be used for a wide range of environmental problem for model uncertainty quantification.

  4. Hydrologic Model Selection using Markov chain Monte Carlo methods

    NASA Astrophysics Data System (ADS)

    Marshall, L.; Sharma, A.; Nott, D.

    2002-12-01

    Estimation of parameter uncertainty (and in turn model uncertainty) allows assessment of the risk in likely applications of hydrological models. Bayesian statistical inference provides an ideal means of assessing parameter uncertainty whereby prior knowledge about the parameter is combined with information from the available data to produce a probability distribution (the posterior distribution) that describes uncertainty about the parameter and serves as a basis for selecting appropriate values for use in modelling applications. Widespread use of Bayesian techniques in hydrology has been hindered by difficulties in summarizing and exploring the posterior distribution. These difficulties have been largely overcome by recent advances in Markov chain Monte Carlo (MCMC) methods that involve random sampling of the posterior distribution. This study presents an adaptive MCMC sampling algorithm which has characteristics that are well suited to model parameters with a high degree of correlation and interdependence, as is often evident in hydrological models. The MCMC sampling technique is used to compare six alternative configurations of a commonly used conceptual rainfall-runoff model, the Australian Water Balance Model (AWBM), using 11 years of daily rainfall runoff data from the Bass river catchment in Australia. The alternative configurations considered fall into two classes - those that consider model errors to be independent of prior values, and those that model the errors as an autoregressive process. Each such class consists of three formulations that represent increasing levels of complexity (and parameterisation) of the original model structure. The results from this study point both to the importance of using Bayesian approaches in evaluating model performance, as well as the simplicity of the MCMC sampling framework that has the ability to bring such approaches within the reach of the applied hydrological community.

  5. Bayesian forecasting and uncertainty quantifying of stream flows using Metropolis–Hastings Markov Chain Monte Carlo algorithm

    DOE PAGES

    Wang, Hongrui; Wang, Cheng; Wang, Ying; ...

    2017-04-05

    This paper presents a Bayesian approach using Metropolis-Hastings Markov Chain Monte Carlo algorithm and applies this method for daily river flow rate forecast and uncertainty quantification for Zhujiachuan River using data collected from Qiaotoubao Gage Station and other 13 gage stations in Zhujiachuan watershed in China. The proposed method is also compared with the conventional maximum likelihood estimation (MLE) for parameter estimation and quantification of associated uncertainties. While the Bayesian method performs similarly in estimating the mean value of daily flow rate, it performs over the conventional MLE method on uncertainty quantification, providing relatively narrower reliable interval than the MLEmore » confidence interval and thus more precise estimation by using the related information from regional gage stations. As a result, the Bayesian MCMC method might be more favorable in the uncertainty analysis and risk management.« less

  6. Mathematical modeling, analysis and Markov Chain Monte Carlo simulation of Ebola epidemics

    NASA Astrophysics Data System (ADS)

    Tulu, Thomas Wetere; Tian, Boping; Wu, Zunyou

    Ebola virus infection is a severe infectious disease with the highest case fatality rate which become the global public health treat now. What makes the disease the worst of all is no specific effective treatment available, its dynamics is not much researched and understood. In this article a new mathematical model incorporating both vaccination and quarantine to study the dynamics of Ebola epidemic has been developed and comprehensively analyzed. The existence as well as uniqueness of the solution to the model is also verified and the basic reproduction number is calculated. Besides, stability conditions are also checked and finally simulation is done using both Euler method and one of the top ten most influential algorithm known as Markov Chain Monte Carlo (MCMC) method. Different rates of vaccination to predict the effect of vaccination on the infected individual over time and that of quarantine are discussed. The results show that quarantine and vaccination are very effective ways to control Ebola epidemic. From our study it was also seen that there is less possibility of an individual for getting Ebola virus for the second time if they survived his/her first infection. Last but not least real data has been fitted to the model, showing that it can used to predict the dynamic of Ebola epidemic.

  7. Markov switching multinomial logit model: An application to accident-injury severities.

    PubMed

    Malyshkina, Nataliya V; Mannering, Fred L

    2009-07-01

    In this study, two-state Markov switching multinomial logit models are proposed for statistical modeling of accident-injury severities. These models assume Markov switching over time between two unobserved states of roadway safety as a means of accounting for potential unobserved heterogeneity. The states are distinct in the sense that in different states accident-severity outcomes are generated by separate multinomial logit processes. To demonstrate the applicability of the approach, two-state Markov switching multinomial logit models are estimated for severity outcomes of accidents occurring on Indiana roads over a four-year time period. Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for model estimation. The estimated Markov switching models result in a superior statistical fit relative to the standard (single-state) multinomial logit models for a number of roadway classes and accident types. It is found that the more frequent state of roadway safety is correlated with better weather conditions and that the less frequent state is correlated with adverse weather conditions.

  8. The generalization ability of SVM classification based on Markov sampling.

    PubMed

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

    2015-06-01

    The previously known works studying the generalization ability of support vector machine classification (SVMC) algorithm are usually based on the assumption of independent and identically distributed samples. In this paper, we go far beyond this classical framework by studying the generalization ability of SVMC based on uniformly ergodic Markov chain (u.e.M.c.) samples. We analyze the excess misclassification error of SVMC based on u.e.M.c. samples, and obtain the optimal learning rate of SVMC for u.e.M.c. We also introduce a new Markov sampling algorithm for SVMC to generate u.e.M.c. samples from given dataset, and present the numerical studies on the learning performance of SVMC based on Markov sampling for benchmark datasets. The numerical studies show that the SVMC based on Markov sampling not only has better generalization ability as the number of training samples are bigger, but also the classifiers based on Markov sampling are sparsity when the size of dataset is bigger with regard to the input dimension.

  9. Snow Water Equivalent Retrieval By Markov Chain Monte Carlo Based on Memls and Hut Snow Emission Model

    NASA Astrophysics Data System (ADS)

    Pan, J.; Durand, M. T.; Vanderjagt, B. J.

    2014-12-01

    The Markov chain Monte Carlo (MCMC) method had been proved to be successful in snow water equivalent retrieval based on synthetic point-scale passive microwave brightness temperature (TB) observations. This method needs only general prior information about distribution of snow parameters, and could estimate layered snow properties, including the thickness, temperature, density and snow grain size (or exponential correlation length) of each layer. In this study, the multi-layer HUT (Helsinki University of Technology) model and the MEMLS (Microwave Emission Model of Layered Snowpacks) will be used as observation models to assimilate the observed TB into snow parameter prediction. Previous studies had shown that the multi-layer HUT model tends to underestimate TB at 37 GHz for deep snow, while the MEMLS does not show sensitivity of model bias to snow depth. Therefore, results using HUT model and MEMLS will be compared to see how the observation model will influence the retrieval of snow parameters. The radiometric measurements at 10.65, 18.7, 36.5 and 90 GHz at Sodankyla, Finland will be used as MCMC input, and the statistics of all snow property measurement will be used to calculate the prior information. 43 dry snowpits with complete measurements of all snow parameters will be used for validation. The entire dataset are from NorSREx (Nordic Snow Radar Experiment) experiments carried out by Juha Lemmetyinen, Anna Kontu and Jouni Pulliainen in FMI in 2009-2011 winters, and continued two more winters from 2011 to Spring of 2013. Besides the snow thickness and snow density that are directly related to snow water equivalent, other parameters will be compared with observations, too. For thin snow, the previous studies showed that influence of underlying soil is considerable, especially when the soil is half frozen with part of unfrozen liquid water and part of ice. Therefore, this study will also try to employ a simple frozen soil permittivity model to improve the

  10. Integration of logistic regression, Markov chain and cellular automata models to simulate urban expansion

    NASA Astrophysics Data System (ADS)

    Jokar Arsanjani, Jamal; Helbich, Marco; Kainz, Wolfgang; Darvishi Boloorani, Ali

    2013-04-01

    This research analyses the suburban expansion in the metropolitan area of Tehran, Iran. A hybrid model consisting of logistic regression model, Markov chain (MC), and cellular automata (CA) was designed to improve the performance of the standard logistic regression model. Environmental and socio-economic variables dealing with urban sprawl were operationalised to create a probability surface of spatiotemporal states of built-up land use for the years 2006, 2016, and 2026. For validation, the model was evaluated by means of relative operating characteristic values for different sets of variables. The approach was calibrated for 2006 by cross comparing of actual and simulated land use maps. The achieved outcomes represent a match of 89% between simulated and actual maps of 2006, which was satisfactory to approve the calibration process. Thereafter, the calibrated hybrid approach was implemented for forthcoming years. Finally, future land use maps for 2016 and 2026 were predicted by means of this hybrid approach. The simulated maps illustrate a new wave of suburban development in the vicinity of Tehran at the western border of the metropolis during the next decades.

  11. Joint coverage probability in a simulation study on Continuous-Time Markov Chain parameter estimation.

    PubMed

    Benoit, Julia S; Chan, Wenyaw; Doody, Rachelle S

    2015-01-01

    Parameter dependency within data sets in simulation studies is common, especially in models such as Continuous-Time Markov Chains (CTMC). Additionally, the literature lacks a comprehensive examination of estimation performance for the likelihood-based general multi-state CTMC. Among studies attempting to assess the estimation, none have accounted for dependency among parameter estimates. The purpose of this research is twofold: 1) to develop a multivariate approach for assessing accuracy and precision for simulation studies 2) to add to the literature a comprehensive examination of the estimation of a general 3-state CTMC model. Simulation studies are conducted to analyze longitudinal data with a trinomial outcome using a CTMC with and without covariates. Measures of performance including bias, component-wise coverage probabilities, and joint coverage probabilities are calculated. An application is presented using Alzheimer's disease caregiver stress levels. Comparisons of joint and component-wise parameter estimates yield conflicting inferential results in simulations from models with and without covariates. In conclusion, caution should be taken when conducting simulation studies aiming to assess performance and choice of inference should properly reflect the purpose of the simulation.

  12. Sequential Markov chain Monte Carlo filter with simultaneous model selection for electrocardiogram signal modeling.

    PubMed

    Edla, Shwetha; Kovvali, Narayan; Papandreou-Suppappola, Antonia

    2012-01-01

    Constructing statistical models of electrocardiogram (ECG) signals, whose parameters can be used for automated disease classification, is of great importance in precluding manual annotation and providing prompt diagnosis of cardiac diseases. ECG signals consist of several segments with different morphologies (namely the P wave, QRS complex and the T wave) in a single heart beat, which can vary across individuals and diseases. Also, existing statistical ECG models exhibit a reliance upon obtaining a priori information from the ECG data by using preprocessing algorithms to initialize the filter parameters, or to define the user-specified model parameters. In this paper, we propose an ECG modeling technique using the sequential Markov chain Monte Carlo (SMCMC) filter that can perform simultaneous model selection, by adaptively choosing from different representations depending upon the nature of the data. Our results demonstrate the ability of the algorithm to track various types of ECG morphologies, including intermittently occurring ECG beats. In addition, we use the estimated model parameters as the feature set to classify between ECG signals with normal sinus rhythm and four different types of arrhythmia.

  13. Exceptional motifs in different Markov chain models for a statistical analysis of DNA sequences.

    PubMed

    Schbath, S; Prum, B; de Turckheim, E

    1995-01-01

    Identifying exceptional motifs is often used for extracting information from long DNA sequences. The two difficulties of the method are the choice of the model that defines the expected frequencies of words and the approximation of the variance of the difference T(W) between the number of occurrences of a word W and its estimation. We consider here different Markov chain models, either with stationary or periodic transition probabilities. We estimate the variance of the difference T(W) by the conditional variance of the number of occurrences of W given the oligonucleotides counts that define the model. Two applications show how to use asymptotically standard normal statistics associated with the counts to describe a given sequence in terms of its outlying words. Sequences of Escherichia coli and of Bacillus subtilis are compared with respect to their exceptional tri- and tetranucleotides. For both bacteria, exceptional 3-words are mainly found in the coding frame. E. coli palindrome counts are analyzed in different models, showing that many overabundant words are one-letter mutations of avoided palindromes.

  14. Eternal non-Markovianity: from random unitary to Markov chain realisations.

    PubMed

    Megier, Nina; Chruściński, Dariusz; Piilo, Jyrki; Strunz, Walter T

    2017-07-25

    The theoretical description of quantum dynamics in an intriguing way does not necessarily imply the underlying dynamics is indeed intriguing. Here we show how a known very interesting master equation with an always negative decay rate [eternal non-Markovianity (ENM)] arises from simple stochastic Schrödinger dynamics (random unitary dynamics). Equivalently, it may be seen as arising from a mixture of Markov (semi-group) open system dynamics. Both these approaches lead to a more general family of CPT maps, characterized by a point within a parameter triangle. Our results show how ENM quantum dynamics can be realised easily in the laboratory. Moreover, we find a quantum time-continuously measured (quantum trajectory) realisation of the dynamics of the ENM master equation based on unitary transformations and projective measurements in an extended Hilbert space, guided by a classical Markov process. Furthermore, a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) representation of the dynamics in an extended Hilbert space can be found, with a remarkable property: there is no dynamics in the ancilla state. Finally, analogous constructions for two qubits extend these results from non-CP-divisible to non-P-divisible dynamics.

  15. Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains: the role of mixing statistics and frame shift of neighboring genes.

    PubMed

    Cocho, Germinal; Miramontes, Pedro; Mansilla, Ricardo; Li, Wentian

    2014-12-01

    We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies. Copyright © 2014 Elsevier Ltd. All rights reserved.

  16. Markov Chains for Investigating and Predicting Migration: A Case from Southwestern China

    NASA Astrophysics Data System (ADS)

    Qin, Bo; Wang, Yiyu; Xu, Haoming

    2018-03-01

    In order to accurately predict the population’s happiness, this paper conducted two demographic surveys on a new district of a city in western China, and carried out a dynamic analysis using related mathematical methods. This paper argues that the migration of migrants in the city will change the pattern of spatial distribution of human resources in the city and thus affect the social and economic development in all districts. The migration status of the population will change randomly with the passage of time, so it can be predicted and analyzed through the Markov process. The Markov process provides the local government and decision-making bureau a valid basis for the dynamic analysis of the mobility of migrants in the city as well as the ways for promoting happiness of local people’s lives.

  17. Updating categorical soil maps using limited survey data by Bayesian Markov chain cosimulation.

    PubMed

    Li, Weidong; Zhang, Chuanrong; Dey, Dipak K; Willig, Michael R

    2013-01-01

    Updating categorical soil maps is necessary for providing current, higher-quality soil data to agricultural and environmental management but may not require a costly thorough field survey because latest legacy maps may only need limited corrections. This study suggests a Markov chain random field (MCRF) sequential cosimulation (Co-MCSS) method for updating categorical soil maps using limited survey data provided that qualified legacy maps are available. A case study using synthetic data demonstrates that Co-MCSS can appreciably improve simulation accuracy of soil types with both contributions from a legacy map and limited sample data. The method indicates the following characteristics: (1) if a soil type indicates no change in an update survey or it has been reclassified into another type that similarly evinces no change, it will be simply reproduced in the updated map; (2) if a soil type has changes in some places, it will be simulated with uncertainty quantified by occurrence probability maps; (3) if a soil type has no change in an area but evinces changes in other distant areas, it still can be captured in the area with unobvious uncertainty. We concluded that Co-MCSS might be a practical method for updating categorical soil maps with limited survey data.

  18. Updating Categorical Soil Maps Using Limited Survey Data by Bayesian Markov Chain Cosimulation

    PubMed Central

    Dey, Dipak K.; Willig, Michael R.

    2013-01-01

    Updating categorical soil maps is necessary for providing current, higher-quality soil data to agricultural and environmental management but may not require a costly thorough field survey because latest legacy maps may only need limited corrections. This study suggests a Markov chain random field (MCRF) sequential cosimulation (Co-MCSS) method for updating categorical soil maps using limited survey data provided that qualified legacy maps are available. A case study using synthetic data demonstrates that Co-MCSS can appreciably improve simulation accuracy of soil types with both contributions from a legacy map and limited sample data. The method indicates the following characteristics: (1) if a soil type indicates no change in an update survey or it has been reclassified into another type that similarly evinces no change, it will be simply reproduced in the updated map; (2) if a soil type has changes in some places, it will be simulated with uncertainty quantified by occurrence probability maps; (3) if a soil type has no change in an area but evinces changes in other distant areas, it still can be captured in the area with unobvious uncertainty. We concluded that Co-MCSS might be a practical method for updating categorical soil maps with limited survey data. PMID:24027447

  19. Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems

    NASA Astrophysics Data System (ADS)

    Suwa, Hidemaro

    2013-03-01

    We have developed novel Monte Carlo methods for precisely calculating quantum spin-boson models and investigated the critical phenomena of the spin-Peierls systems. Three significant methods are presented. The first is a new optimization algorithm of the Markov chain transition kernel based on the geometric weight allocation. This algorithm, for the first time, satisfies the total balance generally without imposing the detailed balance and always minimizes the average rejection rate, being better than the Metropolis algorithm. The second is the extension of the worm (directed-loop) algorithm to non-conserved particles, which cannot be treated efficiently by the conventional methods. The third is the combination with the level spectroscopy. Proposing a new gap estimator, we are successful in eliminating the systematic error of the conventional moment method. Then we have elucidated the phase diagram and the universality class of the one-dimensional XXZ spin-Peierls system. The criticality is totally consistent with the J1 -J2 model, an effective model in the antiadiabatic limit. Through this research, we have succeeded in investigating the critical phenomena of the effectively frustrated quantum spin system by the quantum Monte Carlo method without the negative sign. JSPS Postdoctoral Fellow for Research Abroad

  20. Quantum Model of Emerging Grammars

    NASA Technical Reports Server (NTRS)

    Zak, M.

    1999-01-01

    A special class of quantum recurrent nets simulating Markov chains with absorbing states is introduced. The absorbing states are exploited for pattern recognition: each class of patterns, each combination of patterns acquires its own meaning.

  1. Analysis of mean time to data loss of fault-tolerant disk arrays RAID-6 based on specialized Markov chain

    NASA Astrophysics Data System (ADS)

    Rahman, P. A.; D'K Novikova Freyre Shavier, G.

    2018-03-01

    This scientific paper is devoted to the analysis of the mean time to data loss of redundant disk arrays RAID-6 with alternation of data considering different failure rates of disks both in normal state of the disk array and in degraded and rebuild states, and also nonzero time of the disk replacement. The reliability model developed by the authors on the basis of the Markov chain and obtained calculation formula for estimation of the mean time to data loss (MTTDL) of the RAID-6 disk arrays are also presented. At last, the technique of estimation of the initial reliability parameters and examples of calculation of the MTTDL of the RAID-6 disk arrays for the different numbers of disks are also given.

  2. Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

    PubMed

    Hössjer, Ola; Tyvand, Peder A; Miloh, Touvia

    2016-02-01

    The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates. Copyright © 2015 Elsevier Inc. All rights reserved.

  3. Markov chain Monte Carlo linkage analysis: effect of bin width on the probability of linkage.

    PubMed

    Slager, S L; Juo, S H; Durner, M; Hodge, S E

    2001-01-01

    We analyzed part of the Genetic Analysis Workshop (GAW) 12 simulated data using Monte Carlo Markov chain (MCMC) methods that are implemented in the computer program Loki. The MCMC method reports the "probability of linkage" (PL) across the chromosomal regions of interest. The point of maximum PL can then be taken as a "location estimate" for the location of the quantitative trait locus (QTL). However, Loki does not provide a formal statistical test of linkage. In this paper, we explore how the bin width used in the calculations affects the max PL and the location estimate. We analyzed age at onset (AO) and quantitative trait number 5, Q5, from 26 replicates of the general simulated data in one region where we knew a major gene, MG5, is located. For each trait, we found the max PL and the corresponding location estimate, using four different bin widths. We found that bin width, as expected, does affect the max PL and the location estimate, and we recommend that users of Loki explore how their results vary with different bin widths.

  4. Predictability of Circulation Transitions (Observed and Modeled): Non-diffusive Dynamics, Markov Chains and Error Growth.

    NASA Astrophysics Data System (ADS)

    Straus, D. M.

    2006-12-01

    The transitions between portions of the state space of the large-scale flow is studied from daily wintertime data over the Pacific North America region using the NCEP reanalysis data set (54 winters) and very large suites of hindcasts made with the COLA atmospheric GCM with observed SST (55 members for each of 18 winters). The partition of the large-scale state space is guided by cluster analysis, whose statistical significance and relationship to SST is reviewed (Straus and Molteni, 2004; Straus, Corti and Molteni, 2006). The determination of the global nature of the flow through state space is studied using Markov Chains (Crommelin, 2004). In particular the non-diffusive part of the flow is contrasted in nature (small data sample) and the AGCM (large data sample). The intrinsic error growth associated with different portions of the state space is studied through sets of identical twin AGCM simulations. The goal is to obtain realistic estimates of predictability times for large-scale transitions that should be useful in long-range forecasting.

  5. Atmospheric Tracer Inverse Modeling Using Markov Chain Monte Carlo (MCMC)

    NASA Astrophysics Data System (ADS)

    Kasibhatla, P.

    2004-12-01

    In recent years, there has been an increasing emphasis on the use of Bayesian statistical estimation techniques to characterize the temporal and spatial variability of atmospheric trace gas sources and sinks. The applications have been varied in terms of the particular species of interest, as well as in terms of the spatial and temporal resolution of the estimated fluxes. However, one common characteristic has been the use of relatively simple statistical models for describing the measurement and chemical transport model error statistics and prior source statistics. For example, multivariate normal probability distribution functions (pdfs) are commonly used to model these quantities and inverse source estimates are derived for fixed values of pdf paramaters. While the advantage of this approach is that closed form analytical solutions for the a posteriori pdfs of interest are available, it is worth exploring Bayesian analysis approaches which allow for a more general treatment of error and prior source statistics. Here, we present an application of the Markov Chain Monte Carlo (MCMC) methodology to an atmospheric tracer inversion problem to demonstrate how more gereral statistical models for errors can be incorporated into the analysis in a relatively straightforward manner. The MCMC approach to Bayesian analysis, which has found wide application in a variety of fields, is a statistical simulation approach that involves computing moments of interest of the a posteriori pdf by efficiently sampling this pdf. The specific inverse problem that we focus on is the annual mean CO2 source/sink estimation problem considered by the TransCom3 project. TransCom3 was a collaborative effort involving various modeling groups and followed a common modeling and analysis protocoal. As such, this problem provides a convenient case study to demonstrate the applicability of the MCMC methodology to atmospheric tracer source/sink estimation problems.

  6. Application of stochastic automata networks for creation of continuous time Markov chain models of voltage gating of gap junction channels.

    PubMed

    Snipas, Mindaugas; Pranevicius, Henrikas; Pranevicius, Mindaugas; Pranevicius, Osvaldas; Paulauskas, Nerijus; Bukauskas, Feliksas F

    2015-01-01

    The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ~20 times.

  7. Application of Stochastic Automata Networks for Creation of Continuous Time Markov Chain Models of Voltage Gating of Gap Junction Channels

    PubMed Central

    Pranevicius, Henrikas; Pranevicius, Mindaugas; Pranevicius, Osvaldas; Bukauskas, Feliksas F.

    2015-01-01

    The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ∼20 times. PMID:25705700

  8. The behavior of Metropolis-coupled Markov chains when sampling rugged phylogenetic distributions.

    PubMed

    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.

  9. Cosmological constraints on generalized Chaplygin gas model: Markov Chain Monte Carlo approach

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Xu, Lixin; Lu, Jianbo, E-mail: lxxu@dlut.edu.cn, E-mail: lvjianbo819@163.com

    2010-03-01

    We use the Markov Chain Monte Carlo method to investigate a global constraints on the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy from the latest observational data: the Constitution dataset of type supernovae Ia (SNIa), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. In a non-flat universe, the constraint results for GCG model are, Ω{sub b}h{sup 2} = 0.0235{sup +0.0021}{sub −0.0018} (1σ) {sup +0.0028}{sub −0.0022} (2σ), Ω{sub k} = 0.0035{sup +0.0172}{sub −0.0182} (1σ) {sup +0.0226}{sub −0.0204} (2σ), A{submore » s} = 0.753{sup +0.037}{sub −0.035} (1σ) {sup +0.045}{sub −0.044} (2σ), α = 0.043{sup +0.102}{sub −0.106} (1σ) {sup +0.134}{sub −0.117} (2σ), and H{sub 0} = 70.00{sup +3.25}{sub −2.92} (1σ) {sup +3.77}{sub −3.67} (2σ), which is more stringent than the previous results for constraint on GCG model parameters. Furthermore, according to the information criterion, it seems that the current observations much support ΛCDM model relative to the GCG model.« less

  10. Improving Markov Chain Models for Road Profiles Simulation via Definition of States

    DTIC Science & Technology

    2012-04-01

    wavelet transform in pavement profile analysis," Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility, vol. 47, no. 4...34Estimating Markov Transition Probabilities from Micro -Unit Data," Journal of the Royal Statistical Society. Series C (Applied Statistics), pp. 355-371

  11. Using Markov chains of nucleotide sequences as a possible precursor to predict functional roles of human genome: a case study on inactive chromatin regions.

    PubMed

    Lee, K-E; Lee, E-J; Park, H-S

    2016-08-30

    Recent advances in computational epigenetics have provided new opportunities to evaluate n-gram probabilistic language models. In this paper, we describe a systematic genome-wide approach for predicting functional roles in inactive chromatin regions by using a sequence-based Markovian chromatin map of the human genome. We demonstrate that Markov chains of sequences can be used as a precursor to predict functional roles in heterochromatin regions and provide an example comparing two publicly available chromatin annotations of large-scale epigenomics projects: ENCODE project consortium and Roadmap Epigenomics consortium.

  12. Reciprocal Sliding Friction Model for an Electro-Deposited Coating and Its Parameter Estimation Using Markov Chain Monte Carlo Method

    PubMed Central

    Kim, Kyungmok; Lee, Jaewook

    2016-01-01

    This paper describes a sliding friction model for an electro-deposited coating. Reciprocating sliding tests using ball-on-flat plate test apparatus are performed to determine an evolution of the kinetic friction coefficient. The evolution of the friction coefficient is classified into the initial running-in period, steady-state sliding, and transition to higher friction. The friction coefficient during the initial running-in period and steady-state sliding is expressed as a simple linear function. The friction coefficient in the transition to higher friction is described with a mathematical model derived from Kachanov-type damage law. The model parameters are then estimated using the Markov Chain Monte Carlo (MCMC) approach. It is identified that estimated friction coefficients obtained by MCMC approach are in good agreement with measured ones. PMID:28773359

  13. OPTIMIZING OBSERVER EFFORT FOR FIELD DETECTION OF REPRODUCTIVE EFFECTS IN BIRDS

    EPA Science Inventory

    Avian nest survival is best viewed as a Markov process with two absorbing states, death and fledging. We present a column-stochastic Markov chain from which all major Mayfield formulations of daily nest-survival can be derived contingent upon the degree of observer knowledge of e...

  14. Markov stochasticity coordinates

    DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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

  15. Enhancing hydrologic data assimilation by evolutionary Particle Filter and Markov Chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    Abbaszadeh, Peyman; Moradkhani, Hamid; Yan, Hongxiang

    2018-01-01

    Particle Filters (PFs) have received increasing attention by researchers from different disciplines including the hydro-geosciences, as an effective tool to improve model predictions in nonlinear and non-Gaussian dynamical systems. The implication of dual state and parameter estimation using the PFs in hydrology has evolved since 2005 from the PF-SIR (sampling importance resampling) to PF-MCMC (Markov Chain Monte Carlo), and now to the most effective and robust framework through evolutionary PF approach based on Genetic Algorithm (GA) and MCMC, the so-called EPFM. In this framework, the prior distribution undergoes an evolutionary process based on the designed mutation and crossover operators of GA. The merit of this approach is that the particles move to an appropriate position by using the GA optimization and then the number of effective particles is increased by means of MCMC, whereby the particle degeneracy is avoided and the particle diversity is improved. In this study, the usefulness and effectiveness of the proposed EPFM is investigated by applying the technique on a conceptual and highly nonlinear hydrologic model over four river basins located in different climate and geographical regions of the United States. Both synthetic and real case studies demonstrate that the EPFM improves both the state and parameter estimation more effectively and reliably as compared with the PF-MCMC.

  16. Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites

    PubMed Central

    Newton, Paul K; Mason, Jeremy; Venkatappa, Neethi; Jochelson, Maxine S; Hurt, Brian; Nieva, Jorge; Comen, Elizabeth; Norton, Larry; Kuhn, Peter

    2015-01-01

    Background: Cancer cell migration patterns are critical for understanding metastases and clinical evolution. Breast cancer spreads from one organ system to another via hematogenous and lymphatic routes. Although patterns of spread may superficially seem random and unpredictable, we explored the possibility that this is not the case. Aims: Develop a Markov based model of breast cancer progression that has predictive capability. Methods: On the basis of a longitudinal data set of 446 breast cancer patients, we created a Markov chain model of metastasis that describes the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Progression is modeled as a random walk on a directed graph, where nodes represent anatomical sites where tumors can develop. Results: We quantify how survival depends on the location of the first metastatic site for different patient subcategories. In addition, we classify metastatic sites as “sponges” or “spreaders” with implications regarding anatomical pathway prediction and long-term survival. As metastatic tumors to the bone (main spreader) are most prominent, we focus in more detail on differences between groups of patients who form subsequent metastases to the lung as compared with the liver. Conclusions: We have found that spatiotemporal patterns of metastatic spread in breast cancer are neither random nor unpredictable. Furthermore, the novel concept of classifying organ sites as sponges or spreaders may motivate experiments seeking a biological basis for these phenomena and allow us to quantify the potential consequences of therapeutic targeting of sites in the oligometastatic setting and shed light on organotropic aspects of the disease. PMID:28721371

  17. Preliminary testing for the Markov property of the fifteen chromatin states of the Broad Histone Track.

    PubMed

    Lee, Kyung-Eun; Park, Hyun-Seok

    2015-01-01

    Epigenetic computational analyses based on Markov chains can integrate dependencies between regions in the genome that are directly adjacent. In this paper, the BED files of fifteen chromatin states of the Broad Histone Track of the ENCODE project are parsed, and comparative nucleotide frequencies of regional chromatin blocks are thoroughly analyzed to detect the Markov property in them. We perform various tests to examine the Markov property embedded in a frequency domain by checking for the presence of the Markov property in the various chromatin states. We apply these tests to each region of the fifteen chromatin states. The results of our simulation indicate that some of the chromatin states possess a stronger Markov property than others. We discuss the significance of our findings in statistical models of nucleotide sequences that are necessary for the computational analysis of functional units in noncoding DNA.

  18. Solving inverse problem for Markov chain model of customer lifetime value using flower pollination algorithm

    NASA Astrophysics Data System (ADS)

    Al-Ma'shumah, Fathimah; Permana, Dony; Sidarto, Kuntjoro Adji

    2015-12-01

    Customer Lifetime Value is an important and useful concept in marketing. One of its benefits is to help a company for budgeting marketing expenditure for customer acquisition and customer retention. Many mathematical models have been introduced to calculate CLV considering the customer retention/migration classification scheme. A fairly new class of these models which will be described in this paper uses Markov Chain Models (MCM). This class of models has the major advantage for its flexibility to be modified to several different cases/classification schemes. In this model, the probabilities of customer retention and acquisition play an important role. From Pfeifer and Carraway, 2000, the final formula of CLV obtained from MCM usually contains nonlinear form of the transition probability matrix. This nonlinearity makes the inverse problem of CLV difficult to solve. This paper aims to solve this inverse problem, yielding the approximate transition probabilities for the customers, by applying metaheuristic optimization algorithm developed by Yang, 2013, Flower Pollination Algorithm. The major interpretation of obtaining the transition probabilities are to set goals for marketing teams in keeping the relative frequencies of customer acquisition and customer retention.

  19. RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

    PubMed Central

    Griego, R. J.; Hersh, R.

    1969-01-01

    Several authors have considered Markov processes defined by the motion of a particle on a fixed line with a random velocity1, 6, 8, 10 or a random diffusivity.5, 12 A “random evolution” is a natural but apparently new generalization of this notion. In this note we hope to show that this concept leads to simple and powerful applications of probabilistic tools to initial-value problems of both parabolic and hyperbolic type. We obtain existence theorems, representation theorems, and asymptotic formulas, both old and new. PMID:16578690

  20. Semi-Markov adjunction to the Computer-Aided Markov Evaluator (CAME)

    NASA Technical Reports Server (NTRS)

    Rosch, Gene; Hutchins, Monica A.; Leong, Frank J.; Babcock, Philip S., IV

    1988-01-01

    The rule-based Computer-Aided Markov Evaluator (CAME) program was expanded in its ability to incorporate the effect of fault-handling processes into the construction of a reliability model. The fault-handling processes are modeled as semi-Markov events and CAME constructs and appropriate semi-Markov model. To solve the model, the program outputs it in a form which can be directly solved with the Semi-Markov Unreliability Range Evaluator (SURE) program. As a means of evaluating the alterations made to the CAME program, the program is used to model the reliability of portions of the Integrated Airframe/Propulsion Control System Architecture (IAPSA 2) reference configuration. The reliability predictions are compared with a previous analysis. The results bear out the feasibility of utilizing CAME to generate appropriate semi-Markov models to model fault-handling processes.

  1. Markov chain Monte Carlo techniques and spatial-temporal modelling for medical EIT.

    PubMed

    West, Robert M; Aykroyd, Robert G; Meng, Sha; Williams, Richard A

    2004-02-01

    Many imaging problems such as imaging with electrical impedance tomography (EIT) can be shown to be inverse problems: that is either there is no unique solution or the solution does not depend continuously on the data. As a consequence solution of inverse problems based on measured data alone is unstable, particularly if the mapping between the solution distribution and the measurements is also nonlinear as in EIT. To deliver a practical stable solution, it is necessary to make considerable use of prior information or regularization techniques. The role of a Bayesian approach is therefore of fundamental importance, especially when coupled with Markov chain Monte Carlo (MCMC) sampling to provide information about solution behaviour. Spatial smoothing is a commonly used approach to regularization. In the human thorax EIT example considered here nonlinearity increases the difficulty of imaging, using only boundary data, leading to reconstructions which are often rather too smooth. In particular, in medical imaging the resistivity distribution usually contains substantial jumps at the boundaries of different anatomical regions. With spatial smoothing these boundaries can be masked by blurring. This paper focuses on the medical application of EIT to monitor lung and cardiac function and uses explicit geometric information regarding anatomical structure and incorporates temporal correlation. Some simple properties are assumed known, or at least reliably estimated from separate studies, whereas others are estimated from the voltage measurements. This structural formulation will also allow direct estimation of clinically important quantities, such as ejection fraction and residual capacity, along with assessment of precision.

  2. An informational transition in conditioned Markov chains: Applied to genetics and evolution.

    PubMed

    Zhao, Lei; Lascoux, Martin; Waxman, David

    2016-08-07

    In this work we assume that we have some knowledge about the state of a population at two known times, when the dynamics is governed by a Markov chain such as a Wright-Fisher model. Such knowledge could be obtained, for example, from observations made on ancient and contemporary DNA, or during laboratory experiments involving long term evolution. A natural assumption is that the behaviour of the population, between observations, is related to (or constrained by) what was actually observed. The present work shows that this assumption has limited validity. When the time interval between observations is larger than a characteristic value, which is a property of the population under consideration, there is a range of intermediate times where the behaviour of the population has reduced or no dependence on what was observed and an equilibrium-like distribution applies. Thus, for example, if the frequency of an allele is observed at two different times, then for a large enough time interval between observations, the population has reduced or no dependence on the two observed frequencies for a range of intermediate times. Given observations of a population at two times, we provide a general theoretical analysis of the behaviour of the population at all intermediate times, and determine an expression for the characteristic time interval, beyond which the observations do not constrain the population's behaviour over a range of intermediate times. The findings of this work relate to what can be meaningfully inferred about a population at intermediate times, given knowledge of terminal states. Copyright © 2016 Elsevier Ltd. All rights reserved.

  3. Unifying framework for multimodal brain MRI segmentation based on Hidden Markov Chains.

    PubMed

    Bricq, S; Collet, Ch; Armspach, J P

    2008-12-01

    In the frame of 3D medical imaging, accurate segmentation of multimodal brain MR images is of interest for many brain disorders. However, due to several factors such as noise, imaging artifacts, intrinsic tissue variation and partial volume effects, tissue classification remains a challenging task. In this paper, we present a unifying framework for unsupervised segmentation of multimodal brain MR images including partial volume effect, bias field correction, and information given by a probabilistic atlas. Here-proposed method takes into account neighborhood information using a Hidden Markov Chain (HMC) model. Due to the limited resolution of imaging devices, voxels may be composed of a mixture of different tissue types, this partial volume effect is included to achieve an accurate segmentation of brain tissues. Instead of assigning each voxel to a single tissue class (i.e., hard classification), we compute the relative amount of each pure tissue class in each voxel (mixture estimation). Further, a bias field estimation step is added to the proposed algorithm to correct intensity inhomogeneities. Furthermore, atlas priors were incorporated using probabilistic brain atlas containing prior expectations about the spatial localization of different tissue classes. This atlas is considered as a complementary sensor and the proposed method is extended to multimodal brain MRI without any user-tunable parameter (unsupervised algorithm). To validate this new unifying framework, we present experimental results on both synthetic and real brain images, for which the ground truth is available. Comparison with other often used techniques demonstrates the accuracy and the robustness of this new Markovian segmentation scheme.

  4. Delirium superimposed on dementia: defining disease states and course from longitudinal measurements of a multivariate index using latent class analysis and hidden Markov chains.

    PubMed

    Ciampi, Antonio; Dyachenko, Alina; Cole, Martin; McCusker, Jane

    2011-12-01

    The study of mental disorders in the elderly presents substantial challenges due to population heterogeneity, coexistence of different mental disorders, and diagnostic uncertainty. While reliable tools have been developed to collect relevant data, new approaches to study design and analysis are needed. We focus on a new analytic approach. Our framework is based on latent class analysis and hidden Markov chains. From repeated measurements of a multivariate disease index, we extract the notion of underlying state of a patient at a time point. The course of the disorder is then a sequence of transitions among states. States and transitions are not observable; however, the probability of being in a state at a time point, and the transition probabilities from one state to another over time can be estimated. Data from 444 patients with and without diagnosis of delirium and dementia were available from a previous study. The Delirium Index was measured at diagnosis, and at 2 and 6 months from diagnosis. Four latent classes were identified: fairly healthy, moderately ill, clearly sick, and very sick. Dementia and delirium could not be separated on the basis of these data alone. Indeed, as the probability of delirium increased, so did the probability of decline of mental functions. Eight most probable courses were identified, including good and poor stable courses, and courses exhibiting various patterns of improvement. Latent class analysis and hidden Markov chains offer a promising tool for studying mental disorders in the elderly. Its use may show its full potential as new data become available.

  5. Theory and Applications of Weakly Interacting Markov Processes

    DTIC Science & Technology

    2018-02-03

    Moderate deviation principles for stochastic dynamical systems. Boston University, Math Colloquium, March 27, 2015. • Moderate Deviation Principles for...Markov chain approximation method. Submitted. [8] E. Bayraktar and M. Ludkovski. Optimal trade execution in illiquid markets. Math . Finance, 21(4):681...701, 2011. [9] E. Bayraktar and M. Ludkovski. Liquidation in limit order books with controlled intensity. Math . Finance, 24(4):627–650, 2014. [10] P.D

  6. Discovering Beaten Paths in Collaborative Ontology-Engineering Projects using Markov Chains

    PubMed Central

    Walk, Simon; Singer, Philipp; Strohmaier, Markus; Tudorache, Tania; Musen, Mark A.; Noy, Natalya F.

    2014-01-01

    Biomedical taxonomies, thesauri and ontologies in the form of the International Classification of Diseases as a taxonomy or the National Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in acquiring, representing and processing information about human health. With increasing adoption and relevance, biomedical ontologies have also significantly increased in size. For example, the 11th revision of the International Classification of Diseases, which is currently under active development by the World Health Organization contains nearly 50, 000 classes representing a vast variety of different diseases and causes of death. This evolution in terms of size was accompanied by an evolution in the way ontologies are engineered. Because no single individual has the expertise to develop such large-scale ontologies, ontology-engineering projects have evolved from small-scale efforts involving just a few domain experts to large-scale projects that require effective collaboration between dozens or even hundreds of experts, practitioners and other stakeholders. Understanding the way these different stakeholders collaborate will enable us to improve editing environments that support such collaborations. In this paper, we uncover how large ontology-engineering projects, such as the International Classification of Diseases in its 11th revision, unfold by analyzing usage logs of five different biomedical ontology-engineering projects of varying sizes and scopes using Markov chains. We discover intriguing interaction patterns (e.g., which properties users frequently change after specific given ones) that suggest that large collaborative ontology-engineering projects are governed by a few general principles that determine and drive development. From our analysis, we identify commonalities and differences between different projects that have implications for project managers, ontology editors, developers and contributors working on collaborative ontology

  7. Discovering beaten paths in collaborative ontology-engineering projects using Markov chains.

    PubMed

    Walk, Simon; Singer, Philipp; Strohmaier, Markus; Tudorache, Tania; Musen, Mark A; Noy, Natalya F

    2014-10-01

    Biomedical taxonomies, thesauri and ontologies in the form of the International Classification of Diseases as a taxonomy or the National Cancer Institute Thesaurus as an OWL-based ontology, play a critical role in acquiring, representing and processing information about human health. With increasing adoption and relevance, biomedical ontologies have also significantly increased in size. For example, the 11th revision of the International Classification of Diseases, which is currently under active development by the World Health Organization contains nearly 50,000 classes representing a vast variety of different diseases and causes of death. This evolution in terms of size was accompanied by an evolution in the way ontologies are engineered. Because no single individual has the expertise to develop such large-scale ontologies, ontology-engineering projects have evolved from small-scale efforts involving just a few domain experts to large-scale projects that require effective collaboration between dozens or even hundreds of experts, practitioners and other stakeholders. Understanding the way these different stakeholders collaborate will enable us to improve editing environments that support such collaborations. In this paper, we uncover how large ontology-engineering projects, such as the International Classification of Diseases in its 11th revision, unfold by analyzing usage logs of five different biomedical ontology-engineering projects of varying sizes and scopes using Markov chains. We discover intriguing interaction patterns (e.g., which properties users frequently change after specific given ones) that suggest that large collaborative ontology-engineering projects are governed by a few general principles that determine and drive development. From our analysis, we identify commonalities and differences between different projects that have implications for project managers, ontology editors, developers and contributors working on collaborative ontology

  8. Reconciling a geophysical model to data using a Markov chain Monte Carlo algorithm: An application to the Yellow Sea-Korean Peninsula region

    NASA Astrophysics Data System (ADS)

    Pasyanos, Michael E.; Franz, Gregory A.; Ramirez, Abelardo L.

    2006-03-01

    In an effort to build seismic models that are the most consistent with multiple data sets we have applied a new probabilistic inverse technique. This method uses a Markov chain Monte Carlo (MCMC) algorithm to sample models from a prior distribution and test them against multiple data types to generate a posterior distribution. While computationally expensive, this approach has several advantages over deterministic models, notably the seamless reconciliation of different data types that constrain the model, the proper handling of both data and model uncertainties, and the ability to easily incorporate a variety of prior information, all in a straightforward, natural fashion. A real advantage of the technique is that it provides a more complete picture of the solution space. By mapping out the posterior probability density function, we can avoid simplistic assumptions about the model space and allow alternative solutions to be identified, compared, and ranked. Here we use this method to determine the crust and upper mantle structure of the Yellow Sea and Korean Peninsula region. The model is parameterized as a series of seven layers in a regular latitude-longitude grid, each of which is characterized by thickness and seismic parameters (Vp, Vs, and density). We use surface wave dispersion and body wave traveltime data to drive the model. We find that when properly tuned (i.e., the Markov chains have had adequate time to fully sample the model space and the inversion has converged), the technique behaves as expected. The posterior model reflects the prior information at the edge of the model where there is little or no data to constrain adjustments, but the range of acceptable models is significantly reduced in data-rich regions, producing values of sediment thickness, crustal thickness, and upper mantle velocities consistent with expectations based on knowledge of the regional tectonic setting.

  9. Graph transformation method for calculating waiting times in Markov chains.

    PubMed

    Trygubenko, Semen A; Wales, David J

    2006-06-21

    We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then calculate averages over a given ensemble of paths for both additive and multiplicative properties in a nonstochastic and noniterative fashion. In particular, we can calculate the mean first-passage time between arbitrary groups of stationary points for discrete path sampling databases, and hence extract phenomenological rate constants. We present a number of examples to demonstrate the efficiency and robustness of this approach.

  10. Assessment of capabilities of multiangle imaging photo-polarimetry for atmospheric correction in presence of absorbing aerosols

    NASA Astrophysics Data System (ADS)

    Kalashnikova, O. V.; Garay, M. J.; Xu, F.; Seidel, F. C.; Diner, D. J.

    2015-12-01

    Satellite remote sensing of ocean color is a critical tool for assessing the productivity of marine ecosystems and monitoring changes resulting from climatic or environmental influences. Yet water-leaving radiance comprises less than 10% of the signal measured from space, making correction for absorption and scattering by the intervening atmosphere imperative. Traditional ocean color retrieval algorithms utilize a standard set of aerosol models and the assumption of negligible water-leaving radiance in the near-infrared. Modern improvements have been developed to handle absorbing aerosols such as urban particulates in coastal areas and transported desert dust over the open ocean, where ocean fertilization can impact biological productivity at the base of the marine food chain. Even so, imperfect knowledge of the absorbing aerosol optical properties or their height distribution results in well-documented sources of error. In the UV, the problem of UV-enhanced absorption and nonsphericity of certain aerosol types are amplified due to the increased Rayleigh and aerosol optical depth, especially at off-nadir view angles. Multi-angle spectro-polarimetric measurements have been advocated as an additional tool to better understand and retrieve the aerosol properties needed for atmospheric correction for ocean color retrievals. The central concern of the work to be described is the assessment of the effects of absorbing aerosol properties on water leaving radiance measurement uncertainty by neglecting UV-enhanced absorption of carbonaceous particles and by not accounting for dust nonsphericity. In addition, we evaluate the polarimetric sensitivity of absorbing aerosol properties in light of measurement uncertainties achievable for the next generation of multi-angle polarimetric imaging instruments, and demonstrate advantages and disadvantages of wavelength selection in the UV/VNIR range. The phase matrices for the spherical smoke particles were calculated using a standard

  11. Unfolding Neutron Spectrum with Markov Chain Monte Carlo at MIT Research Reactor with He-3 Neutral Current Detectors

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Leder, A.; Anderson, A. J.; Billard, J.

    2018-02-02

    The Ricochet experiment seeks to measure Coherent (neutral-current) Elastic Neutrino-Nucleus Scattering (CEνNS) using dark-matter-style detectors with sub-keV thresholds placed near a neutrino source, such as the MIT (research) Reactor (MITR), which operates at 5.5 MW generating approximately 2.2 × 1018 ν/second in its core. Currently, Ricochet is characterizing the backgrounds at MITR, the main component of which comes in the form of neutrons emitted from the core simultaneous with the neutrino signal. To characterize this background, we wrapped Bonner cylinders around a 32He thermal neutron detector, whose data was then unfolded via a Markov Chain Monte Carlo (MCMC) to produce a neutron energymore » spectrum across several orders of magnitude. We discuss the resulting spectrum and its implications for deploying Ricochet at the MITR site as well as the feasibility of reducing this background level via the addition of polyethylene shielding around the detector setup.« less

  12. Unfolding neutron spectrum with Markov Chain Monte Carlo at MIT research Reactor with He-3 Neutral Current Detectors

    NASA Astrophysics Data System (ADS)

    Leder, A.; Anderson, A. J.; Billard, J.; Figueroa-Feliciano, E.; Formaggio, J. A.; Hasselkus, C.; Newman, E.; Palladino, K.; Phuthi, M.; Winslow, L.; Zhang, L.

    2018-02-01

    The Ricochet experiment seeks to measure Coherent (neutral-current) Elastic Neutrino-Nucleus Scattering (CEνNS) using dark-matter-style detectors with sub-keV thresholds placed near a neutrino source, such as the MIT (research) Reactor (MITR), which operates at 5.5 MW generating approximately 2.2 × 1018 ν/second in its core. Currently, Ricochet is characterizing the backgrounds at MITR, the main component of which comes in the form of neutrons emitted from the core simultaneous with the neutrino signal. To characterize this background, we wrapped Bonner cylinders around a 32He thermal neutron detector, whose data was then unfolded via a Markov Chain Monte Carlo (MCMC) to produce a neutron energy spectrum across several orders of magnitude. We discuss the resulting spectrum and its implications for deploying Ricochet at the MITR site as well as the feasibility of reducing this background level via the addition of polyethylene shielding around the detector setup.

  13. Numerical estimation of structure constants in the three-dimensional Ising conformal field theory through Markov chain uv sampler

    NASA Astrophysics Data System (ADS)

    Herdeiro, Victor

    2017-09-01

    Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] introduced a numerical recipe, dubbed uv sampler, offering precise estimations of the conformal field theory (CFT) data of the planar two-dimensional (2D) critical Ising model. It made use of scale invariance emerging at the critical point in order to sample finite sublattice marginals of the infinite plane Gibbs measure of the model by producing holographic boundary distributions. The main ingredient of the Markov chain Monte Carlo sampler is the invariance under dilation. This paper presents a generalization to higher dimensions with the critical 3D Ising model. This leads to numerical estimations of a subset of the CFT data—scaling weights and structure constants—through fitting of measured correlation functions. The results are shown to agree with the recent most precise estimations from numerical bootstrap methods [Kos, Poland, Simmons-Duffin, and Vichi, J. High Energy Phys. 08 (2016) 036, 10.1007/JHEP08(2016)036].

  14. Markov chain decomposition of monthly rainfall into daily rainfall: Evaluation of climate change impact

    DOE PAGES

    Yoo, Chulsang; Lee, Jinwook; Ro, Yonghun

    2016-01-01

    This paper evaluates the effect of climate change on daily rainfall, especially on the mean number of wet days and the mean rainfall intensity. Assuming that the mechanism of daily rainfall occurrences follows the first-order Markov chain model, the possible changes in the transition probabilities are estimated by considering the climate change scenarios. Also, the change of the stationary probabilities of wet and dry day occurrences and finally the change in the number of wet days are derived for the comparison of current (1x CO 2) and 2x CO 2conditions. As a result of this study, the increase or decreasemore » in the mean number of wet days was found to be not enough to explain all of the change in monthly rainfall amounts, so rainfall intensity should also be modified. The application to the Seoul weather station in Korea shows that about 30% of the total change in monthly rainfall amount can be explained by the change in the number of wet days and the remaining 70% by the change in the rainfall intensity. That is, as an effect of climate change, the increase in the rainfall intensity could be more significant than the increase in the wet days and, thus, the risk of flood will be much highly increased.« less

  15. A novel framework to simulating non-stationary, non-linear, non-Normal hydrological time series using Markov Switching Autoregressive Models

    NASA Astrophysics Data System (ADS)

    Birkel, C.; Paroli, R.; Spezia, L.; Tetzlaff, D.; Soulsby, C.

    2012-12-01

    In this paper we present a novel model framework using the class of Markov Switching Autoregressive Models (MSARMs) to examine catchments as complex stochastic systems that exhibit non-stationary, non-linear and non-Normal rainfall-runoff and solute dynamics. Hereby, MSARMs are pairs of stochastic processes, one observed and one unobserved, or hidden. We model the unobserved process as a finite state Markov chain and assume that the observed process, given the hidden Markov chain, is conditionally autoregressive, which means that the current observation depends on its recent past (system memory). The model is fully embedded in a Bayesian analysis based on Markov Chain Monte Carlo (MCMC) algorithms for model selection and uncertainty assessment. Hereby, the autoregressive order and the dimension of the hidden Markov chain state-space are essentially self-selected. The hidden states of the Markov chain represent unobserved levels of variability in the observed process that may result from complex interactions of hydroclimatic variability on the one hand and catchment characteristics affecting water and solute storage on the other. To deal with non-stationarity, additional meteorological and hydrological time series along with a periodic component can be included in the MSARMs as covariates. This extension allows identification of potential underlying drivers of temporal rainfall-runoff and solute dynamics. We applied the MSAR model framework to streamflow and conservative tracer (deuterium and oxygen-18) time series from an intensively monitored 2.3 km2 experimental catchment in eastern Scotland. Statistical time series analysis, in the form of MSARMs, suggested that the streamflow and isotope tracer time series are not controlled by simple linear rules. MSARMs showed that the dependence of current observations on past inputs observed by transport models often in form of the long-tailing of travel time and residence time distributions can be efficiently explained by

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

    NASA Astrophysics Data System (ADS)

    Ye, Jing; Dang, Yaoguo; Li, Bingjun

    2018-01-01

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

  17. Predicting airborne particle deposition by a modified Markov chain model for fast estimation of potential contaminant spread

    NASA Astrophysics Data System (ADS)

    Mei, Xiong; Gong, Guangcai

    2018-07-01

    As potential carriers of hazardous pollutants, airborne particles may deposit onto surfaces due to gravitational settling. A modified Markov chain model to predict gravity induced particle dispersion and deposition is proposed in the paper. The gravity force is considered as a dominant weighting factor to adjust the State Transfer Matrix, which represents the probabilities of the change of particle spatial distributions between consecutive time steps within an enclosure. The model performance has been further validated by particle deposition in a ventilation chamber and a horizontal turbulent duct flow in pre-existing literatures. Both the proportion of deposited particles and the dimensionless deposition velocity are adopted to characterize the validation results. Comparisons between our simulated results and the experimental data from literatures show reasonable accuracy. Moreover, it is also found that the dimensionless deposition velocity can be remarkably influenced by particle size and stream-wise velocity in a typical horizontal flow. This study indicates that the proposed model can predict the gravity-dominated airborne particle deposition with reasonable accuracy and acceptable computing time.

  18. Inverse Modeling Using Markov Chain Monte Carlo Aided by Adaptive Stochastic Collocation Method with Transformation

    NASA Astrophysics Data System (ADS)

    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

  19. Markov Chain Model-Based Optimal Cluster Heads Selection for Wireless Sensor Networks

    PubMed Central

    Ahmed, Gulnaz; Zou, Jianhua; Zhao, Xi; Sadiq Fareed, Mian Muhammad

    2017-01-01

    The longer network lifetime of Wireless Sensor Networks (WSNs) is a goal which is directly related to energy consumption. This energy consumption issue becomes more challenging when the energy load is not properly distributed in the sensing area. The hierarchal clustering architecture is the best choice for these kind of issues. In this paper, we introduce a novel clustering protocol called Markov chain model-based optimal cluster heads (MOCHs) selection for WSNs. In our proposed model, we introduce a simple strategy for the optimal number of cluster heads selection to overcome the problem of uneven energy distribution in the network. The attractiveness of our model is that the BS controls the number of cluster heads while the cluster heads control the cluster members in each cluster in such a restricted manner that a uniform and even load is ensured in each cluster. We perform an extensive range of simulation using five quality measures, namely: the lifetime of the network, stable and unstable region in the lifetime of the network, throughput of the network, the number of cluster heads in the network, and the transmission time of the network to analyze the proposed model. We compare MOCHs against Sleep-awake Energy Efficient Distributed (SEED) clustering, Artificial Bee Colony (ABC), Zone Based Routing (ZBR), and Centralized Energy Efficient Clustering (CEEC) using the above-discussed quality metrics and found that the lifetime of the proposed model is almost 1095, 2630, 3599, and 2045 rounds (time steps) greater than SEED, ABC, ZBR, and CEEC, respectively. The obtained results demonstrate that the MOCHs is better than SEED, ABC, ZBR, and CEEC in terms of energy efficiency and the network throughput. PMID:28241492

  20. Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots.

    PubMed

    Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores

    2015-09-16

    One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot's pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area.

  1. Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots

    PubMed Central

    Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores

    2015-01-01

    One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot’s pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area. PMID:26389914

  2. Chronic escitalopram treatment attenuated the accelerated rapid eye movement sleep transitions after selective rapid eye movement sleep deprivation: a model-based analysis using Markov chains.

    PubMed

    Kostyalik, Diána; Vas, Szilvia; Kátai, Zita; Kitka, Tamás; Gyertyán, István; Bagdy, Gyorgy; Tóthfalusi, László

    2014-11-19

    Shortened rapid eye movement (REM) sleep latency and increased REM sleep amount are presumed biological markers of depression. These sleep alterations are also observable in several animal models of depression as well as during the rebound sleep after selective REM sleep deprivation (RD). Furthermore, REM sleep fragmentation is typically associated with stress procedures and anxiety. The selective serotonin reuptake inhibitor (SSRI) antidepressants reduce REM sleep time and increase REM latency after acute dosing in normal condition and even during REM rebound following RD. However, their therapeutic outcome evolves only after weeks of treatment, and the effects of chronic treatment in REM-deprived animals have not been studied yet. Chronic escitalopram- (10 mg/kg/day, osmotic minipump for 24 days) or vehicle-treated rats were subjected to a 3-day-long RD on day 21 using the flower pot procedure or kept in home cage. On day 24, fronto-parietal electroencephalogram, electromyogram and motility were recorded in the first 2 h of the passive phase. The observed sleep patterns were characterized applying standard sleep metrics, by modelling the transitions between sleep phases using Markov chains and by spectral analysis. Based on Markov chain analysis, chronic escitalopram treatment attenuated the REM sleep fragmentation [accelerated transition rates between REM and non-REM (NREM) stages, decreased REM sleep residence time between two transitions] during the rebound sleep. Additionally, the antidepressant avoided the frequent awakenings during the first 30 min of recovery period. The spectral analysis showed that the SSRI prevented the RD-caused elevation in theta (5-9 Hz) power during slow-wave sleep. Conversely, based on the aggregate sleep metrics, escitalopram had only moderate effects and it did not significantly attenuate the REM rebound after RD. In conclusion, chronic SSRI treatment is capable of reducing several effects on sleep which might be the consequence

  3. A Markov chain analysis of the movements of juvenile salmonids, including sockeye salmon, in the forebay of McNary Dam, Washington and Oregon, 2006-09

    USGS Publications Warehouse

    Adams, Noah S.; Hatton, Tyson W.

    2012-01-01

    Passage and survival data were collected at McNary Dam between 2006 and 2009. These data have provided critical information for resource managers to implement structural and operational changes designed to improve the survival of juvenile salmonids as they migrate past the dam. Much of the valuable information collected at McNary Dam was in the form of three-dimensional (hereafter referred to as 3-D) tracks of fish movements in the forebay. These data depicted the behavior of multiple species (in three dimensions) during different diel periods, spill conditions, powerhouse operations, and testing of the surface bypass structures (temporary spillway weirs; TSWs). One of the challenges in reporting 3-D results is presenting the information in a manner that allows interested parties to summarize the behavior of many fish over many different conditions across multiple years. To accomplish this, we used a Markov chain analysis to characterize fish movement patterns in the forebay of McNary Dam. The Markov chain analysis allowed us to numerically summarize the behavior of fish in the forebay. This report is the second report published in 2012 that uses this analytical method. The first report included only fish released as part of the annual studies conducted at McNary Dam. This second report includes sockeye salmon that were released as part of studies conducted by the Chelan and Grant County Public Utility Districts at mid-Columbia River dams. The studies conducted in the mid-Columbia used the same transmitters as were used for McNary Dam studies, but transmitter pulse width was different between studies. Additionally, no passive integrated transponder tags were implanted in sockeye salmon. Differences in transmitter pulse width resulted in lower detection probabilities for sockeye salmon at McNary Dam. The absence of passive integrated transponder tags prevented us from determining if fish passed the powerhouse through the juvenile bypass system (JBS) or turbines. To

  4. Markov chain-incorporated and synthetic data-supported conditional artificial neural network models for forecasting monthly precipitation in arid regions

    NASA Astrophysics Data System (ADS)

    Aksoy, Hafzullah; Dahamsheh, Ahmad

    2018-07-01

    For forecasting monthly precipitation in an arid region, the feed forward back-propagation, radial basis function and generalized regression artificial neural networks (ANNs) are used in this study. The ANN models are improved after incorporation of a Markov chain-based algorithm (MC-ANNs) with which the percentage of dry months is forecasted perfectly, thus generation of any non-physical negative precipitation is eliminated. Due to the fact that recorded precipitation time series are usually shorter than the length needed for a proper calibration of ANN models, synthetic monthly precipitation data are generated by Thomas-Fiering model to further improve the performance of forecasting. For case studies from Jordan, it is seen that only a slightly better performance is achieved with the use of MC and synthetic data. A conditional statement is, therefore, established and imbedded into the ANN models after the incorporation of MC and support of synthetic data, to substantially improve the ability of the models for forecasting monthly precipitation in arid regions.

  5. Crossing over...Markov meets Mendel.

    PubMed

    Mneimneh, Saad

    2012-01-01

    Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the

  6. Crossing Over…Markov Meets Mendel

    PubMed Central

    Mneimneh, Saad

    2012-01-01

    Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage—one of the first efforts towards a computational approach to biology—relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the

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

    PubMed

    Bulashevska, Alla; Eils, Roland

    2006-06-14

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

  8. Markov Chain Monte Carlo Joint Analysis of Chandra X-Ray Imaging Spectroscopy and Sunyaev-Zel'dovich Effect Data

    NASA Technical Reports Server (NTRS)

    Bonamente, Massimillano; Joy, Marshall K.; Carlstrom, John E.; Reese, Erik D.; LaRoque, Samuel J.

    2004-01-01

    X-ray and Sunyaev-Zel'dovich effect data can be combined to determine the distance to galaxy clusters. High-resolution X-ray data are now available from Chandra, which provides both spatial and spectral information, and Sunyaev-Zel'dovich effect data were obtained from the BIMA and Owens Valley Radio Observatory (OVRO) arrays. We introduce a Markov Chain Monte Carlo procedure for the joint analysis of X-ray and Sunyaev- Zel'dovich effect data. The advantages of this method are the high computational efficiency and the ability to measure simultaneously the probability distribution of all parameters of interest, such as the spatial and spectral properties of the cluster gas and also for derivative quantities such as the distance to the cluster. We demonstrate this technique by applying it to the Chandra X-ray data and the OVRO radio data for the galaxy cluster A611. Comparisons with traditional likelihood ratio methods reveal the robustness of the method. This method will be used in follow-up paper to determine the distances to a large sample of galaxy cluster.

  9. Numerical simulation of seasonality in the distribution and fate of pyrene in multimedia aquatic environments with Markov chains.

    PubMed

    Sun, Caiyun; Xu, Liang; Sun, Dazhi; Chen, Libo; Zou, Jiying; Zhang, Zhenxing

    2017-08-29

    This case study investigated the distribution and fate of organic pollutants in aquatic environments based on laboratory experiments and modeling. Pyrene (Pyr) is a hydrocarbon pollutant with adverse effects on aquatic ecosystems and human health, and was thus selected for this case study. The movement of Pyr was primarily influenced by its sorption from water onto sediment, and its desorption from sediment into water. Its elimination was mainly via biodegradation by microorganisms in sediment and by volatilization from water into air. The transport and elimination rates for Pyr were considerably influenced by temperature and moisture. Results of modeling with Markov chains revealed that the elimination of Pyr from water/sediment systems was the most rapid under wet conditions. Under average conditions, a Pyr concentration of 100 μg/L of in water in such a system declined to a negligible level over 250 h. Under wet conditions, this decrease occurred over 120 h. Finally, under dry conditions, it took 550 h to achieve the same degree of elimination.

  10. Self-Organizing Hidden Markov Model Map (SOHMMM).

    PubMed

    Ferles, Christos; Stafylopatis, Andreas

    2013-12-01

    A hybrid approach combining the Self-Organizing Map (SOM) and the Hidden Markov Model (HMM) is presented. The Self-Organizing Hidden Markov Model Map (SOHMMM) establishes a cross-section between the theoretic foundations and algorithmic realizations of its constituents. The respective architectures and learning methodologies are fused in an attempt to meet the increasing requirements imposed by the properties of deoxyribonucleic acid (DNA), ribonucleic acid (RNA), and protein chain molecules. The fusion and synergy of the SOM unsupervised training and the HMM dynamic programming algorithms bring forth a novel on-line gradient descent unsupervised learning algorithm, which is fully integrated into the SOHMMM. Since the SOHMMM carries out probabilistic sequence analysis with little or no prior knowledge, it can have a variety of applications in clustering, dimensionality reduction and visualization of large-scale sequence spaces, and also, in sequence discrimination, search and classification. Two series of experiments based on artificial sequence data and splice junction gene sequences demonstrate the SOHMMM's characteristics and capabilities. Copyright © 2013 Elsevier Ltd. All rights reserved.

  11. Markov chain formalism for generalized radiative transfer in a plane-parallel medium, accounting for polarization

    NASA Astrophysics Data System (ADS)

    Xu, Feng; Davis, Anthony B.; Diner, David J.

    2016-11-01

    A Markov chain formalism is developed for computing the transport of polarized radiation according to Generalized Radiative Transfer (GRT) theory, which was developed recently to account for unresolved random fluctuations of scattering particle density and can also be applied to unresolved spectral variability of gaseous absorption as an improvement over the standard correlated-k method. Using Gamma distribution to describe the probability density function of the extinction or absorption coefficient, a shape parameter a that quantifies the variability is introduced, defined as the mean extinction or absorption coefficient squared divided by its variance. It controls the decay rate of a power-law transmission that replaces the usual exponential Beer-Lambert-Bouguer law. Exponential transmission, hence classic RT, is recovered when a→∞. The new approach is verified to high accuracy against numerical benchmark results obtained with a custom Monte Carlo method. For a<∞, angular reciprocity is violated to a degree that increases with the spatial variability, as observed for finite portions of real-world cloudy scenes. While the degree of linear polarization in liquid water cloudbows, supernumerary bows, and glories is affected by spatial heterogeneity, the positions in scattering angle of these features are relatively unchanged. As a result, a single-scattering model based on the assumption of subpixel homogeneity can still be used to derive droplet size distributions from polarimetric measurements of extended stratocumulus clouds.

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

    NASA Astrophysics Data System (ADS)

    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.

  13. Determining coding CpG islands by identifying regions significant for pattern statistics on Markov chains.

    PubMed

    Singer, Meromit; Engström, Alexander; Schönhuth, Alexander; Pachter, Lior

    2011-09-23

    Recent experimental and computational work confirms that CpGs can be unmethylated inside coding exons, thereby showing that codons may be subjected to both genomic and epigenomic constraint. It is therefore of interest to identify coding CpG islands (CCGIs) that are regions inside exons enriched for CpGs. The difficulty in identifying such islands is that coding exons exhibit sequence biases determined by codon usage and constraints that must be taken into account. We present a method for finding CCGIs that showcases a novel approach we have developed for identifying regions of interest that are significant (with respect to a Markov chain) for the counts of any pattern. Our method begins with the exact computation of tail probabilities for the number of CpGs in all regions contained in coding exons, and then applies a greedy algorithm for selecting islands from among the regions. We show that the greedy algorithm provably optimizes a biologically motivated criterion for selecting islands while controlling the false discovery rate. We applied this approach to the human genome (hg18) and annotated CpG islands in coding exons. The statistical criterion we apply to evaluating islands reduces the number of false positives in existing annotations, while our approach to defining islands reveals significant numbers of undiscovered CCGIs in coding exons. Many of these appear to be examples of functional epigenetic specialization in coding exons.

  14. Efficient Learning of Continuous-Time Hidden Markov Models for Disease Progression

    PubMed Central

    Liu, Yu-Ying; Li, Shuang; Li, Fuxin; Song, Le; Rehg, James M.

    2016-01-01

    The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer’s disease dataset. PMID:27019571

  15. Application of spatial Markov chains to the analysis of the temporal-spatial evolution of soil erosion.

    PubMed

    Liu, Ruimin; Men, Cong; Wang, Xiujuan; Xu, Fei; Yu, Wenwen

    Soil and water conservation in the Three Gorges Reservoir Area of China is important, and soil erosion is a significant issue. In the present study, spatial Markov chains were applied to explore the impacts of the regional context on soil erosion in the Xiangxi River watershed, and Thematic Mapper remote sensing data from 1999 and 2007 were employed. The results indicated that the observed changes in soil erosion were closely related to the soil erosion levels of the surrounding areas. When neighboring regions were not considered, the probability that moderate erosion transformed into slight and severe erosion was 0.8330 and 0.0049, respectively. However, when neighboring regions that displayed intensive erosion were considered, the probabilities were 0.2454 and 0.7513, respectively. Moreover, the different levels of soil erosion in neighboring regions played different roles in soil erosion. If the erosion levels in the neighboring region were lower, the probability of a high erosion class transferring to a lower level was relatively high. In contrast, if erosion levels in the neighboring region were higher, the probability was lower. The results of the present study provide important information for the planning and implementation of soil conservation measures in the study area.

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

    PubMed Central

    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

  17. On Markov parameters in system identification

    NASA Technical Reports Server (NTRS)

    Phan, Minh; Juang, Jer-Nan; Longman, Richard W.

    1991-01-01

    A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.

  18. Significance testing of clinical data using virus dynamics models with a Markov chain Monte Carlo method: application to emergence of lamivudine-resistant hepatitis B virus.

    PubMed Central

    Burroughs, N J; Pillay, D; Mutimer, D

    1999-01-01

    Bayesian analysis using a virus dynamics model is demonstrated to facilitate hypothesis testing of patterns in clinical time-series. Our Markov chain Monte Carlo implementation demonstrates that the viraemia time-series observed in two sets of hepatitis B patients on antiviral (lamivudine) therapy, chronic carriers and liver transplant patients, are significantly different, overcoming clinical trial design differences that question the validity of non-parametric tests. We show that lamivudine-resistant mutants grow faster in transplant patients than in chronic carriers, which probably explains the differences in emergence times and failure rates between these two sets of patients. Incorporation of dynamic models into Bayesian parameter analysis is of general applicability in medical statistics. PMID:10643081

  19. Nonlinear Markov Control Processes and Games

    DTIC Science & Technology

    2012-11-15

    the analysis of a new class of stochastic games , nonlinear Markov games , as they arise as a ( competitive ) controlled version of nonlinear Markov... competitive interests) a nonlinear Markov game that we are investigating. I 0. :::tUt::JJt:.l.. I I t:t11VI;:, nonlinear Markov game , nonlinear Markov...corresponding stochastic game Γ+(T, h). In a slightly different setting one can assume that changes in a competitive control process occur as a

  20. The use of simple reparameterizations to improve the efficiency of Markov chain Monte Carlo estimation for multilevel models with applications to discrete time survival models.

    PubMed

    Browne, William J; Steele, Fiona; Golalizadeh, Mousa; Green, Martin J

    2009-06-01

    We consider the application of Markov chain Monte Carlo (MCMC) estimation methods to random-effects models and in particular the family of discrete time survival models. Survival models can be used in many situations in the medical and social sciences and we illustrate their use through two examples that differ in terms of both substantive area and data structure. A multilevel discrete time survival analysis involves expanding the data set so that the model can be cast as a standard multilevel binary response model. For such models it has been shown that MCMC methods have advantages in terms of reducing estimate bias. However, the data expansion results in very large data sets for which MCMC estimation is often slow and can produce chains that exhibit poor mixing. Any way of improving the mixing will result in both speeding up the methods and more confidence in the estimates that are produced. The MCMC methodological literature is full of alternative algorithms designed to improve mixing of chains and we describe three reparameterization techniques that are easy to implement in available software. We consider two examples of multilevel survival analysis: incidence of mastitis in dairy cattle and contraceptive use dynamics in Indonesia. For each application we show where the reparameterization techniques can be used and assess their performance.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lu, Dan; Ricciuto, Daniel M.; Walker, Anthony P.

    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 inmore » 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. Here, 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.« less

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

    DOE PAGES

    Lu, Dan; Ricciuto, Daniel M.; Walker, Anthony P.; ...

    2017-09-27

    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 inmore » 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. Here, 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.« less

  3. Characterization of environmental quality of forest fragments changes in Jundiaí-Mirim river basin-Brazil using the Markov Chain model

    NASA Astrophysics Data System (ADS)

    Hasimoto Fengler, Felipe; Leite de Moraes, Jener Fernando; Irio Ribeiro, Admilson; Peche Filho, Afonso; Araujo de Medeiros, Gerson; Baldin Damame, Desirée; Márcia Longo, Regina

    2015-04-01

    In Brazil is common practice the concurrency of large urban centers water catchment in distant sites. There's no policy to preserve strategic springs in the urban territory. Thus, rural areas, located in the surrounds of municipals, usually provide water and others environment services to the population that reside on cities. The Jundiaí-Mirim river basin, located in the most urbanized state in Brazil, São Paulo, composes an interesting example of this situation. It is located in a rural area near large urban centers, with large industrial parks, near the capital of state. As result of expansion of the cities on its surrounds their lands have had a historic of monetary valorization, making its territories attractive to the housing market. Consequently, the region has an intense process of urbanization that resulted in an increasing environmental disturbance in the areas of natural vegetation. In the other hand, the watershed is the principal water supplier of Jundiaí city, and houses forest remaining of an important Biome in Brazil, the Atlantic Rain Forest. Given the need to preserve its water production capacity and the forest remnants there, this study modeled the environmental quality of forest fragments through indicators of disturbance and evaluated the changes that occur between 1972 and 2013 using the Markov Chain model. The environment quality was determined by nine indicators of environmental disturbance (distance of urban areas, roads, edge land use, size, distance of others forest fragments, land capacity of use, watershed forest cover, number of forest fragments in the watersheds, shape of the forest fragment), obtained by techniques of Geoprocessing, and integrated by Multicriteria Analysis. The Markov Chain model showed a constant tendency of deteriorating in natural vegetation environmental quality, attributed to the intense process of occupation of the river basin. The results showed a historical trend of transformation in forest fragments with

  4. Using hidden Markov models to align multiple sequences.

    PubMed

    Mount, David W

    2009-07-01

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

  5. Approximate Bayesian Computation Using Markov Chain Monte Carlo Simulation: Theory, Concepts, and Applications

    NASA Astrophysics Data System (ADS)

    Sadegh, M.; Vrugt, J. A.

    2013-12-01

    The ever increasing pace of computational power, along with continued advances in measurement technologies and improvements in process understanding has stimulated the development of increasingly complex hydrologic models that simulate soil moisture flow, groundwater recharge, surface runoff, root water uptake, and river discharge at increasingly finer spatial and temporal scales. Reconciling these system models with field and remote sensing data is a difficult task, particularly because average measures of model/data similarity inherently lack the power to provide a meaningful comparative evaluation of the consistency in model form and function. The very construction of the likelihood function - as a summary variable of the (usually averaged) properties of the error residuals - dilutes and mixes the available information into an index having little remaining correspondence to specific behaviors of the system (Gupta et al., 2008). The quest for a more powerful method for model evaluation has inspired Vrugt and Sadegh [2013] to introduce "likelihood-free" inference as vehicle for diagnostic model evaluation. This class of methods is also referred to as Approximate Bayesian Computation (ABC) and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics rooted in hydrologic theory that together have a much stronger and compelling diagnostic power than some aggregated measure of the size of the error residuals. Here, we will introduce an efficient ABC sampling method that is orders of magnitude faster in exploring the posterior parameter distribution than commonly used rejection and Population Monte Carlo (PMC) samplers. Our methodology uses Markov Chain Monte Carlo simulation with DREAM, and takes advantage of a simple computational trick to resolve discontinuity problems with the application of set-theoretic summary statistics. We will also demonstrate a set of summary statistics that are rather insensitive to

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

    PubMed

    Raffa, Jesse D; Dubin, Joel A

    2015-09-01

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

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

    PubMed

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

    2009-12-01

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

  8. [Succession caused by beaver (Castor fiber L.) life activity: I. What is learnt from the calibration of a simple Markov model].

    PubMed

    Logofet, D O; Evstigneev, O I; Aleĭnikov, A A; Morozova, A O

    2014-01-01

    A homogeneous Markov chain of three aggregated states "pond--swamp--wood" is proposed as a model of cyclic zoogenic successions caused by beaver (Castor fiber L.) life activity in a forest biogeocoenosis. To calibrate the chain transition matrix, the data have appeared sufficient that were gained from field studies undertaken in "Bryanskii Les" Reserve in the years of 2002-2008. Major outcomes of the calibrated model ensue from the formulae of finite homogeneous Markov chain theory: the stationary probability distribution of states, thematrix (T) of mean first passage times, and the mean durations (M(j)) of succession stages. The former illustrates the distribution of relative areas under succession stages if the current trends and transition rates of succession are conserved in the long-term--it has appeared close to the observed distribution. Matrix T provides for quantitative characteristics of the cyclic process, specifying the ranges the experts proposed for the duration of stages in the conceptual scheme of succession. The calculated values of M(j) detect potential discrepancies between empirical data, the expert knowledge that summarizes the data, and the postulates accepted in the mathematical model. The calculated M2 value falls outside the expert range, which gives a reason to doubt the validity of expert estimation proposed, the aggregation mode chosen for chain states, or/and the accuracy-of data available, i.e., to draw certain "lessons" from partially successful calibration. Refusal to postulate the time homogeneity or the Markov property of the chain is also discussed among possible ways to improve the model.

  9. A Test of the Need Hierarchy Concept by a Markov Model of Change in Need Strength.

    ERIC Educational Resources Information Center

    Rauschenberger, John; And Others

    1980-01-01

    In this study of 547 high school graduates, Alderfer's and Maslow's need hierarchy theories were expressed in Markov chain form and were subjected to empirical test. Both models were disconfirmed. Corroborative multiwave correlational analysis also failed to support the need hierarchy concept. (Author/IRT)

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

    PubMed

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

    2015-01-01

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

  11. Caliber Corrected Markov Modeling (C2M2): Correcting Equilibrium Markov Models.

    PubMed

    Dixit, Purushottam D; Dill, Ken A

    2018-02-13

    Rate processes are often modeled using Markov State Models (MSMs). Suppose you know a prior MSM and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them while also giving the wrong overall folding rate when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (C 2 M 2 ), an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory-based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.

  12. Population Synthesis of Radio and Y-ray Normal, Isolated Pulsars Using Markov Chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    Billman, Caleb; Gonthier, P. L.; Harding, A. K.

    2013-04-01

    We present preliminary results of a population statistics study of normal pulsars (NP) from the Galactic disk using Markov Chain Monte Carlo techniques optimized according to two different methods. The first method compares the detected and simulated cumulative distributions of series of pulsar characteristics, varying the model parameters to maximize the overall agreement. The advantage of this method is that the distributions do not have to be binned. The other method varies the model parameters to maximize the log of the maximum likelihood obtained from the comparisons of four-two dimensional distributions of radio and γ-ray pulsar characteristics. The advantage of this method is that it provides a confidence region of the model parameter space. The computer code simulates neutron stars at birth using Monte Carlo procedures and evolves them to the present assuming initial spatial, kick velocity, magnetic field, and period distributions. Pulsars are spun down to the present and given radio and γ-ray emission characteristics, implementing an empirical γ-ray luminosity model. A comparison group of radio NPs detected in ten-radio surveys is used to normalize the simulation, adjusting the model radio luminosity to match a birth rate. We include the Fermi pulsars in the forthcoming second pulsar catalog. We present preliminary results comparing the simulated and detected distributions of radio and γ-ray NPs along with a confidence region in the parameter space of the assumed models. We express our gratitude for the generous support of the National Science Foundation (REU and RUI), Fermi Guest Investigator Program and the NASA Astrophysics Theory and Fundamental Program.

  13. Ascertainment correction for Markov chain Monte Carlo segregation and linkage analysis of a quantitative trait.

    PubMed

    Ma, Jianzhong; Amos, Christopher I; Warwick Daw, E

    2007-09-01

    Although extended pedigrees are often sampled through probands with extreme levels of a quantitative trait, Markov chain Monte Carlo (MCMC) methods for segregation and linkage analysis have not been able to perform ascertainment corrections. Further, the extent to which ascertainment of pedigrees leads to biases in the estimation of segregation and linkage parameters has not been previously studied for MCMC procedures. In this paper, we studied these issues with a Bayesian MCMC approach for joint segregation and linkage analysis, as implemented in the package Loki. We first simulated pedigrees ascertained through individuals with extreme values of a quantitative trait in spirit of the sequential sampling theory of Cannings and Thompson [Cannings and Thompson [1977] Clin. Genet. 12:208-212]. Using our simulated data, we detected no bias in estimates of the trait locus location. However, in addition to allele frequencies, when the ascertainment threshold was higher than or close to the true value of the highest genotypic mean, bias was also found in the estimation of this parameter. When there were multiple trait loci, this bias destroyed the additivity of the effects of the trait loci, and caused biases in the estimation all genotypic means when a purely additive model was used for analyzing the data. To account for pedigree ascertainment with sequential sampling, we developed a Bayesian ascertainment approach and implemented Metropolis-Hastings updates in the MCMC samplers used in Loki. Ascertainment correction greatly reduced biases in parameter estimates. Our method is designed for multiple, but a fixed number of trait loci. Copyright (c) 2007 Wiley-Liss, Inc.

  14. Simulation of land use change and effect on potential deforestation using Markov Chain - Cellular Automata

    NASA Astrophysics Data System (ADS)

    Mujiono, Indra, T. L.; Harmantyo, D.; Rukmana, I. P.; Nadia, Z.

    2017-07-01

    The purpose of this study was to simulate land use change in 1996-2016 and its prediction in 2035 as well as its potential to deforestation. Both of these purposes were obtained through modeling analysis using Markov Chain Cellular Automata. This modeling method was considered important for understanding the causes and impacts. Based on the analysis, the land use change between 1996 to 2007 has caused forest loss (the region and non-region) covering an area of 62,012 ha. While in the period of 2007 to 2016, the change has lead to the east side of the slope grade of 0-15 percent and an altitude between 500-1000 meters above sea level. In this period, plantation area has increased by 50,822 ha, while the forest area has reduced from 80,038 ha. In a period of 20 years, North Bengkulu Regency has lost the forest area of 80,038 ha. The amount of intervention against forest suggested the potential for deforestation in this area. Simulation of land use change in 2035 did not indicate significant deforestation due to the limited land on physical factors such as slope and elevation. However, it should be noted that, in 2035, the area of conservation forest was reduced by 16,793 ha (29 %), while the areas of protected and production forest were reduced by 4,933 ha (19 %) and 2,114 ha (3 %), respectively. Land use change is a serious threat of deforestation, especially in forest areas in North Bengkulu Regency, where any decline in forest area means the addition of plantation area.

  15. SU-E-J-115: Using Markov Chain Modeling to Elucidate Patterns in Breast Cancer Metastasis Over Time and Space

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Comen, E; Mason, J; Kuhn, P

    2014-06-01

    Purpose: Traditionally, breast cancer metastasis is described as a process wherein cancer cells spread from the breast to multiple organ systems via hematogenous and lymphatic routes. Mapping organ specific patterns of cancer spread over time is essential to understanding metastatic progression. In order to better predict sites of metastases, here we demonstrate modeling of the patterned migration of metastasis. Methods: We reviewed the clinical history of 453 breast cancer patients from Memorial Sloan Kettering Cancer Center who were non-metastatic at diagnosis but developed metastasis over time. We used the variables of organ site of metastases as well as time tomore » create a Markov chain model of metastasis. We illustrate the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Results: Based on the clinical histories of 453 breast cancer patients who developed metastasis, we have learned (i) how to create the Markov transition matrix governing the probabilities of cancer progression from site to site; (ii) how to create a systemic network diagram governing disease progression modeled as a random walk on a directed graph; (iii) how to classify metastatic sites as ‘sponges’ that tend to only receive cancer cells or ‘spreaders’ that receive and release them; (iv) how to model the time-scales of disease progression as a Weibull probability distribution function; (v) how to perform Monte Carlo simulations of disease progression; and (vi) how to interpret disease progression as an entropy-increasing stochastic process. Conclusion: Based on our modeling, metastatic spread may follow predictable pathways. Mapping metastasis not simply by organ site, but by function as either a ‘spreader’ or ‘sponge’ fundamentally reframes our understanding of metastatic processes. This model serves as a novel platform from which we may integrate the evolving genomic landscape that drives cancer

  16. Inferring soil salinity in a drip irrigation system from multi-configuration EMI measurements using adaptive Markov chain Monte Carlo

    NASA Astrophysics Data System (ADS)

    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.

  17. A Hybrid Secure Scheme for Wireless Sensor Networks against Timing Attacks Using Continuous-Time Markov Chain and Queueing Model.

    PubMed

    Meng, Tianhui; Li, Xiaofan; Zhang, Sha; Zhao, Yubin

    2016-09-28

    Wireless sensor networks (WSNs) have recently gained popularity for a wide spectrum of applications. Monitoring tasks can be performed in various environments. This may be beneficial in many scenarios, but it certainly exhibits new challenges in terms of security due to increased data transmission over the wireless channel with potentially unknown threats. Among possible security issues are timing attacks, which are not prevented by traditional cryptographic security. Moreover, the limited energy and memory resources prohibit the use of complex security mechanisms in such systems. Therefore, balancing between security and the associated energy consumption becomes a crucial challenge. This paper proposes a secure scheme for WSNs while maintaining the requirement of the security-performance tradeoff. In order to proceed to a quantitative treatment of this problem, a hybrid continuous-time Markov chain (CTMC) and queueing model are put forward, and the tradeoff analysis of the security and performance attributes is carried out. By extending and transforming this model, the mean time to security attributes failure is evaluated. Through tradeoff analysis, we show that our scheme can enhance the security of WSNs, and the optimal rekeying rate of the performance and security tradeoff can be obtained.

  18. A Hybrid Secure Scheme for Wireless Sensor Networks against Timing Attacks Using Continuous-Time Markov Chain and Queueing Model

    PubMed Central

    Meng, Tianhui; Li, Xiaofan; Zhang, Sha; Zhao, Yubin

    2016-01-01

    Wireless sensor networks (WSNs) have recently gained popularity for a wide spectrum of applications. Monitoring tasks can be performed in various environments. This may be beneficial in many scenarios, but it certainly exhibits new challenges in terms of security due to increased data transmission over the wireless channel with potentially unknown threats. Among possible security issues are timing attacks, which are not prevented by traditional cryptographic security. Moreover, the limited energy and memory resources prohibit the use of complex security mechanisms in such systems. Therefore, balancing between security and the associated energy consumption becomes a crucial challenge. This paper proposes a secure scheme for WSNs while maintaining the requirement of the security-performance tradeoff. In order to proceed to a quantitative treatment of this problem, a hybrid continuous-time Markov chain (CTMC) and queueing model are put forward, and the tradeoff analysis of the security and performance attributes is carried out. By extending and transforming this model, the mean time to security attributes failure is evaluated. Through tradeoff analysis, we show that our scheme can enhance the security of WSNs, and the optimal rekeying rate of the performance and security tradeoff can be obtained. PMID:27690042

  19. Application and Evaluation of a Snowmelt Runoff Model in the Tamor River Basin, Eastern Himalaya Using a Markov Chain Monte Carlo (MCMC) Data Assimilation Approach

    NASA Technical Reports Server (NTRS)

    Panday, Prajjwal K.; Williams, Christopher A.; Frey, Karen E.; Brown, Molly E.

    2013-01-01

    Previous studies have drawn attention to substantial hydrological changes taking place in mountainous watersheds where hydrology is dominated by cryospheric processes. Modelling is an important tool for understanding these changes but is particularly challenging in mountainous terrain owing to scarcity of ground observations and uncertainty of model parameters across space and time. This study utilizes a Markov Chain Monte Carlo data assimilation approach to examine and evaluate the performance of a conceptual, degree-day snowmelt runoff model applied in the Tamor River basin in the eastern Nepalese Himalaya. The snowmelt runoff model is calibrated using daily streamflow from 2002 to 2006 with fairly high accuracy (average Nash-Sutcliffe metric approx. 0.84, annual volume bias <3%). The Markov Chain Monte Carlo approach constrains the parameters to which the model is most sensitive (e.g. lapse rate and recession coefficient) and maximizes model fit and performance. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall compared with simulations using observed station precipitation. The average snowmelt contribution to total runoff in the Tamor River basin for the 2002-2006 period is estimated to be 29.7+/-2.9% (which includes 4.2+/-0.9% from snowfall that promptly melts), whereas 70.3+/-2.6% is attributed to contributions from rainfall. On average, the elevation zone in the 4000-5500m range contributes the most to basin runoff, averaging 56.9+/-3.6% of all snowmelt input and 28.9+/-1.1% of all rainfall input to runoff. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall versus snowmelt compared with simulations using observed station precipitation. Model experiments indicate that the hydrograph itself does not constrain estimates of snowmelt versus rainfall contributions to total outflow but that this derives from the degree

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

    PubMed

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

    2012-04-01

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

  1. Multiple-Event Seismic Location Using the Markov-Chain Monte Carlo Technique

    NASA Astrophysics Data System (ADS)

    Myers, S. C.; Johannesson, G.; Hanley, W.

    2005-12-01

    We develop a new multiple-event location algorithm (MCMCloc) that utilizes the Markov-Chain Monte Carlo (MCMC) method. Unlike most inverse methods, the MCMC approach produces a suite of solutions, each of which is consistent with observations and prior estimates of data and model uncertainties. Model parameters in MCMCloc consist of event hypocenters, and travel-time predictions. Data are arrival time measurements and phase assignments. Posteriori estimates of event locations, path corrections, pick errors, and phase assignments are made through analysis of the posteriori suite of acceptable solutions. Prior uncertainty estimates include correlations between travel-time predictions, correlations between measurement errors, the probability of misidentifying one phase for another, and the probability of spurious data. Inclusion of prior constraints on location accuracy allows direct utilization of ground-truth locations or well-constrained location parameters (e.g. from InSAR) that aid in the accuracy of the solution. Implementation of a correlation structure for travel-time predictions allows MCMCloc to operate over arbitrarily large geographic areas. Transition in behavior between a multiple-event locator for tightly clustered events and a single-event locator for solitary events is controlled by the spatial correlation of travel-time predictions. We test the MCMC locator on a regional data set of Nevada Test Site nuclear explosions. Event locations and origin times are known for these events, allowing us to test the features of MCMCloc using a high-quality ground truth data set. Preliminary tests suggest that MCMCloc provides excellent relative locations, often outperforming traditional multiple-event location algorithms, and excellent absolute locations are attained when constraints from one or more ground truth event are included. When phase assignments are switched, we find that MCMCloc properly corrects the error when predicted arrival times are separated by

  2. Equivalence of Szegedy's and coined quantum walks

    NASA Astrophysics Data System (ADS)

    Wong, Thomas G.

    2017-09-01

    Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To search, one can simply quantize a Markov chain with absorbing vertices. Recently, Santos proposed two alternative search algorithms that instead utilize the sign-flip oracle in Grover's algorithm rather than absorbing vertices. In this paper, we show that these two algorithms are exactly equivalent to two algorithms involving coined quantum walks, which are walks on the vertices of the original graph with an internal degree of freedom. The first scheme is equivalent to a coined quantum walk with one walk step per query of Grover's oracle, and the second is equivalent to a coined quantum walk with two walk steps per query of Grover's oracle. These equivalences lie outside the previously known equivalence of Szegedy's quantum walk with absorbing vertices and the coined quantum walk with the negative identity operator as the coin for marked vertices, whose precise relationships we also investigate.

  3. Combined state and parameter identification of nonlinear structural dynamical systems based on Rao-Blackwellization and Markov chain Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Abhinav, S.; Manohar, C. S.

    2018-03-01

    The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blackwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam-moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion.

  4. Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes

    PubMed Central

    Li, Degui; Li, Runze

    2016-01-01

    In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general Harris recurrent Markov process which includes both the stationary (positive recurrent) and nonstationary (null recurrent) cases. Under some mild conditions, we establish the asymptotic theory for the proposed local polynomial CQR estimator of the mean regression function, and show that the convergence rate for the estimator in nonstationary case is slower than that in stationary case. Furthermore, a weighted type local polynomial CQR estimator is provided to improve the estimation efficiency, and a data-driven bandwidth selection is introduced to choose the optimal bandwidth involved in the nonparametric estimators. Finally, we give some numerical studies to examine the finite sample performance of the developed methodology and theory. PMID:27667894

  5. Harnessing graphical structure in Markov chain Monte Carlo learning

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Stolorz, P.E.; Chew P.C.

    1996-12-31

    The Monte Carlo method is recognized as a useful tool in learning and probabilistic inference methods common to many datamining problems. Generalized Hidden Markov Models and Bayes nets are especially popular applications. However, the presence of multiple modes in many relevant integrands and summands often renders the method slow and cumbersome. Recent mean field alternatives designed to speed things up have been inspired by experience gleaned from physics. The current work adopts an approach very similar to this in spirit, but focusses instead upon dynamic programming notions as a basis for producing systematic Monte Carlo improvements. The idea is tomore » approximate a given model by a dynamic programming-style decomposition, which then forms a scaffold upon which to build successively more accurate Monte Carlo approximations. Dynamic programming ideas alone fail to account for non-local structure, while standard Monte Carlo methods essentially ignore all structure. However, suitably-crafted hybrids can successfully exploit the strengths of each method, resulting in algorithms that combine speed with accuracy. The approach relies on the presence of significant {open_quotes}local{close_quotes} information in the problem at hand. This turns out to be a plausible assumption for many important applications. Example calculations are presented, and the overall strengths and weaknesses of the approach are discussed.« less

  6. Application of Markov chain Monte Carlo analysis to biomathematical modeling of respirable dust in US and UK coal miners

    PubMed Central

    Sweeney, Lisa M.; Parker, Ann; Haber, Lynne T.; Tran, C. Lang; Kuempel, Eileen D.

    2015-01-01

    A biomathematical model was previously developed to describe the long-term clearance and retention of particles in the lungs of coal miners. The model structure was evaluated and parameters were estimated in two data sets, one from the United States and one from the United Kingdom. The three-compartment model structure consists of deposition of inhaled particles in the alveolar region, competing processes of either clearance from the alveolar region or translocation to the lung interstitial region, and very slow, irreversible sequestration of interstitialized material in the lung-associated lymph nodes. Point estimates of model parameter values were estimated separately for the two data sets. In the current effort, Bayesian population analysis using Markov chain Monte Carlo simulation was used to recalibrate the model while improving assessments of parameter variability and uncertainty. When model parameters were calibrated simultaneously to the two data sets, agreement between the derived parameters for the two groups was very good, and the central tendency values were similar to those derived from the deterministic approach. These findings are relevant to the proposed update of the ICRP human respiratory tract model with revisions to the alveolar-interstitial region based on this long-term particle clearance and retention model. PMID:23454101

  7. An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites

    NASA Astrophysics Data System (ADS)

    Liu, Boda; Liang, Yan

    2017-04-01

    Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications. In Earth sciences applications of MCMC simulations are primarily in the field of geophysics. The purpose of this study is to introduce MCMC methods to geochemical inverse problems related to trace element fractionation during mantle melting. MCMC methods have several advantages over least squares methods in deciphering melting processes from trace element abundances in basalts and mantle rocks. Here we use an MCMC method to invert for extent of melting, fraction of melt present during melting, and extent of chemical disequilibrium between the melt and residual solid from REE abundances in clinopyroxene in abyssal peridotites from Mid-Atlantic Ridge, Central Indian Ridge, Southwest Indian Ridge, Lena Trough, and American-Antarctic Ridge. We consider two melting models: one with exact analytical solution and the other without. We solve the latter numerically in a chain of melting models according to the Metropolis-Hastings algorithm. The probability distribution of inverted melting parameters depends on assumptions of the physical model, knowledge of mantle source composition, and constraints from the REE data. Results from MCMC inversion are consistent with and provide more reliable uncertainty estimates than results based on nonlinear least squares inversion. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites during partial melting beneath mid-ocean ridge spreading centers. MCMC simulation is well suited for more complicated but physically more realistic melting problems that do not have analytical solutions.

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

    USGS Publications Warehouse

    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.

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

    PubMed

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

    2011-06-09

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

  10. Markov models of genome segmentation

    NASA Astrophysics Data System (ADS)

    Thakur, Vivek; Azad, Rajeev K.; Ramaswamy, Ram

    2007-01-01

    We introduce Markov models for segmentation of symbolic sequences, extending a segmentation procedure based on the Jensen-Shannon divergence that has been introduced earlier. Higher-order Markov models are more sensitive to the details of local patterns and in application to genome analysis, this makes it possible to segment a sequence at positions that are biologically meaningful. We show the advantage of higher-order Markov-model-based segmentation procedures in detecting compositional inhomogeneity in chimeric DNA sequences constructed from genomes of diverse species, and in application to the E. coli K12 genome, boundaries of genomic islands, cryptic prophages, and horizontally acquired regions are accurately identified.

  11. Model Reduction via Principe Component Analysis and Markov Chain Monte Carlo (MCMC) Methods

    NASA Astrophysics Data System (ADS)

    Gong, R.; Chen, J.; Hoversten, M. G.; Luo, J.

    2011-12-01

    Geophysical and hydrogeological inverse problems often include a large number of unknown parameters, ranging from hundreds to millions, depending on parameterization and problems undertaking. This makes inverse estimation and uncertainty quantification very challenging, especially for those problems in two- or three-dimensional spatial domains. Model reduction technique has the potential of mitigating the curse of dimensionality by reducing total numbers of unknowns while describing the complex subsurface systems adequately. In this study, we explore the use of principal component analysis (PCA) and Markov chain Monte Carlo (MCMC) sampling methods for model reduction through the use of synthetic datasets. We compare the performances of three different but closely related model reduction approaches: (1) PCA methods with geometric sampling (referred to as 'Method 1'), (2) PCA methods with MCMC sampling (referred to as 'Method 2'), and (3) PCA methods with MCMC sampling and inclusion of random effects (referred to as 'Method 3'). We consider a simple convolution model with five unknown parameters as our goal is to understand and visualize the advantages and disadvantages of each method by comparing their inversion results with the corresponding analytical solutions. We generated synthetic data with noise added and invert them under two different situations: (1) the noised data and the covariance matrix for PCA analysis are consistent (referred to as the unbiased case), and (2) the noise data and the covariance matrix are inconsistent (referred to as biased case). In the unbiased case, comparison between the analytical solutions and the inversion results show that all three methods provide good estimates of the true values and Method 1 is computationally more efficient. In terms of uncertainty quantification, Method 1 performs poorly because of relatively small number of samples obtained, Method 2 performs best, and Method 3 overestimates uncertainty due to inclusion

  12. AEOLUS: A MARKOV CHAIN MONTE CARLO CODE FOR MAPPING ULTRACOOL ATMOSPHERES. AN APPLICATION ON JUPITER AND BROWN DWARF HST LIGHT CURVES

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Karalidi, Theodora; Apai, Dániel; Schneider, Glenn

    Deducing the cloud cover and its temporal evolution from the observed planetary spectra and phase curves can give us major insight into the atmospheric dynamics. In this paper, we present Aeolus, a Markov chain Monte Carlo code that maps the structure of brown dwarf and other ultracool atmospheres. We validated Aeolus on a set of unique Jupiter Hubble Space Telescope (HST) light curves. Aeolus accurately retrieves the properties of the major features of the Jovian atmosphere, such as the Great Red Spot and a major 5 μm hot spot. Aeolus is the first mapping code validated on actual observations of amore » giant planet over a full rotational period. For this study, we applied Aeolus to J- and H-band HST light curves of 2MASS J21392676+0220226 and 2MASS J0136565+093347. Aeolus retrieves three spots at the top of the atmosphere (per observational wavelength) of these two brown dwarfs, with a surface coverage of 21% ± 3% and 20.3% ± 1.5%, respectively. The Jupiter HST light curves will be publicly available via ADS/VIZIR.« less

  13. How old is this bird? The age distribution under some phase sampling schemes.

    PubMed

    Hautphenne, Sophie; Massaro, Melanie; Taylor, Peter

    2017-12-01

    In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an individual's lifetime. Under this model, the time of death follows a phase-type distribution, and the transient states of the Markov chain are known as phases. We then attempt to provide an answer to the simple question "What is the conditional age distribution of the individual, given its current phase"? We show that the answer depends on how we interpret the question, and in particular, on the phase observation scheme under consideration. We then apply our results to the computation of the age pyramid for the endangered Chatham Island black robin Petroica traversi during the monitoring period 2007-2014.

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

    USGS Publications Warehouse

    Minsley, B.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 frequency-domain 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 favourably 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. ?? 2011. Geophysical Journal International ?? 2011 RAS.

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

    NASA Astrophysics Data System (ADS)

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

    2017-08-01

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

  16. SIMULATION FROM ENDPOINT-CONDITIONED, CONTINUOUS-TIME MARKOV CHAINS ON A FINITE STATE SPACE, WITH APPLICATIONS TO MOLECULAR EVOLUTION.

    PubMed

    Hobolth, Asger; Stone, Eric A

    2009-09-01

    Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete and finite state space. Specifically, we consider the generation of sample paths, including intermediate states and times of transition, from a CTMC whose beginning and ending states are known across a time interval of length T. We first unify the literature through a discussion of the three predominant approaches: (1) modified rejection sampling, (2) direct sampling, and (3) uniformization. We then give analytical results for the complexity and efficiency of each method in terms of the instantaneous transition rate matrix Q of the CTMC, its beginning and ending states, and the length of sampling time T. In doing so, we show that no method dominates the others across all model specifications, and we give explicit proof of which method prevails for any given Q, T, and endpoints. Finally, we introduce and compare three applications of CTMCs to demonstrate the pitfalls of choosing an inefficient sampler.

  17. A Markov model of the Indus script

    PubMed Central

    Rao, Rajesh P. N.; Yadav, Nisha; Vahia, Mayank N.; Joglekar, Hrishikesh; Adhikari, R.; Mahadevan, Iravatham

    2009-01-01

    Although no historical information exists about the Indus civilization (flourished ca. 2600–1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system. PMID:19666571

  18. Algorithms for Discovery of Multiple Markov Boundaries

    PubMed Central

    Statnikov, Alexander; Lytkin, Nikita I.; Lemeire, Jan; Aliferis, Constantin F.

    2013-01-01

    Algorithms for Markov boundary discovery from data constitute an important recent development in machine learning, primarily because they offer a principled solution to the variable/feature selection problem and give insight on local causal structure. Over the last decade many sound algorithms have been proposed to identify a single Markov boundary of the response variable. Even though faithful distributions and, more broadly, distributions that satisfy the intersection property always have a single Markov boundary, other distributions/data sets may have multiple Markov boundaries of the response variable. The latter distributions/data sets are common in practical data-analytic applications, and there are several reasons why it is important to induce multiple Markov boundaries from such data. However, there are currently no sound and efficient algorithms that can accomplish this task. This paper describes a family of algorithms TIE* that can discover all Markov boundaries in a distribution. The broad applicability as well as efficiency of the new algorithmic family is demonstrated in an extensive benchmarking study that involved comparison with 26 state-of-the-art algorithms/variants in 15 data sets from a diversity of application domains. PMID:25285052

  19. Geochemical Characterization Using Geophysical Data and Markov Chain Monte Carlo Methods

    NASA Astrophysics Data System (ADS)

    Chen, J.; Hubbard, S.; Rubin, Y.; Murray, C.; Roden, E.; Majer, E.

    2002-12-01

    if they were available from direct measurements or as variables otherwise. To estimate the geochemical parameters, we first assigned a prior model for each variable and a likelihood model for each type of data, which together define posterior probability distributions for each variable on the domain. Since the posterior probability distribution may involve hundreds of variables, we used a Markov Chain Monte Carlo (MCMC) method to explore each variable by generating and subsequently evaluating hundreds of realizations. Results from this case study showed that although geophysical attributes are not necessarily directly related to geochemical parameters, geophysical data could be very useful for providing accurate and high-resolution information about geochemical parameter distribution through their joint and indirect connections with hydrogeological properties such as lithofacies. This case study also demonstrated that MCMC methods were particularly useful for geochemical parameter estimation using geophysical data because they allow incorporation into the procedure of spatial correlation information, measurement errors, and cross correlations among different types of parameters.

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

    NASA Astrophysics Data System (ADS)

    Berradja, Khadidja; Boughanmi, Nabil

    2016-09-01

    In dynamic cardiac PET FDG studies the assessment of myocardial metabolic rate of glucose (MMRG) requires the knowledge of the blood input function (IF). IF can be obtained by manual or automatic blood sampling and cross calibrated with PET. These procedures are cumbersome, invasive and generate uncertainties. The IF is contaminated by spillover of radioactivity from the adjacent myocardium and this could cause important error in the estimated MMRG. In this study, we show that the IF can be extracted from the images in a rat heart study with 18F-fluorodeoxyglucose (18F-FDG) by means of Independent Component Analysis (ICA) based on Bayesian theory and Markov Chain Monte Carlo (MCMC) sampling method (BICA). Images of the heart from rats were acquired with the Sherbrooke small animal PET scanner. A region of interest (ROI) was drawn around the rat image and decomposed into blood and tissue using BICA. The Statistical study showed that there is a significant difference (p < 0.05) between MMRG obtained with IF extracted by BICA with respect to IF extracted from measured images corrupted with spillover.

  1. Site-percolation threshold of carbon nanotube fibers-Fast inspection of percolation with Markov stochastic theory

    NASA Astrophysics Data System (ADS)

    Xu, Fangbo; Xu, Zhiping; Yakobson, Boris I.

    2014-08-01

    We present a site-percolation model based on a modified FCC lattice, as well as an efficient algorithm of inspecting percolation which takes advantage of the Markov stochastic theory, in order to study the percolation threshold of carbon nanotube (CNT) fibers. Our Markov-chain based algorithm carries out the inspection of percolation by performing repeated sparse matrix-vector multiplications, which allows parallelized computation to accelerate the inspection for a given configuration. With this approach, we determine that the site-percolation transition of CNT fibers occurs at pc=0.1533±0.0013, and analyze the dependence of the effective percolation threshold (corresponding to 0.5 percolation probability) on the length and the aspect ratio of a CNT fiber on a finite-size-scaling basis. We also discuss the aspect ratio dependence of percolation probability with various values of p (not restricted to pc).

  2. Modelling the cost-effectiveness of impact-absorbing flooring in Swedish residential care facilities.

    PubMed

    Ryen, Linda; Svensson, Mikael

    2016-06-01

    Fall-related injuries among the elderly, specifically hip fractures, cause significant morbidity and mortality as well as imposing a substantial financial cost on the health care system. Impact-absorbing flooring has been advocated as an effective method for preventing hip fractures resulting from falls. This study identifies the cost-effectiveness of impact-absorbing flooring compared to standard flooring in residential care facilities for the elderly in a Swedish setting. An incremental cost-effectiveness analysis was performed comparing impact-absorbing flooring to standard flooring using a Markov decision model. A societal perspective was adopted and incremental costs were compared to incremental gains in quality-adjusted life years (QALYs). Data on costs, probability transitions and health-related quality of life measures were retrieved from the published literature and from Swedish register data. Probabilistic sensitivity analysis was performed through a Monte Carlo simulation. The base-case analysis indicates that the impact-absorbing flooring reduces costs and increases QALYs. When allowing for uncertainty we find that 60% of the simulations indicate that impact-absorbing flooring is cost-saving compared to standard flooring and an additional 20% that it has a cost per QALY below a commonly used threshold value : Using a modelling approach, we find that impact-absorbing flooring is a dominant strategy at the societal level considering that it can save resources and improve health in a vulnerable population. © The Author 2015. Published by Oxford University Press on behalf of the European Public Health Association. All rights reserved.

  3. Derivation of Markov processes that violate detailed balance

    NASA Astrophysics Data System (ADS)

    Lee, Julian

    2018-03-01

    Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.

  4. Preparation and characterization of functional poly(vinylidene fluoride) (PVDF) membranes with ultraviolet-absorbing property

    NASA Astrophysics Data System (ADS)

    Dong, Li; Liu, Xiangdong; Xiong, Zhengrong; Sheng, Dekun; Lin, Changhong; Zhou, Yan; Yang, Yuming

    2018-06-01

    We first reported a strategy to prepare functional poly(vinylidene fluoride) (PVDF) membranes with excellent ultraviolet-absorbing property through chemically induced grafting. Herein, the polymerizable ultraviolet (UV) absorber 2-hydroxy-4-(3-methacryloxy-2-hydroxylpropoxy) benzophenone (BPMA) made by ourselves was grafted onto the PVDF chains that have been pretreated with tetraethylammonium hydroxide (TEAH) alkaline solution. Moreover, the effect of experiment conditions such as the alkali and monomer concentrations, alkali treatment time on the UV-absorbing property of the obtained PVDF-g-PBPMA membranes were studied in detail. The chemical structure of the modified membranes was confirmed by 1H NMR, FT-IR and XPS measurements. Meanwhile, the thermal and UV-absorbing properties were characterized by TGA, DSC and UV-Vis spectrophotometer, respectively. The results indicated that BPMA side chains were successfully introduced onto PVDF backbones. Most importantly, the obtained PVDF-g-PBPMA membranes exhibited excellent UV-absorbing property. The transmittance of UV light at 300 nm decreased to as low as 0.02% and the UV light below 388 nm could be completely absorbed by the PVDF-g-PBPMA membrane made under optimal condition.

  5. Thermodynamically accurate modeling of the catalytic cycle of photosynthetic oxygen evolution: a mathematical solution to asymmetric Markov chains.

    PubMed

    Vinyard, David J; Zachary, Chase E; Ananyev, Gennady; Dismukes, G Charles

    2013-07-01

    Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions. To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions. This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

  6. Twelve years of succession on sandy substrates in a post-mining landscape: a Markov chain analysis.

    PubMed

    Baasch, Annett; Tischew, Sabine; Bruelheide, Helge

    2010-06-01

    Knowledge of succession rates and pathways is crucial for devising restoration strategies for highly disturbed ecosystems such as surface-mined land. As these processes have often only been described in qualitative terms, we used Markov models to quantify transitions between successional stages. However, Markov models are often considered not attractive for some reasons, such as model assumptions (e.g., stationarity in space and time, or the high expenditure of time required to estimate successional transitions in the field). Here we present a solution for converting multivariate ecological time series into transition matrices and demonstrate the applicability of this approach for a data set that resulted from monitoring the succession of sandy dry grassland in a post-mining landscape. We analyzed five transition matrices, four one-step matrices referring to specific periods of transition (1995-1998, 1998-2001, 2001-2004, 2004-2007), and one matrix for the whole study period (stationary model, 1995-2007). Finally, the stationary model was enhanced to a partly time-variable model. Applying the stationary and the time-variable models, we started a prediction well outside our calibration period, beginning with 100% bare soil in 1974 as the known start of the succession, and generated the coverage of 12 predefined vegetation types in three-year intervals. Transitions among vegetation types changed significantly in space and over time. While the probability of colonization was almost constant over time, the replacement rate tended to increase, indicating that the speed of succession accelerated with time or fluctuations became stronger. The predictions of both models agreed surprisingly well with the vegetation data observed more than two decades later. This shows that our dry grassland succession in a post-mining landscape can be adequately described by comparably simple types of Markov models, although some model assumptions have not been fulfilled and within

  7. Markov Processes in Image Processing

    NASA Astrophysics Data System (ADS)

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

    2018-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-12-01

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

  9. Application of the Markov Chain Monte Carlo method for snow water equivalent retrieval based on passive microwave measurements

    NASA Astrophysics Data System (ADS)

    Pan, J.; Durand, M. T.; Vanderjagt, B. J.

    2015-12-01

    Markov Chain Monte Carlo (MCMC) method is a retrieval algorithm based on Bayes' rule, which starts from an initial state of snow/soil parameters, and updates it to a series of new states by comparing the posterior probability of simulated snow microwave signals before and after each time of random walk. It is a realization of the Bayes' rule, which gives an approximation to the probability of the snow/soil parameters in condition of the measured microwave TB signals at different bands. Although this method could solve all snow parameters including depth, density, snow grain size and temperature at the same time, it still needs prior information of these parameters for posterior probability calculation. How the priors will influence the SWE retrieval is a big concern. Therefore, in this paper at first, a sensitivity test will be carried out to study how accurate the snow emission models and how explicit the snow priors need to be to maintain the SWE error within certain amount. The synthetic TB simulated from the measured snow properties plus a 2-K observation error will be used for this purpose. It aims to provide a guidance on the MCMC application under different circumstances. Later, the method will be used for the snowpits at different sites, including Sodankyla, Finland, Churchill, Canada and Colorado, USA, using the measured TB from ground-based radiometers at different bands. Based on the previous work, the error in these practical cases will be studied, and the error sources will be separated and quantified.

  10. Computational Toxicology of Chloroform: Reverse Dosimetry Using Bayesian Inference, Markov Chain Monte Carlo Simulation, and Human Biomonitoring Data

    PubMed Central

    Lyons, Michael A.; Yang, Raymond S.H.; Mayeno, Arthur N.; Reisfeld, Brad

    2008-01-01

    Background One problem of interpreting population-based biomonitoring data is the reconstruction of corresponding external exposure in cases where no such data are available. Objectives We demonstrate the use of a computational framework that integrates physiologically based pharmacokinetic (PBPK) modeling, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of environmental chloroform source concentrations consistent with human biomonitoring data. The biomonitoring data consist of chloroform blood concentrations measured as part of the Third National Health and Nutrition Examination Survey (NHANES III), and for which no corresponding exposure data were collected. Methods We used a combined PBPK and shower exposure model to consider several routes and sources of exposure: ingestion of tap water, inhalation of ambient household air, and inhalation and dermal absorption while showering. We determined posterior distributions for chloroform concentration in tap water and ambient household air using U.S. Environmental Protection Agency Total Exposure Assessment Methodology (TEAM) data as prior distributions for the Bayesian analysis. Results Posterior distributions for exposure indicate that 95% of the population represented by the NHANES III data had likely chloroform exposures ≤ 67 μg/L in tap water and ≤ 0.02 μg/L in ambient household air. Conclusions Our results demonstrate the application of computer simulation to aid in the interpretation of human biomonitoring data in the context of the exposure–health evaluation–risk assessment continuum. These results should be considered as a demonstration of the method and can be improved with the addition of more detailed data. PMID:18709138

  11. Comparison of Bootstrapping and Markov Chain Monte Carlo for Copula Analysis of Hydrological Droughts

    NASA Astrophysics Data System (ADS)

    Yang, P.; Ng, T. L.; Yang, W.

    2015-12-01

    Effective water resources management depends on the reliable estimation of the uncertainty of drought events. Confidence intervals (CIs) are commonly applied to quantify this uncertainty. A CI seeks to be at the minimal length necessary to cover the true value of the estimated variable with the desired probability. In drought analysis where two or more variables (e.g., duration and severity) are often used to describe a drought, copulas have been found suitable for representing the joint probability behavior of these variables. However, the comprehensive assessment of the parameter uncertainties of copulas of droughts has been largely ignored, and the few studies that have recognized this issue have not explicitly compared the various methods to produce the best CIs. Thus, the objective of this study to compare the CIs generated using two widely applied uncertainty estimation methods, bootstrapping and Markov Chain Monte Carlo (MCMC). To achieve this objective, (1) the marginal distributions lognormal, Gamma, and Generalized Extreme Value, and the copula functions Clayton, Frank, and Plackett are selected to construct joint probability functions of two drought related variables. (2) The resulting joint functions are then fitted to 200 sets of simulated realizations of drought events with known distribution and extreme parameters and (3) from there, using bootstrapping and MCMC, CIs of the parameters are generated and compared. The effect of an informative prior on the CIs generated by MCMC is also evaluated. CIs are produced for different sample sizes (50, 100, and 200) of the simulated drought events for fitting the joint probability functions. Preliminary results assuming lognormal marginal distributions and the Clayton copula function suggest that for cases with small or medium sample sizes (~50-100), MCMC to be superior method if an informative prior exists. Where an informative prior is unavailable, for small sample sizes (~50), both bootstrapping and MCMC

  12. A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S.

    2008-05-15

    We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive globalmore » information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.« less

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

    NASA Technical Reports Server (NTRS)

    English, Thomas

    2005-01-01

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

  14. Application of Markov chain model to daily maximum temperature for thermal comfort in Malaysia

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nordin, Muhamad Asyraf bin Che; Hassan, Husna

    2015-10-22

    The Markov chain’s first order principle has been widely used to model various meteorological fields, for prediction purposes. In this study, a 14-year (2000-2013) data of daily maximum temperatures in Bayan Lepas were used. Earlier studies showed that the outdoor thermal comfort range based on physiologically equivalent temperature (PET) index in Malaysia is less than 34°C, thus the data obtained were classified into two state: normal state (within thermal comfort range) and hot state (above thermal comfort range). The long-run results show the probability of daily temperature exceed TCR will be only 2.2%. On the other hand, the probability dailymore » temperature within TCR will be 97.8%.« less

  15. Event-chain algorithm for the Heisenberg model: Evidence for z≃1 dynamic scaling.

    PubMed

    Nishikawa, Yoshihiko; Michel, Manon; Krauth, Werner; Hukushima, Koji

    2015-12-01

    We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z≃2.

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

    PubMed Central

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

    2014-01-01

    The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential. PMID:25523357

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

    PubMed

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

    2014-12-19

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

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

  19. Path-integral theory of an axially confined worm-like chain

    NASA Astrophysics Data System (ADS)

    Smith, D. A.

    2001-06-01

    A path-integral formulation is developed for the thermodynamic properties of a worm-like chain moving on a surface and laterally confined by a harmonic potential. The free energy of the chain is calculated as a function of its length and boundary conditions at each end. Distribution functions for chain displacements can be constructed by utilizing the Markov property as a function of displacement φ(s) and its derivative dφ(s)/ds along the path. These quantities are also calculated in the presence of pinning sites which impose fixed positive or negative displacements, foreshadowing their application to a model for the regulation of striated muscle.

  20. Birch regeneration: a stochastic model

    Treesearch

    William B. Leak

    1968-01-01

    The regeneration of a clearcutting with paper or yellow birch is expressed as an elementary stochastic (probabalistic) model that is computationally similar to an absorbing Markov chain. In the general case, the model contains 29 states beginning with the development of a flower (ament) and terminating with the abortion of a flower or seed, or the development of an...

  1. The Likelihood of Completing a VET Qualification: A Model-Based Approach. Technical Paper

    ERIC Educational Resources Information Center

    Mark, Kevin; Karmel, Tom

    2010-01-01

    This paper estimates vocational education and training (VET) course-completion rates, in order to fill a gap in performance measures for the VET sector. The technique the authors use is to track all VET course enrolments within a three-year window, centred on the year of interest. Then, using an absorbing Markov chain model for a VET course…

  2. Policy Transfer via Markov Logic Networks

    NASA Astrophysics Data System (ADS)

    Torrey, Lisa; Shavlik, Jude

    We propose using a statistical-relational model, the Markov Logic Network, for knowledge transfer in reinforcement learning. Our goal is to extract relational knowledge from a source task and use it to speed up learning in a related target task. We show that Markov Logic Networks are effective models for capturing both source-task Q-functions and source-task policies. We apply them via demonstration, which involves using them for decision making in an initial stage of the target task before continuing to learn. Through experiments in the RoboCup simulated-soccer domain, we show that transfer via Markov Logic Networks can significantly improve early performance in complex tasks, and that transferring policies is more effective than transferring Q-functions.

  3. Application of Markov chain theory to ASTP natural environment launch criteria at Kennedy Space Center

    NASA Technical Reports Server (NTRS)

    Graves, M. E.; Perlmutter, M.

    1974-01-01

    To aid the planning of the Apollo Soyuz Test Program (ASTP), certain natural environment statistical relationships are presented, based on Markov theory and empirical counts. The practical results are in terms of conditional probability of favorable and unfavorable launch conditions at Kennedy Space Center (KSC). They are based upon 15 years of recorded weather data which are analyzed under a set of natural environmental launch constraints. Three specific forecasting problems were treated: (1) the length of record of past weather which is useful to a prediction; (2) the effect of persistence in runs of favorable and unfavorable conditions; and (3) the forecasting of future weather in probabilistic terms.

  4. A New Framework for Analysis of Coevolutionary Systems-Directed Graph Representation and Random Walks.

    PubMed

    Chong, Siang Yew; Tiňo, Peter; He, Jun; Yao, Xin

    2017-11-20

    Studying coevolutionary systems in the context of simplified models (i.e., games with pairwise interactions between coevolving solutions modeled as self plays) remains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problems that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modeled as a specific type of Markov chains-random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provides the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled manner.

  5. Discriminative Learning with Markov Logic Networks

    DTIC Science & Technology

    2009-10-01

    Discriminative Learning with Markov Logic Networks Tuyen N. Huynh Department of Computer Sciences University of Texas at Austin Austin, TX 78712...emerging area of research that addresses the problem of learning from noisy structured/relational data. Markov logic networks (MLNs), sets of weighted...TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) University of Texas at Austin,Department of Computer

  6. NonMarkov Ito Processes with 1- state memory

    NASA Astrophysics Data System (ADS)

    McCauley, Joseph L.

    2010-08-01

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

  7. Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains.

    PubMed

    Allefeld, Carsten; Bialonski, Stephan

    2007-12-01

    Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors of R for cluster identification, analogous to several recent attempts at group identification using eigenvectors of the correlation matrix. All of these approaches assumed a one-to-one correspondence of dominant eigenvectors and clusters, which has however been shown to be wrong in important cases. We clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes, and derive an enhanced clustering method harnessing recent insights from the coarse-graining of finite-state Markov processes. We illustrate the operation of our method using a simulated system of coupled Lorenz oscillators, and we demonstrate its superior performance over the previous approach. Finally we investigate the question of robustness of the algorithm against small sample size, which is important with regard to field applications.

  8. Markov Chain Monte Carlo Inversion of Mantle Temperature and Composition, with Application to Iceland

    NASA Astrophysics Data System (ADS)

    Brown, Eric; Petersen, Kenni; Lesher, Charles

    2017-04-01

    Basalts are formed by adiabatic decompression melting of the asthenosphere, and thus provide records of the thermal, chemical and dynamical state of the upper mantle. However, uniquely constraining the importance of these factors through the lens of melting is challenging given the inevitability that primary basalts are the product of variable mixing of melts derived from distinct lithologies having different melting behaviors (e.g. peridotite vs. pyroxenite). Forward mantle melting models, such as REEBOX PRO [1], are useful tools in this regard, because they can account for differences in melting behavior and melt pooling processes, and provide estimates of bulk crust composition and volume that can be compared with geochemical and geophysical constraints, respectively. Nevertheless, these models require critical assumptions regarding mantle temperature, and lithologic abundance(s)/composition(s), all of which are poorly constrained. To provide better constraints on these parameters and their uncertainties, we have coupled a Markov Chain Monte Carlo (MCMC) sampling technique with the REEBOX PRO melting model. The MCMC method systematically samples distributions of key REEBOX PRO input parameters (mantle potential temperature, and initial abundances and compositions of the source lithologies) based on a likelihood function that describes the 'fit' of the model outputs (bulk crust composition and volume and end-member peridotite and pyroxenite melts) relative to geochemical and geophysical constraints and their associated uncertainties. As a case study, we have tested and applied the model to magmatism along Reykjanes Peninsula in Iceland, where pyroxenite has been inferred to be present in the mantle source. This locale is ideal because there exist sufficient geochemical and geophysical data to estimate bulk crust compositions and volumes, as well as the range of near-parental melts derived from the mantle. We find that for the case of passive upwelling, the models

  9. Communication: Introducing prescribed biases in out-of-equilibrium Markov models

    NASA Astrophysics Data System (ADS)

    Dixit, Purushottam D.

    2018-03-01

    Markov models are often used in modeling complex out-of-equilibrium chemical and biochemical systems. However, many times their predictions do not agree with experiments. We need a systematic framework to update existing Markov models to make them consistent with constraints that are derived from experiments. Here, we present a framework based on the principle of maximum relative path entropy (minimum Kullback-Leibler divergence) to update Markov models using stationary state and dynamical trajectory-based constraints. We illustrate the framework using a biochemical model network of growth factor-based signaling. We also show how to find the closest detailed balanced Markov model to a given Markov model. Further applications and generalizations are discussed.

  10. Combined risk assessment of nonstationary monthly water quality based on Markov chain and time-varying copula.

    PubMed

    Shi, Wei; Xia, Jun

    2017-02-01

    Water quality risk management is a global hot research linkage with the sustainable water resource development. Ammonium nitrogen (NH 3 -N) and permanganate index (COD Mn ) as the focus indicators in Huai River Basin, are selected to reveal their joint transition laws based on Markov theory. The time-varying moments model with either time or land cover index as explanatory variables is applied to build the time-varying marginal distributions of water quality time series. Time-varying copula model, which takes the non-stationarity in the marginal distribution and/or the time variation in dependence structure between water quality series into consideration, is constructed to describe a bivariate frequency analysis for NH 3 -N and COD Mn series at the same monitoring gauge. The larger first-order Markov joint transition probability indicates water quality state Class V w , Class IV and Class III will occur easily in the water body of Bengbu Sluice. Both marginal distribution and copula models are nonstationary, and the explanatory variable time yields better performance than land cover index in describing the non-stationarities in the marginal distributions. In modelling the dependence structure changes, time-varying copula has a better fitting performance than the copula with the constant or the time-trend dependence parameter. The largest synchronous encounter risk probability of NH 3 -N and COD Mn simultaneously reaching Class V is 50.61%, while the asynchronous encounter risk probability is largest when NH 3 -N and COD Mn is inferior to class V and class IV water quality standards, respectively.

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

    PubMed Central

    Wei, Shaoceng; Kryscio, Richard J.

    2015-01-01

    Continuous-time multi-state stochastic processes are useful for modeling the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient, cognitive states and death as a competing risk (Figure 1). Each subject's cognition is assessed periodically resulting in interval censoring for the cognitive states while death without dementia is not interval censored. Since back transitions among the transient states are possible, Markov chains are often applied to this type of panel data. In this manuscript we apply a Semi-Markov process in which we assume that the waiting times are Weibull distributed except for transitions from the baseline state, which are exponentially distributed and in which we assume no additional changes in cognition occur between two assessments. We implement a quasi-Monte Carlo (QMC) method to calculate the higher order integration needed for likelihood estimation. We apply our model to a real dataset, the Nun Study, a cohort of 461 participants. PMID:24821001

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

    PubMed

    Wei, Shaoceng; Kryscio, Richard J

    2016-12-01

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

  13. SAChES: Scalable Adaptive Chain-Ensemble Sampling.

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Swiler, Laura Painton; Ray, Jaideep; Ebeida, Mohamed Salah

    We present the development of a parallel Markov Chain Monte Carlo (MCMC) method called SAChES, Scalable Adaptive Chain-Ensemble Sampling. This capability is targed to Bayesian calibration of com- putationally expensive simulation models. SAChES involves a hybrid of two methods: Differential Evo- lution Monte Carlo followed by Adaptive Metropolis. Both methods involve parallel chains. Differential evolution allows one to explore high-dimensional parameter spaces using loosely coupled (i.e., largely asynchronous) chains. Loose coupling allows the use of large chain ensembles, with far more chains than the number of parameters to explore. This reduces per-chain sampling burden, enables high-dimensional inversions and the usemore » of computationally expensive forward models. The large number of chains can also ameliorate the impact of silent-errors, which may affect only a few chains. The chain ensemble can also be sampled to provide an initial condition when an aberrant chain is re-spawned. Adaptive Metropolis takes the best points from the differential evolution and efficiently hones in on the poste- rior density. The multitude of chains in SAChES is leveraged to (1) enable efficient exploration of the parameter space; and (2) ensure robustness to silent errors which may be unavoidable in extreme-scale computational platforms of the future. This report outlines SAChES, describes four papers that are the result of the project, and discusses some additional results.« less

  14. Markov and non-Markov processes in complex systems by the dynamical information entropy

    NASA Astrophysics Data System (ADS)

    Yulmetyev, R. M.; Gafarov, F. M.

    1999-12-01

    We consider the Markov and non-Markov processes in complex systems by the dynamical information Shannon entropy (DISE) method. The influence and important role of the two mutually dependent channels of entropy alternation (creation or generation of correlation) and anti-correlation (destroying or annihilation of correlation) have been discussed. The developed method has been used for the analysis of the complex systems of various natures: slow neutron scattering in liquid cesium, psychology (short-time numeral and pattern human memory and effect of stress on the dynamical taping-test), random dynamics of RR-intervals in human ECG (problem of diagnosis of various disease of the human cardio-vascular systems), chaotic dynamics of the parameters of financial markets and ecological systems.

  15. Protein sequences clustering of herpes virus by using Tribe Markov clustering (Tribe-MCL)

    NASA Astrophysics Data System (ADS)

    Bustamam, A.; Siswantining, T.; Febriyani, N. L.; Novitasari, I. D.; Cahyaningrum, R. D.

    2017-07-01

    The herpes virus can be found anywhere and one of the important characteristics is its ability to cause acute and chronic infection at certain times so as a result of the infection allows severe complications occurred. The herpes virus is composed of DNA containing protein and wrapped by glycoproteins. In this work, the Herpes viruses family is classified and analyzed by clustering their protein-sequence using Tribe Markov Clustering (Tribe-MCL) algorithm. Tribe-MCL is an efficient clustering method based on the theory of Markov chains, to classify protein families from protein sequences using pre-computed sequence similarity information. We implement the Tribe-MCL algorithm using an open source program of R. We select 24 protein sequences of Herpes virus obtained from NCBI database. The dataset consists of three types of glycoprotein B, F, and H. Each type has eight herpes virus that infected humans. Based on our simulation using different inflation factor r=1.5, 2, 3 we find a various number of the clusters results. The greater the inflation factor the greater the number of their clusters. Each protein will grouped together in the same type of protein.

  16. Identifying and correcting non-Markov states in peptide conformational dynamics

    NASA Astrophysics Data System (ADS)

    Nerukh, Dmitry; Jensen, Christian H.; Glen, Robert C.

    2010-02-01

    Conformational transitions in proteins define their biological activity and can be investigated in detail using the Markov state model. The fundamental assumption on the transitions between the states, their Markov property, is critical in this framework. We test this assumption by analyzing the transitions obtained directly from the dynamics of a molecular dynamics simulated peptide valine-proline-alanine-leucine and states defined phenomenologically using clustering in dihedral space. We find that the transitions are Markovian at the time scale of ≈50 ps and longer. However, at the time scale of 30-40 ps the dynamics loses its Markov property. Our methodology reveals the mechanism that leads to non-Markov behavior. It also provides a way of regrouping the conformations into new states that now possess the required Markov property of their dynamics.

  17. Characterizing the Trade Space Between Capability and Complexity in Next Generation Cloud and Precipitation Observing Systems Using Markov Chain Monte Carlos Techniques

    NASA Astrophysics Data System (ADS)

    Xu, Z.; Mace, G. G.; Posselt, D. J.

    2017-12-01

    As we begin to contemplate the next generation atmospheric observing systems, it will be critically important that we are able to make informed decisions regarding the trade space between scientific capability and the need to keep complexity and cost within definable limits. To explore this trade space as it pertains to understanding key cloud and precipitation processes, we are developing a Markov Chain Monte Carlo (MCMC) algorithm suite that allows us to arbitrarily define the specifications of candidate observing systems and then explore how the uncertainties in key retrieved geophysical parameters respond to that observing system. MCMC algorithms produce a more complete posterior solution space, and allow for an objective examination of information contained in measurements. In our initial implementation, MCMC experiments are performed to retrieve vertical profiles of cloud and precipitation properties from a spectrum of active and passive measurements collected by aircraft during the ACE Radiation Definition Experiments (RADEX). Focusing on shallow cumulus clouds observed during the Integrated Precipitation and Hydrology EXperiment (IPHEX), observing systems in this study we consider W and Ka-band radar reflectivity, path-integrated attenuation at those frequencies, 31 and 94 GHz brightness temperatures as well as visible and near-infrared reflectance. By varying the sensitivity and uncertainty of these measurements, we quantify the capacity of various combinations of observations to characterize the physical properties of clouds and precipitation.

  18. Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

    NASA Astrophysics Data System (ADS)

    Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

    2010-10-01

    Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

  19. A kinetic Monte Carlo approach to diffusion-controlled thermal desorption spectroscopy

    NASA Astrophysics Data System (ADS)

    Schablitzki, T.; Rogal, J.; Drautz, R.

    2017-06-01

    Atomistic simulations of thermal desorption spectra for effusion from bulk materials to characterize binding or trapping sites are a challenging task as large system sizes as well as extended time scales are required. Here, we introduce an approach where we combine kinetic Monte Carlo with an analytic approximation of the superbasins within the framework of absorbing Markov chains. We apply our approach to the effusion of hydrogen from BCC iron, where the diffusion within bulk grains is coarse grained using absorbing Markov chains, which provide an exact solution of the dynamics within a superbasin. Our analytic approximation to the superbasin is transferable with respect to grain size and elliptical shapes and can be applied in simulations with constant temperature as well as constant heating rate. The resulting thermal desorption spectra are in close agreement with direct kinetic Monte Carlo simulations, but the calculations are computationally much more efficient. Our approach is thus applicable to much larger system sizes and provides a first step towards an atomistic understanding of the influence of structural features on the position and shape of peaks in thermal desorption spectra. This article is part of the themed issue 'The challenges of hydrogen and metals'.

  20. Meta-heuristic ant colony optimization technique to forecast the amount of summer monsoon rainfall: skill comparison with Markov chain model

    NASA Astrophysics Data System (ADS)

    Chaudhuri, Sutapa; Goswami, Sayantika; Das, Debanjana; Middey, Anirban

    2014-05-01

    Forecasting summer monsoon rainfall with precision becomes crucial for the farmers to plan for harvesting in a country like India where the national economy is mostly based on regional agriculture. The forecast of monsoon rainfall based on artificial neural network is a well-researched problem. In the present study, the meta-heuristic ant colony optimization (ACO) technique is implemented to forecast the amount of summer monsoon rainfall for the next day over Kolkata (22.6°N, 88.4°E), India. The ACO technique belongs to swarm intelligence and simulates the decision-making processes of ant colony similar to other adaptive learning techniques. ACO technique takes inspiration from the foraging behaviour of some ant species. The ants deposit pheromone on the ground in order to mark a favourable path that should be followed by other members of the colony. A range of rainfall amount replicating the pheromone concentration is evaluated during the summer monsoon season. The maximum amount of rainfall during summer monsoon season (June—September) is observed to be within the range of 7.5-35 mm during the period from 1998 to 2007, which is in the range 4 category set by the India Meteorological Department (IMD). The result reveals that the accuracy in forecasting the amount of rainfall for the next day during the summer monsoon season using ACO technique is 95 % where as the forecast accuracy is 83 % with Markov chain model (MCM). The forecast through ACO and MCM are compared with other existing models and validated with IMD observations from 2008 to 2012.

  1. Evaluating cardiovascular mortality in type 2 diabetes patients: an analysis based on competing risks Markov chains and additive regression models.

    PubMed

    Rosato, Rosalba; Ciccone, G; Bo, S; Pagano, G F; Merletti, F; Gregori, D

    2007-06-01

    Type 2 diabetes represents a condition significantly associated with increased cardiovascular mortality. The aims of the study are: (i) to estimate the cumulative incidence function for cause-specific mortality using Cox and Aalen model; (ii) to describe how the prediction of cardiovascular or other causes mortality changes for patients with different pattern of covariates; (iii) to show if different statistical methods may give different results. Cox and Aalen additive regression model through the Markov chain approach, are used to estimate the cause-specific hazard for cardiovascular or other causes mortality in a cohort of 2865 type 2 diabetic patients without insulin treatment. The models are compared in the estimation of the risk of death for patients of different severity. For younger patients with a better covariates profile, the Cumulative Incidence Function estimated by Cox and Aalen model was almost the same; for patients with the worst covariates profile, models gave different results: at the end of follow-up cardiovascular mortality rate estimated by Cox and Aalen model was 0.26 [95% confidence interval (CI) = 0.21-0.31] and 0.14 (95% CI = 0.09-0.18). Standard Cox and Aalen model capture the risk process for patients equally well with average profiles of co-morbidities. The Aalen model, in addition, is shown to be better at identifying cause-specific risk of death for patients with more severe clinical profiles. This result is relevant in the development of analytic tools for research and resource management within diabetes care.

  2. Measuring the impact of final demand on global production system based on Markov process

    NASA Astrophysics Data System (ADS)

    Xing, Lizhi; Guan, Jun; Wu, Shan

    2018-07-01

    Input-output table is a comprehensive and detailed in describing the national economic systems, consisting of supply and demand information among various industrial sectors. The complex network, a theory and method for measuring the structure of complex system, can depict the structural properties of social and economic systems, and reveal the complicated relationships between the inner hierarchies and the external macroeconomic functions. This paper tried to measure the globalization degree of industrial sectors on the global value chain. Firstly, it constructed inter-country input-output network models to reproduce the topological structure of global economic system. Secondly, it regarded the propagation of intermediate goods on the global value chain as Markov process and introduced counting first passage betweenness to quantify the added processing amount when globally final demand stimulates this production system. Thirdly, it analyzed the features of globalization at both global and country-sector level

  3. Markov Analysis of Sleep Dynamics

    NASA Astrophysics Data System (ADS)

    Kim, J. W.; Lee, J.-S.; Robinson, P. A.; Jeong, D.-U.

    2009-05-01

    A new approach, based on a Markov transition matrix, is proposed to explain frequent sleep and wake transitions during sleep. The matrix is determined by analyzing hypnograms of 113 obstructive sleep apnea patients. Our approach shows that the statistics of sleep can be constructed via a single Markov process and that durations of all states have modified exponential distributions, in contrast to recent reports of a scale-free form for the wake stage and an exponential form for the sleep stage. Hypnograms of the same subjects, but treated with Continuous Positive Airway Pressure, are analyzed and compared quantitatively with the pretreatment ones, suggesting potential clinical applications.

  4. A Markov Environment-dependent Hurricane Intensity Model and Its Comparison with Multiple Dynamic Models

    NASA Astrophysics Data System (ADS)

    Jing, R.; Lin, N.; Emanuel, K.; Vecchi, G. A.; Knutson, T. R.

    2017-12-01

    A Markov environment-dependent hurricane intensity model (MeHiM) is developed to simulate the climatology of hurricane intensity given the surrounding large-scale environment. The model considers three unobserved discrete states representing respectively storm's slow, moderate, and rapid intensification (and deintensification). Each state is associated with a probability distribution of intensity change. The storm's movement from one state to another, regarded as a Markov chain, is described by a transition probability matrix. The initial state is estimated with a Bayesian approach. All three model components (initial intensity, state transition, and intensity change) are dependent on environmental variables including potential intensity, vertical wind shear, midlevel relative humidity, and ocean mixing characteristics. This dependent Markov model of hurricane intensity shows a significant improvement over previous statistical models (e.g., linear, nonlinear, and finite mixture models) in estimating the distributions of 6-h and 24-h intensity change, lifetime maximum intensity, and landfall intensity, etc. Here we compare MeHiM with various dynamical models, including a global climate model [High-Resolution Forecast-Oriented Low Ocean Resolution model (HiFLOR)], a regional hurricane model (Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model), and a simplified hurricane dynamic model [Coupled Hurricane Intensity Prediction System (CHIPS)] and its newly developed fast simulator. The MeHiM developed based on the reanalysis data is applied to estimate the intensity of simulated storms to compare with the dynamical-model predictions under the current climate. The dependences of hurricanes on the environment under current and future projected climates in the various models will also be compared statistically.

  5. Hidden Markov Item Response Theory Models for Responses and Response Times.

    PubMed

    Molenaar, Dylan; Oberski, Daniel; Vermunt, Jeroen; De Boeck, Paul

    2016-01-01

    Current approaches to model responses and response times to psychometric tests solely focus on between-subject differences in speed and ability. Within subjects, speed and ability are assumed to be constants. Violations of this assumption are generally absorbed in the residual of the model. As a result, within-subject departures from the between-subject speed and ability level remain undetected. These departures may be of interest to the researcher as they reflect differences in the response processes adopted on the items of a test. In this article, we propose a dynamic approach for responses and response times based on hidden Markov modeling to account for within-subject differences in responses and response times. A simulation study is conducted to demonstrate acceptable parameter recovery and acceptable performance of various fit indices in distinguishing between different models. In addition, both a confirmatory and an exploratory application are presented to demonstrate the practical value of the modeling approach.

  6. Iodine binding to explore the conformational state of internal chains of amylopectin.

    PubMed

    Shen, Xinyu; Bertoft, Eric; Zhang, Genyi; Hamaker, Bruce R

    2013-10-15

    Previous studies have found that the proportion of long chains of amylopectin correlates to its functional and nutritional properties. As a possible explanation of this correlation, the iodine binding property of amylopectin internal chains was investigated as an indirect evidence of their ability to form helices for intra- or inter-molecular interactions. Waxy and amylose-extender waxy corn starches were hydrolyzed by β-amylase for varying periods of time to incrementally remove the external chains, and the absorbance and the wavelength of maximum absorbance of iodine binding were examined. Experimental results suggest that iodine can bind with both external and internal chains; a significant amount of absorption comes from the latter, as stepwise removal of external chains only somewhat reduced absorption. Internal amylopectin chains, thus, were concluded to likely pre-exist in helical form, as opposed to a conformational change into helices facilitating iodine binding in the absence of external chains. Such internal chain helical structures possibly drive intermolecular interactions that would explain why amylopectin with high proportion of internal chains form harder gels, create pastes less prone to shear breakdown, and are more slowly digesting. Copyright © 2013 Elsevier Ltd. All rights reserved.

  7. Markov model of the loan portfolio dynamics considering influence of management and external economic factors

    NASA Astrophysics Data System (ADS)

    Bozhalkina, Yana; Timofeeva, Galina

    2016-12-01

    Mathematical model of loan portfolio in the form of a controlled Markov chain with discrete time is considered. It is assumed that coefficients of migration matrix depend on corrective actions and external factors. Corrective actions include process of receiving applications, interaction with existing solvent and insolvent clients. External factors are macroeconomic indicators, such as inflation and unemployment rates, exchange rates, consumer price indices, etc. Changes in corrective actions adjust the intensity of transitions in the migration matrix. The mathematical model for forecasting the credit portfolio structure taking into account a cumulative impact of internal and external changes is obtained.

  8. [Development of Markov models for economics evaluation of strategies on hepatitis B vaccination and population-based antiviral treatment in China].

    PubMed

    Yang, P C; Zhang, S X; Sun, P P; Cai, Y L; Lin, Y; Zou, Y H

    2017-07-10

    Objective: To construct the Markov models to reflect the reality of prevention and treatment interventions against hepatitis B virus (HBV) infection, simulate the natural history of HBV infection in different age groups and provide evidence for the economics evaluations of hepatitis B vaccination and population-based antiviral treatment in China. Methods: According to the theory and techniques of Markov chain, the Markov models of Chinese HBV epidemic were developed based on the national data and related literature both at home and abroad, including the settings of Markov model states, allowable transitions and initial and transition probabilities. The model construction, operation and verification were conducted by using software TreeAge Pro 2015. Results: Several types of Markov models were constructed to describe the disease progression of HBV infection in neonatal period, perinatal period or adulthood, the progression of chronic hepatitis B after antiviral therapy, hepatitis B prevention and control in adults, chronic hepatitis B antiviral treatment and the natural progression of chronic hepatitis B in general population. The model for the newborn was fundamental which included ten states, i.e . susceptiblity to HBV, HBsAg clearance, immune tolerance, immune clearance, low replication, HBeAg negative CHB, compensated cirrhosis, decompensated cirrhosis, hepatocellular carcinoma (HCC) and death. The susceptible state to HBV was excluded in the perinatal period model, and the immune tolerance state was excluded in the adulthood model. The model for general population only included two states, survive and death. Among the 5 types of models, there were 9 initial states assigned with initial probabilities, and 27 states for transition probabilities. The results of model verifications showed that the probability curves were basically consistent with the situation of HBV epidemic in China. Conclusion: The Markov models developed can be used in economics evaluation of

  9. Multiensemble Markov models of molecular thermodynamics and kinetics.

    PubMed

    Wu, Hao; Paul, Fabian; Wehmeyer, Christoph; Noé, Frank

    2016-06-07

    We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models-clustering of high-dimensional spaces and modeling of complex many-state systems-with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein-ligand binding model.

  10. Multiensemble Markov models of molecular thermodynamics and kinetics

    PubMed Central

    Wu, Hao; Paul, Fabian; Noé, Frank

    2016-01-01

    We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models—clustering of high-dimensional spaces and modeling of complex many-state systems—with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein–ligand binding model. PMID:27226302

  11. Changes in mangrove species assemblages and future prediction of the Bangladesh Sundarbans using Markov chain model and cellular automata.

    PubMed

    Mukhopadhyay, Anirban; Mondal, Parimal; Barik, Jyotiskona; Chowdhury, S M; Ghosh, Tuhin; Hazra, Sugata

    2015-06-01

    The composition and assemblage of mangroves in the Bangladesh Sundarbans are changing systematically in response to several environmental factors. In order to understand the impact of the changing environmental conditions on the mangrove forest, species composition maps for the years 1985, 1995 and 2005 were studied. In the present study, 1985 and 1995 species zonation maps were considered as base data and the cellular automata-Markov chain model was run to predict the species zonation for the year 2005. The model output was validated against the actual dataset for 2005 and calibrated. Finally, using the model, mangrove species zonation maps for the years 2025, 2055 and 2105 have been prepared. The model was run with the assumption that the continuation of the current tempo and mode of drivers of environmental factors (temperature, rainfall, salinity change) of the last two decades will remain the same in the next few decades. Present findings show that the area distribution of the following species assemblages like Goran (Ceriops), Sundari (Heritiera), Passur (Xylocarpus), and Baen (Avicennia) would decrease in the descending order, whereas the area distribution of Gewa (Excoecaria), Keora (Sonneratia) and Kankra (Bruguiera) dominated assemblages would increase. The spatial distribution of projected mangrove species assemblages shows that more salt tolerant species will dominate in the future; which may be used as a proxy to predict the increase of salinity and its spatial variation in Sundarbans. Considering the present rate of loss of forest land, 17% of the total mangrove cover is predicted to be lost by the year 2105 with a significant loss of fresh water loving mangroves and related ecosystem services. This paper describes a unique approach to assess future changes in species composition and future forest zonation in mangroves under the 'business as usual' scenario of climate change.

  12. Towards robust quantification and reduction of uncertainty in hydrologic predictions: Integration of particle Markov chain Monte Carlo and factorial polynomial chaos expansion

    NASA Astrophysics Data System (ADS)

    Wang, S.; Huang, G. H.; Baetz, B. W.; Ancell, B. C.

    2017-05-01

    The particle filtering techniques have been receiving increasing attention from the hydrologic community due to its ability to properly estimate model parameters and states of nonlinear and non-Gaussian systems. To facilitate a robust quantification of uncertainty in hydrologic predictions, it is necessary to explicitly examine the forward propagation and evolution of parameter uncertainties and their interactions that affect the predictive performance. This paper presents a unified probabilistic framework that merges the strengths of particle Markov chain Monte Carlo (PMCMC) and factorial polynomial chaos expansion (FPCE) algorithms to robustly quantify and reduce uncertainties in hydrologic predictions. A Gaussian anamorphosis technique is used to establish a seamless bridge between the data assimilation using the PMCMC and the uncertainty propagation using the FPCE through a straightforward transformation of posterior distributions of model parameters. The unified probabilistic framework is applied to the Xiangxi River watershed of the Three Gorges Reservoir (TGR) region in China to demonstrate its validity and applicability. Results reveal that the degree of spatial variability of soil moisture capacity is the most identifiable model parameter with the fastest convergence through the streamflow assimilation process. The potential interaction between the spatial variability in soil moisture conditions and the maximum soil moisture capacity has the most significant effect on the performance of streamflow predictions. In addition, parameter sensitivities and interactions vary in magnitude and direction over time due to temporal and spatial dynamics of hydrologic processes.

  13. The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

    NASA Technical Reports Server (NTRS)

    Meyer, C. D., Jr.

    1979-01-01

    The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.

  14. Daily Rainfall Simulation Using Climate Variables and Nonhomogeneous Hidden Markov Model

    NASA Astrophysics Data System (ADS)

    Jung, J.; Kim, H. S.; Joo, H. J.; Han, D.

    2017-12-01

    Markov chain is an easy method to handle when we compare it with other ones for the rainfall simulation. However, it also has limitations in reflecting seasonal variability of rainfall or change on rainfall patterns caused by climate change. This study applied a Nonhomogeneous Hidden Markov Model(NHMM) to consider these problems. The NHMM compared with a Hidden Markov Model(HMM) for the evaluation of a goodness of the model. First, we chose Gum river basin in Korea to apply the models and collected daily rainfall data from the stations. Also, the climate variables of geopotential height, temperature, zonal wind, and meridional wind date were collected from NCEP/NCAR reanalysis data to consider external factors affecting the rainfall event. We conducted a correlation analysis between rainfall and climate variables then developed a linear regression equation using the climate variables which have high correlation with rainfall. The monthly rainfall was obtained by the regression equation and it became input data of NHMM. Finally, the daily rainfall by NHMM was simulated and we evaluated the goodness of fit and prediction capability of NHMM by comparing with those of HMM. As a result of simulation by HMM, the correlation coefficient and root mean square error of daily/monthly rainfall were 0.2076 and 10.8243/131.1304mm each. In case of NHMM, the correlation coefficient and root mean square error of daily/monthly rainfall were 0.6652 and 10.5112/100.9865mm each. We could verify that the error of daily and monthly rainfall simulated by NHMM was improved by 2.89% and 22.99% compared with HMM. Therefore, it is expected that the results of the study could provide more accurate data for hydrologic analysis. Acknowledgements This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT & Future Planning(2017R1A2B3005695)

  15. Modeling carbachol-induced hippocampal network synchronization using hidden Markov models

    NASA Astrophysics Data System (ADS)

    Dragomir, Andrei; Akay, Yasemin M.; Akay, Metin

    2010-10-01

    In this work we studied the neural state transitions undergone by the hippocampal neural network using a hidden Markov model (HMM) framework. We first employed a measure based on the Lempel-Ziv (LZ) estimator to characterize the changes in the hippocampal oscillation patterns in terms of their complexity. These oscillations correspond to different modes of hippocampal network synchronization induced by the cholinergic agonist carbachol in the CA1 region of mice hippocampus. HMMs are then used to model the dynamics of the LZ-derived complexity signals as first-order Markov chains. Consequently, the signals corresponding to our oscillation recordings can be segmented into a sequence of statistically discriminated hidden states. The segmentation is used for detecting transitions in neural synchronization modes in data recorded from wild-type and triple transgenic mice models (3xTG) of Alzheimer's disease (AD). Our data suggest that transition from low-frequency (delta range) continuous oscillation mode into high-frequency (theta range) oscillation, exhibiting repeated burst-type patterns, occurs always through a mode resembling a mixture of the two patterns, continuous with burst. The relatively random patterns of oscillation during this mode may reflect the fact that the neuronal network undergoes re-organization. Further insight into the time durations of these modes (retrieved via the HMM segmentation of the LZ-derived signals) reveals that the mixed mode lasts significantly longer (p < 10-4) in 3xTG AD mice. These findings, coupled with the documented cholinergic neurotransmission deficits in the 3xTG mice model, may be highly relevant for the case of AD.

  16. Modeling Hubble Space Telescope flight data by Q-Markov cover identification

    NASA Technical Reports Server (NTRS)

    Liu, K.; Skelton, R. E.; Sharkey, J. P.

    1992-01-01

    A state space model for the Hubble Space Telescope under the influence of unknown disturbances in orbit is presented. This model was obtained from flight data by applying the Q-Markov covariance equivalent realization identification algorithm. This state space model guarantees the match of the first Q-Markov parameters and covariance parameters of the Hubble system. The flight data were partitioned into high- and low-frequency components for more efficient Q-Markov cover modeling, to reduce some computational difficulties of the Q-Markov cover algorithm. This identification revealed more than 20 lightly damped modes within the bandwidth of the attitude control system. Comparisons with the analytical (TREETOPS) model are also included.

  17. Neutrino masses and cosmological parameters from a Euclid-like survey: Markov Chain Monte Carlo forecasts including theoretical errors

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Audren, Benjamin; Lesgourgues, Julien; Bird, Simeon

    2013-01-01

    We present forecasts for the accuracy of determining the parameters of a minimal cosmological model and the total neutrino mass based on combined mock data for a future Euclid-like galaxy survey and Planck. We consider two different galaxy surveys: a spectroscopic redshift survey and a cosmic shear survey. We make use of the Monte Carlo Markov Chains (MCMC) technique and assume two sets of theoretical errors. The first error is meant to account for uncertainties in the modelling of the effect of neutrinos on the non-linear galaxy power spectrum and we assume this error to be fully correlated in Fouriermore » space. The second error is meant to parametrize the overall residual uncertainties in modelling the non-linear galaxy power spectrum at small scales, and is conservatively assumed to be uncorrelated and to increase with the ratio of a given scale to the scale of non-linearity. It hence increases with wavenumber and decreases with redshift. With these two assumptions for the errors and assuming further conservatively that the uncorrelated error rises above 2% at k = 0.4 h/Mpc and z = 0.5, we find that a future Euclid-like cosmic shear/galaxy survey achieves a 1-σ error on M{sub ν} close to 32 meV/25 meV, sufficient for detecting the total neutrino mass with good significance. If the residual uncorrelated errors indeed rises rapidly towards smaller scales in the non-linear regime as we have assumed here then the data on non-linear scales does not increase the sensitivity to the total neutrino mass. Assuming instead a ten times smaller theoretical error with the same scale dependence, the error on the total neutrino mass decreases moderately from σ(M{sub ν}) = 18 meV to 14 meV when mildly non-linear scales with 0.1 h/Mpc < k < 0.6 h/Mpc are included in the analysis of the galaxy survey data.« less

  18. Markov Chain Monte Carlo estimation of species distributions: a case study of the swift fox in western Kansas

    USGS Publications Warehouse

    Sargeant, Glen A.; Sovada, Marsha A.; Slivinski, Christiane C.; Johnson, Douglas H.

    2005-01-01

    Accurate maps of species distributions are essential tools for wildlife research and conservation. Unfortunately, biologists often are forced to rely on maps derived from observed occurrences recorded opportunistically during observation periods of variable length. Spurious inferences are likely to result because such maps are profoundly affected by the duration and intensity of observation and by methods used to delineate distributions, especially when detection is uncertain. We conducted a systematic survey of swift fox (Vulpes velox) distribution in western Kansas, USA, and used Markov chain Monte Carlo (MCMC) image restoration to rectify these problems. During 1997–1999, we searched 355 townships (ca. 93 km) 1–3 times each for an average cost of $7,315 per year and achieved a detection rate (probability of detecting swift foxes, if present, during a single search) of = 0.69 (95% Bayesian confidence interval [BCI] = [0.60, 0.77]). Our analysis produced an estimate of the underlying distribution, rather than a map of observed occurrences, that reflected the uncertainty associated with estimates of model parameters. To evaluate our results, we analyzed simulated data with similar properties. Results of our simulations suggest negligible bias and good precision when probabilities of detection on ≥1 survey occasions (cumulative probabilities of detection) exceed 0.65. Although the use of MCMC image restoration has been limited by theoretical and computational complexities, alternatives do not possess the same advantages. Image models accommodate uncertain detection, do not require spatially independent data or a census of map units, and can be used to estimate species distributions directly from observations without relying on habitat covariates or parameters that must be estimated subjectively. These features facilitate economical surveys of large regions, the detection of temporal trends in distribution, and assessments of landscape-level relations between

  19. Markov chain Monte Carlo estimation of species distributions: A case study of the swift fox in western Kansas

    USGS Publications Warehouse

    Sargeant, G.A.; Sovada, M.A.; Slivinski, C.C.; Johnson, D.H.

    2005-01-01

    Accurate maps of species distributions are essential tools for wildlife research and conservation. Unfortunately, biologists often are forced to rely on maps derived from observed occurrences recorded opportunistically during observation periods of variable length. Spurious inferences are likely to result because such maps are profoundly affected by the duration and intensity of observation and by methods used to delineate distributions, especially when detection is uncertain. We conducted a systematic survey of swift fox (Vulpes velox) distribution in western Kansas, USA, and used Markov chain Monte Carlo (MCMC) image restoration to rectify these problems. During 1997-1999, we searched 355 townships (ca. 93 km2) 1-3 times each for an average cost of $7,315 per year and achieved a detection rate (probability of detecting swift foxes, if present, during a single search) of ?? = 0.69 (95% Bayesian confidence interval [BCI] = [0.60, 0.77]). Our analysis produced an estimate of the underlying distribution, rather than a map of observed occurrences, that reflected the uncertainty associated with estimates of model parameters. To evaluate our results, we analyzed simulated data with similar properties. Results of our simulations suggest negligible bias and good precision when probabilities of detection on ???1 survey occasions (cumulative probabilities of detection) exceed 0.65. Although the use of MCMC image restoration has been limited by theoretical and computational complexities, alternatives do not possess the same advantages. Image models accommodate uncertain detection, do not require spatially independent data or a census of map units, and can be used to estimate species distributions directly from observations without relying on habitat covariates or parameters that must be estimated subjectively. These features facilitate economical surveys of large regions, the detection of temporal trends in distribution, and assessments of landscape-level relations between

  20. Markov and semi-Markov processes as a failure rate

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Grabski, Franciszek

    2016-06-08

    In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.