Distinguishing Hidden Markov Chains
Kiefer, Stefan; Sistla, A. Prasad
2015-01-01
Hidden Markov Chains (HMCs) are commonly used mathematical models of probabilistic systems. They are employed in various fields such as speech recognition, signal processing, and biological sequence analysis. We consider the problem of distinguishing two given HMCs based on an observation sequence that one of the HMCs generates. More precisely, given two HMCs and an observation sequence, a distinguishing algorithm is expected to identify the HMC that generates the observation sequence. Two HM...
APPLICATION OF HIDDEN MARKOV CHAINS IN QUALITY CONTROL
Directory of Open Access Journals (Sweden)
Hanife DEMIRALP
2013-01-01
Full Text Available The ever growing technological innovations and sophistication in industrial processes require adequate checks on quality. Thus, there is an increasing demand for simple and efficient quality control methods. In this regard the control charts stand out in simplicity and efficiency. In this paper, we propose a method of controlling quality based on the theory of hidden Markov chains. Based on samples drawn at different times from the production process, the method obtains the state of the process probabilistically. The main advantage of the method is that it requires no assumption on the normality of the process output.
Recursive smoothers for hidden discrete-time Markov chains
Directory of Open Access Journals (Sweden)
Lakhdar Aggoun
2005-01-01
Full Text Available We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995. We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM algorithm.
Directory of Open Access Journals (Sweden)
Huilin Huang
2014-01-01
Full Text Available We study strong limit theorems for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees. We mainly establish the strong law of large numbers for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees and give the strong limit law of the conditional sample entropy rate.
Barbu, Vlad
2008-01-01
Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. This book concerns with the estimation of discrete-time semi-Markov and hidden semi-Markov processes
An Approach of Diagnosis Based On The Hidden Markov Chains Model
Directory of Open Access Journals (Sweden)
Karim Bouamrane
2008-07-01
Full Text Available Diagnosis is a key element in industrial system maintenance process performance. A diagnosis tool is proposed allowing the maintenance operators capitalizing on the knowledge of their trade and subdividing it for better performance improvement and intervention effectiveness within the maintenance process service. The Tool is based on the Markov Chain Model and more precisely the Hidden Markov Chains (HMC which has the system failures determination advantage, taking into account the causal relations, stochastic context modeling of their dynamics and providing a relevant diagnosis help by their ability of dubious information use. Since the FMEA method is a well adapted artificial intelligence field, the modeling with Markov Chains is carried out with its assistance. Recently, a dynamic programming recursive algorithm, called 'Viterbi Algorithm', is being used in the Hidden Markov Chains field. This algorithm provides as input to the HMC a set of system observed effects and generates at exit the various causes having caused the loss from one or several system functions.
Under-reported data analysis with INAR-hidden Markov chains.
Fernández-Fontelo, Amanda; Cabaña, Alejandra; Puig, Pedro; Moriña, David
2016-11-20
In this work, we deal with correlated under-reported data through INAR(1)-hidden Markov chain models. These models are very flexible and can be identified through its autocorrelation function, which has a very simple form. A naïve method of parameter estimation is proposed, jointly with the maximum likelihood method based on a revised version of the forward algorithm. The most-probable unobserved time series is reconstructed by means of the Viterbi algorithm. Several examples of application in the field of public health are discussed illustrating the utility of the models. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Partially Hidden Markov Models
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Rissanen, Jorma
1996-01-01
Partially Hidden Markov Models (PHMM) are introduced. They differ from the ordinary HMM's in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations. As an illustration they are applied to black and white image compression where...
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.
Fuzzy hidden Markov chains segmentation for volume determination and quantitation in PET
Energy Technology Data Exchange (ETDEWEB)
Hatt, M [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Lamare, F [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609, (France); Boussion, N [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Turzo, A [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Collet, C [Ecole Nationale Superieure de Physique de Strasbourg (ENSPS), ULP, Strasbourg, F-67000 (France); Salzenstein, F [Institut d' Electronique du Solide et des Systemes (InESS), ULP, Strasbourg, F-67000 (France); Roux, C [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Jarritt, P [Medical Physics Agency, Royal Victoria Hospital, Belfast (United Kingdom); Carson, K [Medical Physics Agency, Royal Victoria Hospital, Belfast (United Kingdom); Rest, C Cheze-Le [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France); Visvikis, D [INSERM U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), CHU Morvan, Bat 2bis (I3S), 5 avenue Foch, Brest, 29609 (France)
2007-07-21
Accurate volume of interest (VOI) estimation in PET is crucial in different oncology applications such as response to therapy evaluation and radiotherapy treatment planning. The objective of our study was to evaluate the performance of the proposed algorithm for automatic lesion volume delineation; namely the fuzzy hidden Markov chains (FHMC), with that of current state of the art in clinical practice threshold based techniques. As the classical hidden Markov chain (HMC) algorithm, FHMC takes into account noise, voxel intensity and spatial correlation, in order to classify a voxel as background or functional VOI. However the novelty of the fuzzy model consists of the inclusion of an estimation of imprecision, which should subsequently lead to a better modelling of the 'fuzzy' nature of the object of interest boundaries in emission tomography data. The performance of the algorithms has been assessed on both simulated and acquired datasets of the IEC phantom, covering a large range of spherical lesion sizes (from 10 to 37 mm), contrast ratios (4:1 and 8:1) and image noise levels. Both lesion activity recovery and VOI determination tasks were assessed in reconstructed images using two different voxel sizes (8 mm{sup 3} and 64 mm{sup 3}). In order to account for both the functional volume location and its size, the concept of % classification errors was introduced in the evaluation of volume segmentation using the simulated datasets. Results reveal that FHMC performs substantially better than the threshold based methodology for functional volume determination or activity concentration recovery considering a contrast ratio of 4:1 and lesion sizes of <28 mm. Furthermore differences between classification and volume estimation errors evaluated were smaller for the segmented volumes provided by the FHMC algorithm. Finally, the performance of the automatic algorithms was less susceptible to image noise levels in comparison to the threshold based techniques. The
Zipf exponent of trajectory distribution in the hidden Markov model
Bochkarev, V. V.; Lerner, E. Yu
2014-03-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.
Zipf exponent of trajectory distribution in the hidden Markov model
International Nuclear Information System (INIS)
Bochkarev, V V; Lerner, E Yu
2014-01-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different
Unifying framework for multimodal brain MRI segmentation based on Hidden Markov Chains.
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.
Markov Chains and Markov Processes
Ogunbayo, Segun
2016-01-01
Markov chain, which was named after Andrew Markov is a mathematical system that transfers a state to another state. Many real world systems contain uncertainty. This study helps us to understand the basic idea of a Markov chain and how is been useful in our daily lives. For some times there had been suspense on distinct predictions and future existences. Also in different games there had been different expectations or results involved. That is the reason why we need Markov chains to predict o...
Abdulla, Parosh Aziz; Henda, Noomene Ben; Mayr, Richard
2007-01-01
We consider qualitative and quantitative verification problems for infinite-state Markov chains. We call a Markov chain decisive w.r.t. a given set of target states F if it almost certainly eventually reaches either F or a state from which F can no longer be reached. While all finite Markov chains are trivially decisive (for every set F), this also holds for many classes of infinite Markov chains. Infinite Markov chains which contain a finite attractor are decisive w.r.t. every set F. In part...
Adaptive Partially Hidden Markov Models
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Rasmussen, Tage
1996-01-01
Partially Hidden Markov Models (PHMM) have recently been introduced. The transition and emission probabilities are conditioned on the past. In this report, the PHMM is extended with a multiple token version. The different versions of the PHMM are applied to bi-level image coding....
Context Tree Estimation in Variable Length Hidden Markov Models
Dumont, Thierry
2011-01-01
We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove that the estimator is strongly consistent. This uses information-theoretic mixture inequalities in the spirit of Finesso and Lorenzo(Consistent estimation of the order for Markov and hidden Markov chains(1990)) and E.Gassiat and S.Boucheron (Optimal error exp...
Detecting Structural Breaks using Hidden Markov Models
DEFF Research Database (Denmark)
Ntantamis, Christos
Testing for structural breaks and identifying their location is essential for econometric modeling. In this paper, a Hidden Markov Model (HMM) approach is used in order to perform these tasks. Breaks are defined as the data points where the underlying Markov Chain switches from one state to another....... The estimation of the HMM is conducted using a variant of the Iterative Conditional Expectation-Generalized Mixture (ICE-GEMI) algorithm proposed by Delignon et al. (1997), that permits analysis of the conditional distributions of economic data and allows for different functional forms across regimes...
DEFF Research Database (Denmark)
Justesen, Jørn
2005-01-01
A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly.......A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly....
janssen, Anja; Segers, Johan
2013-01-01
The extremes of a univariate Markov chain with regularly varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper we extend this fact to Markov chains with multivariate regularly varying marginal distributions in Rd. We analyze both the forward and the backward tail process and show that they mutually determine each other through a kind of adjoint relation. In ...
Pruning Boltzmann networks and hidden Markov models
DEFF Research Database (Denmark)
Pedersen, Morten With; Stork, D.
1996-01-01
We present sensitivity-based pruning algorithms for general Boltzmann networks. Central to our methods is the efficient calculation of a second-order approximation to the true weight saliencies in a cross-entropy error. Building upon previous work which shows a formal correspondence between linear...... Boltzmann chains and hidden Markov models (HMMs), we argue that our method can be applied to HMMs as well. We illustrate pruning on Boltzmann zippers, which are equivalent to two HMMs with cross-connection links. We verify that our second-order approximation preserves the rank ordering of weight saliencies...
Directory of Open Access Journals (Sweden)
Persson Bengt
2010-10-01
Full Text Available Abstract Background The Medium-chain Dehydrogenases/Reductases (MDR form a protein superfamily whose size and complexity defeats traditional means of subclassification; it currently has over 15000 members in the databases, the pairwise sequence identity is typically around 25%, there are members from all kingdoms of life, the chain-lengths vary as does the oligomericity, and the members are partaking in a multitude of biological processes. There are profile hidden Markov models (HMMs available for detecting MDR superfamily members, but none for determining which MDR family each protein belongs to. The current torrential influx of new sequence data enables elucidation of more and more protein families, and at an increasingly fine granularity. However, gathering good quality training data usually requires manual attention by experts and has therefore been the rate limiting step for expanding the number of available models. Results We have developed an automated algorithm for HMM refinement that produces stable and reliable models for protein families. This algorithm uses relationships found in data to generate confident seed sets. Using this algorithm we have produced HMMs for 86 distinct MDR families and 34 of their subfamilies which can be used in automated annotation of new sequences. We find that MDR forms with 2 Zn2+ ions in general are dehydrogenases, while MDR forms with no Zn2+ in general are reductases. Furthermore, in Bacteria MDRs without Zn2+ are more frequent than those with Zn2+, while the opposite is true for eukaryotic MDRs, indicating that Zn2+ has been recruited into the MDR superfamily after the initial life kingdom separations. We have also developed a web site http://mdr-enzymes.org that provides textual and numeric search against various characterised MDR family properties, as well as sequence scan functions for reliable classification of novel MDR sequences. Conclusions Our method of refinement can be readily applied to
Markov processes and controlled Markov chains
Filar, Jerzy; Chen, Anyue
2002-01-01
The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South Ameri...
Directory of Open Access Journals (Sweden)
Andrey Borisovich Nikolaev
2017-05-01
Full Text Available In this article a statistical analysis of supply volumes of spare parts, components and accessories was carried out, with some persistent patterns and laws of distribution of failures of major components revealed. There are suggested evaluation models of components and assemblies reliability for the formation of order management procedures of spare parts, components and accessories for the maintenance and repair of transport and technological machines. For the purpose of identification of components operational condition there is proposed a model of hidden Markov chain which allows to classify the condition by indirect evidence, based on the collected statistics.
Hartfiel, Darald J
1998-01-01
In this study extending classical Markov chain theory to handle fluctuating transition matrices, the author develops a theory of Markov set-chains and provides numerous examples showing how that theory can be applied. Chapters are concluded with a discussion of related research. Readers who can benefit from this monograph are those interested in, or involved with, systems whose data is imprecise or that fluctuate with time. A background equivalent to a course in linear algebra and one in probability theory should be sufficient.
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.
Indian Academy of Sciences (India)
be obtained as a limiting value of a sample path of a suitable ... makes a mathematical model of chance and deals with the problem by .... Is the Markov chain aperiodic? It is! Here is how you can see it. Suppose that after you do the cut, you hold the top half in your right hand, and the bottom half in your left. Then there.
Solan, Eilon; Vieille, Nicolas
2015-01-01
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 3. Markov Chain Monte Carlo - Examples. Arnab Chakraborty. General Article Volume 7 Issue 3 March 2002 pp 25-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/007/03/0025-0034. Keywords.
Process Algebra and Markov Chains
Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Process algebra and Markov chains
Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.
2001-01-01
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Fitting Hidden Markov Models to Psychological Data
Directory of Open Access Journals (Sweden)
Ingmar Visser
2002-01-01
Full Text Available Markov models have been used extensively in psychology of learning. Applications of hidden Markov models are rare however. This is partially due to the fact that comprehensive statistics for model selection and model assessment are lacking in the psychological literature. We present model selection and model assessment statistics that are particularly useful in applying hidden Markov models in psychology. These statistics are presented and evaluated by simulation studies for a toy example. We compare AIC, BIC and related criteria and introduce a prediction error measure for assessing goodness-of-fit. In a simulation study, two methods of fitting equality constraints are compared. In two illustrative examples with experimental data we apply selection criteria, fit models with constraints and assess goodness-of-fit. First, data from a concept identification task is analyzed. Hidden Markov models provide a flexible approach to analyzing such data when compared to other modeling methods. Second, a novel application of hidden Markov models in implicit learning is presented. Hidden Markov models are used in this context to quantify knowledge that subjects express in an implicit learning task. This method of analyzing implicit learning data provides a comprehensive approach for addressing important theoretical issues in the field.
Coding with partially hidden Markov models
DEFF Research Database (Denmark)
Forchhammer, Søren; Rissanen, J.
1995-01-01
Partially hidden Markov models (PHMM) are introduced. They are a variation of the hidden Markov models (HMM) combining the power of explicit conditioning on past observations and the power of using hidden states. (P)HMM may be combined with arithmetic coding for lossless data compression. A general...... 2-part coding scheme for given model order but unknown parameters based on PHMM is presented. A forward-backward reestimation of parameters with a redefined backward variable is given for these models and used for estimating the unknown parameters. Proof of convergence of this reestimation is given....... The PHMM structure and the conditions of the convergence proof allows for application of the PHMM to image coding. Relations between the PHMM and hidden Markov models (HMM) are treated. Results of coding bi-level images with the PHMM coding scheme is given. The results indicate that the PHMM can adapt...
Ragain, Stephen; Ugander, Johan
2016-01-01
As datasets capturing human choices grow in richness and scale---particularly in online domains---there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume any of the above axioms while still satisfying the foundational axiom of uniform expansio...
Approximate quantum Markov chains
Sutter, David
2018-01-01
This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...
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.
Mallak, Saed
1996-01-01
Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent University, 1996. Thesis (Master's) -- Bilkent University, 1996. Includes bibliographical references leaves leaf 29 In thi.s work, we studierl the Ergodicilv of Non-Stationary .Markov chains. We gave several e.xainples with different cases. We proved that given a sec[uence of Markov chains such that the limit of this sec|uence is an Ergodic Markov chain, then the limit of the combination ...
Markov Chain Monte Carlo Methods
Indian Academy of Sciences (India)
Keywords. Markov chain; state space; stationary transition probability; stationary distribution; irreducibility; aperiodicity; stationarity; M-H algorithm; proposal distribution; acceptance probability; image processing; Gibbs sampler.
Hidden Markov Models for Human Genes
DEFF Research Database (Denmark)
Baldi, Pierre; Brunak, Søren; Chauvin, Yves
1997-01-01
We analyse the sequential structure of human genomic DNA by hidden Markov models. We apply models of widely different design: conventional left-right constructs and models with a built-in periodic architecture. The models are trained on segments of DNA sequences extracted such that they cover com...
Hidden Markov models for labeled sequences
DEFF Research Database (Denmark)
Krogh, Anders Stærmose
1994-01-01
A hidden Markov model for labeled observations, called a class HMM, is introduced and a maximum likelihood method is developed for estimating the parameters of the model. Instead of training it to model the statistics of the training sequences it is trained to optimize recognition. It resembles MMI...
Multivariate longitudinal data analysis with mixed effects hidden Markov models.
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.
International Nuclear Information System (INIS)
Floriani, Elena; Lima, Ricardo; Ourrad, Ouerdia; Spinelli, Lionel
2016-01-01
Highlights: • The flux through a Markov chain of a conserved quantity (mass) is studied. • Mass is supplied by an external source and ends in the absorbing states of the chain. • Meaningful for modeling open systems whose dynamics has a Markov property. • The analytical expression of mass distribution is given for a constant source. • The expression of mass distribution is given for periodic or random sources. - Abstract: In this paper we study the flux through a finite Markov chain of a quantity, that we will call mass, which moves through the states of the chain according to the Markov transition probabilities. Mass is supplied by an external source and accumulates in the absorbing states of the chain. We believe that studying how this conserved quantity evolves through the transient (non-absorbing) states of the chain could be useful for the modelization of open systems whose dynamics has a Markov property.
Hidden Markov models applied to a subsequence of the Xylella fastidiosa genome
Directory of Open Access Journals (Sweden)
Silva Cibele Q. da
2003-01-01
Full Text Available Dependencies in DNA sequences are frequently modeled using Markov models. However, Markov chains cannot account for heterogeneity that may be present in different regions of the same DNA sequence. Hidden Markov models are more realistic than Markov models since they allow for the identification of heterogeneous regions of a DNA sequence. In this study we present an application of hidden Markov models to a subsequence of the Xylella fastidiosa DNA data. We found that a three-state model provides a good description for the data considered.
Regeneration and general Markov chains
Directory of Open Access Journals (Sweden)
Vladimir V. Kalashnikov
1994-01-01
Full Text Available Ergodicity, continuity, finite approximations and rare visits of general Markov chains are investigated. The obtained results permit further quantitative analysis of characteristics, such as, rates of convergence, continuity (measured as a distance between perturbed and non-perturbed characteristics, deviations between Markov chains, accuracy of approximations and bounds on the distribution function of the first visit time to a chosen subset, etc. The underlying techniques use the embedding of the general Markov chain into a wide sense regenerative process with the help of splitting construction.
Markov chains theory and applications
Sericola, Bruno
2013-01-01
Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
Prediction of Annual Rainfall Pattern Using Hidden Markov Model ...
African Journals Online (AJOL)
ADOWIE PERE
Hidden Markov model is very influential in stochastic world because of its ... the earth from the clouds. The usual ... Rainfall modelling and ... Markov Models have become popular tools ... environment sciences, University of Jos, plateau state,.
Exact solution of the hidden Markov processes
Saakian, David B.
2017-11-01
We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .
Evolving the structure of hidden Markov Models
DEFF Research Database (Denmark)
won, K. J.; Prugel-Bennett, A.; Krogh, A.
2006-01-01
A genetic algorithm (GA) is proposed for finding the structure of hidden Markov Models (HMMs) used for biological sequence analysis. The GA is designed to preserve biologically meaningful building blocks. The search through the space of HMM structures is combined with optimization of the emission...... and transition probabilities using the classic Baum-Welch algorithm. The system is tested on the problem of finding the promoter and coding region of C. jejuni. The resulting HMM has a superior discrimination ability to a handcrafted model that has been published in the literature....
Genetic Algorithms Principles Towards Hidden Markov Model
Directory of Open Access Journals (Sweden)
Nabil M. Hewahi
2011-10-01
Full Text Available In this paper we propose a general approach based on Genetic Algorithms (GAs to evolve Hidden Markov Models (HMM. The problem appears when experts assign probability values for HMM, they use only some limited inputs. The assigned probability values might not be accurate to serve in other cases related to the same domain. We introduce an approach based on GAs to find
out the suitable probability values for the HMM to be mostly correct in more cases than what have been used to assign the probability values.
Epitope discovery with phylogenetic hidden Markov models.
LENUS (Irish Health Repository)
Lacerda, Miguel
2010-05-01
Existing methods for the prediction of immunologically active T-cell epitopes are based on the amino acid sequence or structure of pathogen proteins. Additional information regarding the locations of epitopes may be acquired by considering the evolution of viruses in hosts with different immune backgrounds. In particular, immune-dependent evolutionary patterns at sites within or near T-cell epitopes can be used to enhance epitope identification. We have developed a mutation-selection model of T-cell epitope evolution that allows the human leukocyte antigen (HLA) genotype of the host to influence the evolutionary process. This is one of the first examples of the incorporation of environmental parameters into a phylogenetic model and has many other potential applications where the selection pressures exerted on an organism can be related directly to environmental factors. We combine this novel evolutionary model with a hidden Markov model to identify contiguous amino acid positions that appear to evolve under immune pressure in the presence of specific host immune alleles and that therefore represent potential epitopes. This phylogenetic hidden Markov model provides a rigorous probabilistic framework that can be combined with sequence or structural information to improve epitope prediction. As a demonstration, we apply the model to a data set of HIV-1 protein-coding sequences and host HLA genotypes.
Hidden Markov Model Application to Transfer The Trader Online Forex Brokers
Directory of Open Access Journals (Sweden)
Farida Suharleni
2012-05-01
Full Text Available Hidden Markov Model is elaboration of Markov chain, which is applicable to cases that can’t directly observe. In this research, Hidden Markov Model is used to know trader’s transition to broker forex online. In Hidden Markov Model, observed state is observable part and hidden state is hidden part. Hidden Markov Model allows modeling system that contains interrelated observed state and hidden state. As observed state in trader’s transition to broker forex online is category 1, category 2, category 3, category 4, category 5 by condition of every broker forex online, whereas as hidden state is broker forex online Marketiva, Masterforex, Instaforex, FBS and Others. First step on application of Hidden Markov Model in this research is making construction model by making a probability of transition matrix (A from every broker forex online. Next step is making a probability of observation matrix (B by making conditional probability of five categories, that is category 1, category 2, category 3, category 4, category 5 by condition of every broker forex online and also need to determine an initial state probability (π from every broker forex online. The last step is using Viterbi algorithm to find hidden state sequences that is broker forex online sequences which is the most possible based on model and observed state that is the five categories. Application of Hidden Markov Model is done by making program with Viterbi algorithm using Delphi 7.0 software with observed state based on simulation data. Example: By the number of observation T = 5 and observed state sequences O = (2,4,3,5,1 is found hidden state sequences which the most possible with observed state O as following : where X1 = FBS, X2 = Masterforex, X3 = Marketiva, X4 = Others, and X5 = Instaforex.
Fannes, Mark; Wouters, Jeroen
2012-01-01
We study a quantum process that can be considered as a quantum analogue for the classical Markov process. We specifically construct a version of these processes for free Fermions. For such free Fermionic processes we calculate the entropy density. This can be done either directly using Szeg\\"o's theorem for asymptotic densities of functions of Toeplitz matrices, or through an extension of said theorem to rates of functions, which we present in this article.
An introduction to hidden Markov models for biological sequences
DEFF Research Database (Denmark)
Krogh, Anders Stærmose
1998-01-01
A non-matematical tutorial on hidden Markov models (HMMs) plus a description of one of the applications of HMMs: gene finding.......A non-matematical tutorial on hidden Markov models (HMMs) plus a description of one of the applications of HMMs: gene finding....
Asymptotics for Estimating Equations in Hidden Markov Models
DEFF Research Database (Denmark)
Hansen, Jørgen Vinsløv; Jensen, Jens Ledet
Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...
Markov chains and mixing times
Levin, David A; Wilmer, Elizabeth L
2009-01-01
This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of r
Neuroevolution Mechanism for Hidden Markov Model
Directory of Open Access Journals (Sweden)
Nabil M. Hewahi
2011-12-01
Full Text Available Hidden Markov Model (HMM is a statistical model based on probabilities. HMM is becoming one of the major models involved in many applications such as natural language
processing, handwritten recognition, image processing, prediction systems and many more. In this research we are concerned with finding out the best HMM for a certain application domain. We propose a neuroevolution process that is based first on converting the HMM to a neural network, then generating many neural networks at random where each represents a HMM. We proceed by
applying genetic operators to obtain new set of neural networks where each represents HMMs, and updating the population. Finally select the best neural network based on a fitness function.
Improved hidden Markov model for nosocomial infections.
Khader, Karim; Leecaster, Molly; Greene, Tom; Samore, Matthew; Thomas, Alun
2014-12-01
We propose a novel hidden Markov model (HMM) for parameter estimation in hospital transmission models, and show that commonly made simplifying assumptions can lead to severe model misspecification and poor parameter estimates. A standard HMM that embodies two commonly made simplifying assumptions, namely a fixed patient count and binomially distributed detections is compared with a new alternative HMM that does not require these simplifying assumptions. Using simulated data, we demonstrate how each of the simplifying assumptions used by the standard model leads to model misspecification, whereas the alternative model results in accurate parameter estimates. © The Authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
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.
Hidden Markov Model for Stock Selection
Directory of Open Access Journals (Sweden)
Nguyet Nguyen
2015-10-01
Full Text Available The hidden Markov model (HMM is typically used to predict the hidden regimes of observation data. Therefore, this model finds applications in many different areas, such as speech recognition systems, computational molecular biology and financial market predictions. In this paper, we use HMM for stock selection. We first use HMM to make monthly regime predictions for the four macroeconomic variables: inflation (consumer price index (CPI, industrial production index (INDPRO, stock market index (S&P 500 and market volatility (VIX. At the end of each month, we calibrate HMM’s parameters for each of these economic variables and predict its regimes for the next month. We then look back into historical data to find the time periods for which the four variables had similar regimes with the forecasted regimes. Within those similar periods, we analyze all of the S&P 500 stocks to identify which stock characteristics have been well rewarded during the time periods and assign scores and corresponding weights for each of the stock characteristics. A composite score of each stock is calculated based on the scores and weights of its features. Based on this algorithm, we choose the 50 top ranking stocks to buy. We compare the performances of the portfolio with the benchmark index, S&P 500. With an initial investment of $100 in December 1999, over 15 years, in December 2014, our portfolio had an average gain per annum of 14.9% versus 2.3% for the S&P 500.
Markov chains and mixing times
Levin, David A
2017-01-01
Markov Chains and Mixing Times is a magical book, managing to be both friendly and deep. It gently introduces probabilistic techniques so that an outsider can follow. At the same time, it is the first book covering the geometric theory of Markov chains and has much that will be new to experts. It is certainly THE book that I will use to teach from. I recommend it to all comers, an amazing achievement. -Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University Mixing times are an active research topic within many fields from statistical physics to the theory of algorithms, as well as having intrinsic interest within mathematical probability and exploiting discrete analogs of important geometry concepts. The first edition became an instant classic, being accessible to advanced undergraduates and yet bringing readers close to current research frontiers. This second edition adds chapters on monotone chains, the exclusion process and hitting time parameters. Having both exercises...
Consistency and refinement for Interval Markov Chains
DEFF Research Database (Denmark)
Delahaye, Benoit; Larsen, Kim Guldstrand; Legay, Axel
2012-01-01
Interval Markov Chains (IMC), or Markov Chains with probability intervals in the transition matrix, are the base of a classic specification theory for probabilistic systems [18]. The standard semantics of IMCs assigns to a specification the set of all Markov Chains that satisfy its interval...
Markov Chain Ontology Analysis (MCOA).
Frost, H Robert; McCray, Alexa T
2012-02-03
Biomedical ontologies have become an increasingly critical lens through which researchers analyze the genomic, clinical and bibliographic data that fuels scientific research. Of particular relevance are methods, such as enrichment analysis, that quantify the importance of ontology classes relative to a collection of domain data. Current analytical techniques, however, remain limited in their ability to handle many important types of structural complexity encountered in real biological systems including class overlaps, continuously valued data, inter-instance relationships, non-hierarchical relationships between classes, semantic distance and sparse data. In this paper, we describe a methodology called Markov Chain Ontology Analysis (MCOA) and illustrate its use through a MCOA-based enrichment analysis application based on a generative model of gene activation. MCOA models the classes in an ontology, the instances from an associated dataset and all directional inter-class, class-to-instance and inter-instance relationships as a single finite ergodic Markov chain. The adjusted transition probability matrix for this Markov chain enables the calculation of eigenvector values that quantify the importance of each ontology class relative to other classes and the associated data set members. On both controlled Gene Ontology (GO) data sets created with Escherichia coli, Drosophila melanogaster and Homo sapiens annotations and real gene expression data extracted from the Gene Expression Omnibus (GEO), the MCOA enrichment analysis approach provides the best performance of comparable state-of-the-art methods. A methodology based on Markov chain models and network analytic metrics can help detect the relevant signal within large, highly interdependent and noisy data sets and, for applications such as enrichment analysis, has been shown to generate superior performance on both real and simulated data relative to existing state-of-the-art approaches.
Optimisation of Hidden Markov Model using Baum–Welch algorithm ...
Indian Academy of Sciences (India)
The present work is a part of development of Hidden Markov Model. (HMM) based ... the Himalaya. In this work, HMMs have been developed for forecasting of maximum and minimum ..... data collection teams of Snow and Avalanche Study.
A Novel Method for Decoding Any High-Order Hidden Markov Model
Directory of Open Access Journals (Sweden)
Fei Ye
2014-01-01
Full Text Available This paper proposes a novel method for decoding any high-order hidden Markov model. First, the high-order hidden Markov model is transformed into an equivalent first-order hidden Markov model by Hadar’s transformation. Next, the optimal state sequence of the equivalent first-order hidden Markov model is recognized by the existing Viterbi algorithm of the first-order hidden Markov model. Finally, the optimal state sequence of the high-order hidden Markov model is inferred from the optimal state sequence of the equivalent first-order hidden Markov model. This method provides a unified algorithm framework for decoding hidden Markov models including the first-order hidden Markov model and any high-order hidden Markov model.
Using hidden Markov models to align multiple sequences.
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.
Hidden Markov models in automatic speech recognition
Wrzoskowicz, Adam
1993-11-01
This article describes a method for constructing an automatic speech recognition system based on hidden Markov models (HMMs). The author discusses the basic concepts of HMM theory and the application of these models to the analysis and recognition of speech signals. The author provides algorithms which make it possible to train the ASR system and recognize signals on the basis of distinct stochastic models of selected speech sound classes. The author describes the specific components of the system and the procedures used to model and recognize speech. The author discusses problems associated with the choice of optimal signal detection and parameterization characteristics and their effect on the performance of the system. The author presents different options for the choice of speech signal segments and their consequences for the ASR process. The author gives special attention to the use of lexical, syntactic, and semantic information for the purpose of improving the quality and efficiency of the system. The author also describes an ASR system developed by the Speech Acoustics Laboratory of the IBPT PAS. The author discusses the results of experiments on the effect of noise on the performance of the ASR system and describes methods of constructing HMM's designed to operate in a noisy environment. The author also describes a language for human-robot communications which was defined as a complex multilevel network from an HMM model of speech sounds geared towards Polish inflections. The author also added mandatory lexical and syntactic rules to the system for its communications vocabulary.
Spectral methods for quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Szehr, Oleg
2014-05-08
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Spectral methods for quantum Markov chains
International Nuclear Information System (INIS)
Szehr, Oleg
2014-01-01
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelli; Robert, Philippe
2012-01-01
If ($C_n$) a Markov chain on a discrete state space $S$, a Markov chain ($C_n, M_n$) on the product space $S \\times S$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain behaves like the original Markov chain and the second component changes only when both
Verification of Open Interactive Markov Chains
Brazdil, Tomas; Hermanns, Holger; Krcal, Jan; Kretinsky, Jan; Rehak, Vojtech
2012-01-01
Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation....
Application of Hidden Markov Models in Biomolecular Simulations.
Shukla, Saurabh; Shamsi, Zahra; Moffett, Alexander S; Selvam, Balaji; Shukla, Diwakar
2017-01-01
Hidden Markov models (HMMs) provide a framework to analyze large trajectories of biomolecular simulation datasets. HMMs decompose the conformational space of a biological molecule into finite number of states that interconvert among each other with certain rates. HMMs simplify long timescale trajectories for human comprehension, and allow comparison of simulations with experimental data. In this chapter, we provide an overview of building HMMs for analyzing bimolecular simulation datasets. We demonstrate the procedure for building a Hidden Markov model for Met-enkephalin peptide simulation dataset and compare the timescales of the process.
Detecting Faults By Use Of Hidden Markov Models
Smyth, Padhraic J.
1995-01-01
Frequency of false alarms reduced. Faults in complicated dynamic system (e.g., antenna-aiming system, telecommunication network, or human heart) detected automatically by method of automated, continuous monitoring. Obtains time-series data by sampling multiple sensor outputs at discrete intervals of t and processes data via algorithm determining whether system in normal or faulty state. Algorithm implements, among other things, hidden first-order temporal Markov model of states of system. Mathematical model of dynamics of system not needed. Present method is "prior" method mentioned in "Improved Hidden-Markov-Model Method of Detecting Faults" (NPO-18982).
Quantum Markov Chain Mixing and Dissipative Engineering
DEFF Research Database (Denmark)
Kastoryano, Michael James
2012-01-01
This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state...... of the system at the present point in time, but not on the history of events. Very many important processes in nature are of this type, therefore a good understanding of their behaviour has turned out to be very fruitful for science. Markov chains always have a non-empty set of limiting distributions...... (stationary states). The aim of Markov chain mixing is to obtain (upper and/or lower) bounds on the number of steps it takes for the Markov chain to reach a stationary state. The natural quantum extensions of these notions are density matrices and quantum channels. We set out to develop a general mathematical...
A Constraint Model for Constrained Hidden Markov Models
DEFF Research Database (Denmark)
Christiansen, Henning; Have, Christian Theil; Lassen, Ole Torp
2009-01-01
A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we extend HMMs with constraints and show how the familiar Viterbi algorithm can be generalized, based on constraint solving ...
Optimisation of Hidden Markov Model using Baum–Welch algorithm
Indian Academy of Sciences (India)
Home; Journals; Journal of Earth System Science; Volume 126; Issue 1. Optimisation of Hidden Markov Model using Baum–Welch algorithm for prediction of maximum and minimum temperature over Indian Himalaya. J C Joshi Tankeshwar Kumar Sunita Srivastava Divya Sachdeva. Volume 126 Issue 1 February 2017 ...
Hidden Markov Model for quantitative prediction of snowfall
Indian Academy of Sciences (India)
A Hidden Markov Model (HMM) has been developed for prediction of quantitative snowfall in Pir-Panjal and Great Himalayan mountain ranges of Indian Himalaya. The model predicts snowfall for two days in advance using daily recorded nine meteorological variables of past 20 winters from 1992–2012. There are six ...
Book Review: "Hidden Markov Models for Time Series: An ...
African Journals Online (AJOL)
Hidden Markov Models for Time Series: An Introduction using R. by Walter Zucchini and Iain L. MacDonald. Chapman & Hall (CRC Press), 2009. Full Text: EMAIL FULL TEXT EMAIL FULL TEXT · DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT · http://dx.doi.org/10.4314/saaj.v10i1.61717 · AJOL African Journals Online.
KMEANS CLUSTERING FOR HIDDEN MARKOV MODEL
Perrone, M.P.; Connell, S.D.
2004-01-01
An unsupervised kmeans clustering algorithm for hidden Markov models is described and applied to the task of generating subclass models for individual handwritten character classes. The algorithm is compared to a related clustering method and shown to give a relative change in the error rate of as
Optimal Number of States in Hidden Markov Models and its ...
African Journals Online (AJOL)
In this paper, Hidden Markov Model is applied to model human movements as to facilitate an automatic detection of the same. A number of activities were simulated with the help of two persons. The four movements considered are walking, sitting down-getting up, fall while walking and fall while standing. The data is ...
Markov chains models, algorithms and applications
Ching, Wai-Ki; Ng, Michael K; Siu, Tak-Kuen
2013-01-01
This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods
Markov chains analytic and Monte Carlo computations
Graham, Carl
2014-01-01
Markov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features: Numerous exercises with solutions as well as extended case studies.A detailed and rigorous presentation of Markov chains with discrete time and state space.An appendix presenting probabilistic notions that are nec
Adaptive Markov Chain Monte Carlo
Jadoon, Khan
2016-08-08
A substantial interpretation of electromagnetic induction (EMI) measurements requires quantifying optimal model parameters and uncertainty of a nonlinear inverse problem. For this purpose, an adaptive Bayesian Markov chain Monte Carlo (MCMC) algorithm is used to assess multi-orientation and multi-offset EMI measurements in an agriculture field with non-saline and saline soil. In the MCMC simulations, posterior distribution was computed using Bayes rule. The electromagnetic forward model based on the full solution of Maxwell\\'s equations was used to simulate the apparent electrical conductivity measured with the configurations of EMI instrument, the CMD mini-Explorer. The model parameters and uncertainty for the three-layered earth model are investigated by using synthetic data. Our results show that in the scenario of non-saline soil, the parameters of layer thickness are not well estimated as compared to layers electrical conductivity because layer thicknesses in the model exhibits a low sensitivity to the EMI measurements, and is hence difficult to resolve. Application of the proposed MCMC based inversion to the field measurements in a drip irrigation system demonstrate that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil, and provide useful insight about parameter uncertainty for the assessment of the model outputs.
A hidden markov model derived structural alphabet for proteins.
Camproux, A C; Gautier, R; Tufféry, P
2004-06-04
Understanding and predicting protein structures depends on the complexity and the accuracy of the models used to represent them. We have set up a hidden Markov model that discretizes protein backbone conformation as series of overlapping fragments (states) of four residues length. This approach learns simultaneously the geometry of the states and their connections. We obtain, using a statistical criterion, an optimal systematic decomposition of the conformational variability of the protein peptidic chain in 27 states with strong connection logic. This result is stable over different protein sets. Our model fits well the previous knowledge related to protein architecture organisation and seems able to grab some subtle details of protein organisation, such as helix sub-level organisation schemes. Taking into account the dependence between the states results in a description of local protein structure of low complexity. On an average, the model makes use of only 8.3 states among 27 to describe each position of a protein structure. Although we use short fragments, the learning process on entire protein conformations captures the logic of the assembly on a larger scale. Using such a model, the structure of proteins can be reconstructed with an average accuracy close to 1.1A root-mean-square deviation and for a complexity of only 3. Finally, we also observe that sequence specificity increases with the number of states of the structural alphabet. Such models can constitute a very relevant approach to the analysis of protein architecture in particular for protein structure prediction.
A Bayesian model for binary Markov chains
Directory of Open Access Journals (Sweden)
Belkheir Essebbar
2004-02-01
Full Text Available This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.
Transition Effect Matrices and Quantum Markov Chains
Gudder, Stan
2009-06-01
A transition effect matrix (TEM) is a quantum generalization of a classical stochastic matrix. By employing a TEM we obtain a quantum generalization of a classical Markov chain. We first discuss state and operator dynamics for a quantum Markov chain. We then consider various types of TEMs and vector states. In particular, we study invariant, equilibrium and singular vector states and investigate projective, bistochastic, invertible and unitary TEMs.
Hidden Markov processes theory and applications to biology
Vidyasagar, M
2014-01-01
This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. The book starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are t
Markov Chain Monte Carlo Methods
Indian Academy of Sciences (India)
Systat Software Asia-Pacific. Ltd., in Bangalore, where the technical work for the development of the statistical software Systat takes ... In Part 4, we discuss some applications of the Markov ... one can construct the joint probability distribution of.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelli; Robert, Philippe
Motivated by an original on-line page-ranking algorithm, starting from an arbitrary Markov chain $(C_n)$ on a discrete state space ${\\cal S}$, a Markov chain $(C_n,M_n)$ on the product space ${\\cal S}^2$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain
Inference with constrained hidden Markov models in PRISM
DEFF Research Database (Denmark)
Christiansen, Henning; Have, Christian Theil; Lassen, Ole Torp
2010-01-01
A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we show how HMMs can be extended with side-constraints and present constraint solving techniques for efficient inference. De......_different are integrated. We experimentally validate our approach on the biologically motivated problem of global pairwise alignment.......A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we show how HMMs can be extended with side-constraints and present constraint solving techniques for efficient inference...
HMMEditor: a visual editing tool for profile hidden Markov model
Directory of Open Access Journals (Sweden)
Cheng Jianlin
2008-03-01
Full Text Available Abstract Background Profile Hidden Markov Model (HMM is a powerful statistical model to represent a family of DNA, RNA, and protein sequences. Profile HMM has been widely used in bioinformatics research such as sequence alignment, gene structure prediction, motif identification, protein structure prediction, and biological database search. However, few comprehensive, visual editing tools for profile HMM are publicly available. Results We develop a visual editor for profile Hidden Markov Models (HMMEditor. HMMEditor can visualize the profile HMM architecture, transition probabilities, and emission probabilities. Moreover, it provides functions to edit and save HMM and parameters. Furthermore, HMMEditor allows users to align a sequence against the profile HMM and to visualize the corresponding Viterbi path. Conclusion HMMEditor provides a set of unique functions to visualize and edit a profile HMM. It is a useful tool for biological sequence analysis and modeling. Both HMMEditor software and web service are freely available.
Hidden Markov models: the best models for forager movements?
Joo, Rocio; Bertrand, Sophie; Tam, Jorge; Fablet, Ronan
2013-01-01
One major challenge in the emerging field of movement ecology is the inference of behavioural modes from movement patterns. This has been mainly addressed through Hidden Markov models (HMMs). We propose here to evaluate two sets of alternative and state-of-the-art modelling approaches. First, we consider hidden semi-Markov models (HSMMs). They may better represent the behavioural dynamics of foragers since they explicitly model the duration of the behavioural modes. Second, we consider discriminative models which state the inference of behavioural modes as a classification issue, and may take better advantage of multivariate and non linear combinations of movement pattern descriptors. For this work, we use a dataset of >200 trips from human foragers, Peruvian fishermen targeting anchovy. Their movements were recorded through a Vessel Monitoring System (∼1 record per hour), while their behavioural modes (fishing, searching and cruising) were reported by on-board observers. We compare the efficiency of hidden Markov, hidden semi-Markov, and three discriminative models (random forests, artificial neural networks and support vector machines) for inferring the fishermen behavioural modes, using a cross-validation procedure. HSMMs show the highest accuracy (80%), significantly outperforming HMMs and discriminative models. Simulations show that data with higher temporal resolution, HSMMs reach nearly 100% of accuracy. Our results demonstrate to what extent the sequential nature of movement is critical for accurately inferring behavioural modes from a trajectory and we strongly recommend the use of HSMMs for such purpose. In addition, this work opens perspectives on the use of hybrid HSMM-discriminative models, where a discriminative setting for the observation process of HSMMs could greatly improve inference performance.
Hidden Markov models: the best models for forager movements?
Directory of Open Access Journals (Sweden)
Rocio Joo
Full Text Available One major challenge in the emerging field of movement ecology is the inference of behavioural modes from movement patterns. This has been mainly addressed through Hidden Markov models (HMMs. We propose here to evaluate two sets of alternative and state-of-the-art modelling approaches. First, we consider hidden semi-Markov models (HSMMs. They may better represent the behavioural dynamics of foragers since they explicitly model the duration of the behavioural modes. Second, we consider discriminative models which state the inference of behavioural modes as a classification issue, and may take better advantage of multivariate and non linear combinations of movement pattern descriptors. For this work, we use a dataset of >200 trips from human foragers, Peruvian fishermen targeting anchovy. Their movements were recorded through a Vessel Monitoring System (∼1 record per hour, while their behavioural modes (fishing, searching and cruising were reported by on-board observers. We compare the efficiency of hidden Markov, hidden semi-Markov, and three discriminative models (random forests, artificial neural networks and support vector machines for inferring the fishermen behavioural modes, using a cross-validation procedure. HSMMs show the highest accuracy (80%, significantly outperforming HMMs and discriminative models. Simulations show that data with higher temporal resolution, HSMMs reach nearly 100% of accuracy. Our results demonstrate to what extent the sequential nature of movement is critical for accurately inferring behavioural modes from a trajectory and we strongly recommend the use of HSMMs for such purpose. In addition, this work opens perspectives on the use of hybrid HSMM-discriminative models, where a discriminative setting for the observation process of HSMMs could greatly improve inference performance.
Analysis of a quantum Markov chain
International Nuclear Information System (INIS)
Marbeau, J.; Gudder, S.
1990-01-01
A quantum chain is analogous to a classical stationary Markov chain except that the probability measure is replaced by a complex amplitude measure and the transition probability matrix is replaced by a transition amplitude matrix. After considering the general situation, we study a particular example of a quantum chain whose transition amplitude matrix has the form of a Dirichlet matrix. Such matrices generate a discrete analog of the usual continuum Feynman amplitude. We then compute the probability distribution for these quantum chains
Deviney, Frank A.; Rice, Karen; Brown, Donald E.
2012-01-01
Natural resource managers require information concerning the frequency, duration, and long-term probability of occurrence of water-quality indicator (WQI) violations of defined thresholds. The timing of these threshold crossings often is hidden from the observer, who is restricted to relatively infrequent observations. Here, a model for the hidden process is linked with a model for the observations, and the parameters describing duration, return period, and long-term probability of occurrence are estimated using Bayesian methods. A simulation experiment is performed to evaluate the approach under scenarios based on the equivalent of a total monitoring period of 5-30 years and an observation frequency of 1-50 observations per year. Given constant threshold crossing rate, accuracy and precision of parameter estimates increased with longer total monitoring period and more-frequent observations. Given fixed monitoring period and observation frequency, accuracy and precision of parameter estimates increased with longer times between threshold crossings. For most cases where the long-term probability of being in violation is greater than 0.10, it was determined that at least 600 observations are needed to achieve precise estimates. An application of the approach is presented using 22 years of quasi-weekly observations of acid-neutralizing capacity from Deep Run, a stream in Shenandoah National Park, Virginia. The time series also was sub-sampled to simulate monthly and semi-monthly sampling protocols. Estimates of the long-term probability of violation were unbiased despite sampling frequency; however, the expected duration and return period were over-estimated using the sub-sampled time series with respect to the full quasi-weekly time series.
Observation uncertainty in reversible Markov chains.
Metzner, Philipp; Weber, Marcus; Schütte, Christof
2010-09-01
In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .
Directory of Open Access Journals (Sweden)
Jean B. Lasserre
2000-01-01
Full Text Available We consider the class of Markov kernels for which the weak or strong Feller property fails to hold at some discontinuity set. We provide a simple necessary and sufficient condition for existence of an invariant probability measure as well as a Foster-Lyapunov sufficient condition. We also characterize a subclass, the quasi (weak or strong Feller kernels, for which the sequences of expected occupation measures share the same asymptotic properties as for (weak or strong Feller kernels. In particular, it is shown that the sequences of expected occupation measures of strong and quasi strong-Feller kernels with an invariant probability measure converge setwise to an invariant measure.
Characterization of prokaryotic and eukaryotic promoters using hidden Markov models
DEFF Research Database (Denmark)
Pedersen, Anders Gorm; Baldi, P.; Chauvin, Y.
1996-01-01
In this paper we utilize hidden Markov models (HMMs) and information theory to analyze prokaryotic and eukaryotic promoters. We perform this analysis with special emphasis on the fact that promoters are divided into a number of different classes, depending on which polymerase-associated factors...... that bind to them. We find that HMMs trained on such subclasses of Escherichia coli promoters (specifically, the so-called sigma 70 and sigma 54 classes) give an excellent classification of unknown promoters with respect to sigma-class. HMMs trained on eukaryotic sequences from human genes also model nicely...
Hidden-Markov-Model Analysis Of Telemanipulator Data
Hannaford, Blake; Lee, Paul
1991-01-01
Mathematical model and procedure based on hidden-Markov-model concept undergoing development for use in analysis and prediction of outputs of force and torque sensors of telerobotic manipulators. In model, overall task broken down into subgoals, and transition probabilities encode ease with which operator completes each subgoal. Process portion of model encodes task-sequence/subgoal structure, and probability-density functions for forces and torques associated with each state of manipulation encode sensor signals that one expects to observe at subgoal. Parameters of model constructed from engineering knowledge of task.
Hidden Markov models for the activity profile of terrorist groups
Raghavan, Vasanthan; Galstyan, Aram; Tartakovsky, Alexander G.
2012-01-01
The main focus of this work is on developing models for the activity profile of a terrorist group, detecting sudden spurts and downfalls in this profile, and, in general, tracking it over a period of time. Toward this goal, a $d$-state hidden Markov model (HMM) that captures the latent states underlying the dynamics of the group and thus its activity profile is developed. The simplest setting of $d=2$ corresponds to the case where the dynamics are coarsely quantized as Active and Inactive, re...
A Martingale Decomposition of Discrete Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard
We consider a multivariate time series whose increments are given from a homogeneous Markov chain. We show that the martingale component of this process can be extracted by a filtering method and establish the corresponding martingale decomposition in closed-form. This representation is useful fo...
Bayesian analysis for reversible Markov chains
Diaconis, P.; Rolles, S.W.W.
2006-01-01
We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Pólya’s urn. We give closed form normalizing constants, a simple
Bisimulation and Simulation Relations for Markov Chains
Baier, Christel; Hermanns, H.; Katoen, Joost P.; Wolf, Verena; Aceto, L.; Gordon, A.
2006-01-01
Formal notions of bisimulation and simulation relation play a central role for any kind of process algebra. This short paper sketches the main concepts for bisimulation and simulation relations for probabilistic systems, modelled by discrete- or continuous-time Markov chains.
Revisiting Weak Simulation for Substochastic Markov Chains
DEFF Research Database (Denmark)
Jansen, David N.; Song, Lei; Zhang, Lijun
2013-01-01
of the logic PCTL\\x, and its completeness was conjectured. We revisit this result and show that soundness does not hold in general, but only for Markov chains without divergence. It is refuted for some systems with substochastic distributions. Moreover, we provide a counterexample to completeness...
Multi-dimensional quasitoeplitz Markov chains
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Alexander N. Dudin
1999-01-01
Full Text Available This paper deals with multi-dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector-generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP-input, which operate in synchronous random environment.
Markov chains with quasitoeplitz transition matrix
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Alexander M. Dukhovny
1989-01-01
Full Text Available This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.
Markov Chain Estimation of Avian Seasonal Fecundity
To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...
Model Checking Infinite-State Markov Chains
Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Cloth, L.
2004-01-01
In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state
Model Checking Markov Chains: Techniques and Tools
Zapreev, I.S.
2008-01-01
This dissertation deals with four important aspects of model checking Markov chains: the development of efficient model-checking tools, the improvement of model-checking algorithms, the efficiency of the state-space reduction techniques, and the development of simulation-based model-checking
Model Checking Structured Infinite Markov Chains
Remke, Anne Katharina Ingrid
2008-01-01
In the past probabilistic model checking hast mostly been restricted to finite state models. This thesis explores the possibilities of model checking with continuous stochastic logic (CSL) on infinite-state Markov chains. We present an in-depth treatment of model checking algorithms for two special
Performance Modeling of Communication Networks with Markov Chains
Mo, Jeonghoon
2010-01-01
This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMe and continuous time Markov chain (CTMe. We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probab
Hidden Markov latent variable models with multivariate longitudinal data.
Song, Xinyuan; Xia, Yemao; Zhu, Hongtu
2017-03-01
Cocaine addiction is chronic and persistent, and has become a major social and health problem in many countries. Existing studies have shown that cocaine addicts often undergo episodic periods of addiction to, moderate dependence on, or swearing off cocaine. Given its reversible feature, cocaine use can be formulated as a stochastic process that transits from one state to another, while the impacts of various factors, such as treatment received and individuals' psychological problems on cocaine use, may vary across states. This article develops a hidden Markov latent variable model to study multivariate longitudinal data concerning cocaine use from a California Civil Addict Program. The proposed model generalizes conventional latent variable models to allow bidirectional transition between cocaine-addiction states and conventional hidden Markov models to allow latent variables and their dynamic interrelationship. We develop a maximum-likelihood approach, along with a Monte Carlo expectation conditional maximization (MCECM) algorithm, to conduct parameter estimation. The asymptotic properties of the parameter estimates and statistics for testing the heterogeneity of model parameters are investigated. The finite sample performance of the proposed methodology is demonstrated by simulation studies. The application to cocaine use study provides insights into the prevention of cocaine use. © 2016, The International Biometric Society.
Perturbation theory for Markov chains via Wasserstein distance
Rudolf, Daniel; Schweizer, Nikolaus
2017-01-01
Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the nth step distributions of two Markov chains
PELACAKAN DAN PENGENALAN WAJAH MENGGUNAKAN METODE EMBEDDED HIDDEN MARKOV MODELS
Directory of Open Access Journals (Sweden)
Arie Wirawan Margono
2004-01-01
Full Text Available Tracking and recognizing human face becomes one of the important research subjects nowadays, where it is applicable in security system like room access, surveillance, as well as searching for person identity in police database. Because of applying in security case, it is necessary to have robust system for certain conditions such as: background influence, non-frontal face pose of male or female in different age and race. The aim of this research is to develop software which combines human face tracking using CamShift algorithm and face recognition system using Embedded Hidden Markov Models. The software uses video camera (webcam for real-time input, video AVI for dynamic input, and image file for static input. The software uses Object Oriented Programming (OOP coding style with C++ programming language, Microsoft Visual C++ 6.0® compiler, and assisted by some libraries of Intel Image Processing Library (IPL and Intel Open Source Computer Vision (OpenCV. System testing shows that object tracking based on skin complexion using CamShift algorithm comes out well, for tracking of single or even two face objects at once. Human face recognition system using Embedded Hidden Markov Models method has reach accuracy percentage of 82.76%, using 341 human faces in database that consists of 31 individuals with 11 poses and 29 human face testers. Abstract in Bahasa Indonesia : Pelacakan dan pengenalan wajah manusia merupakan salah satu bidang yang cukup berkembang dewasa ini, dimana aplikasi dapat diterapkan dalam bidang keamanan (security system seperti ijin akses masuk ruangan, pengawasan lokasi (surveillance, maupun pencarian identitas individu pada database kepolisian. Karena diterapkan dalam kasus keamanan, dibutuhkan sistem yang handal terhadap beberapa kondisi, seperti: pengaruh latar belakang, pose wajah non-frontal terhadap pria maupun wanita dalam perbedaan usia dan ras. Tujuan penelitiam ini adalah untuk membuat perangkat lunak yang menggabungkan
On the entropy of a hidden Markov process.
Jacquet, Philippe; Seroussi, Gadiel; Szpankowski, Wojciech
2008-05-01
We study the entropy rate of a hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a first-order binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem. By presenting the probability of a sequence under the model as a product of random matrices, one can see that the entropy rate sought is equal to a top Lyapunov exponent of the product. This offers an explanation for the elusiveness of explicit expressions for the HMP entropy rate, as Lyapunov exponents are notoriously difficult to compute. Consequently, we focus on asymptotic estimates, and apply the same product of random matrices to derive an explicit expression for a Taylor approximation of the entropy rate with respect to the parameter of the binary symmetric channel. The accuracy of the approximation is validated against empirical simulation results. We also extend our results to higher-order Markov processes and to Rényi entropies of any order.
Algorithms for a parallel implementation of Hidden Markov Models with a small state space
DEFF Research Database (Denmark)
Nielsen, Jesper; Sand, Andreas
2011-01-01
Two of the most important algorithms for Hidden Markov Models are the forward and the Viterbi algorithms. We show how formulating these using linear algebra naturally lends itself to parallelization. Although the obtained algorithms are slow for Hidden Markov Models with large state spaces...
Limits of performance for the model reduction problem of hidden Markov models
Kotsalis, Georgios
2015-12-15
We introduce system theoretic notions of a Hankel operator, and Hankel norm for hidden Markov models. We show how the related Hankel singular values provide lower bounds on the norm of the difference between a hidden Markov model of order n and any lower order approximant of order n̂ < n.
Limits of performance for the model reduction problem of hidden Markov models
Kotsalis, Georgios; Shamma, Jeff S.
2015-01-01
We introduce system theoretic notions of a Hankel operator, and Hankel norm for hidden Markov models. We show how the related Hankel singular values provide lower bounds on the norm of the difference between a hidden Markov model of order n and any lower order approximant of order n̂ < n.
Noise can speed convergence in Markov chains.
Franzke, Brandon; Kosko, Bart
2011-10-01
A new theorem shows that noise can speed convergence to equilibrium in discrete finite-state Markov chains. The noise applies to the state density and helps the Markov chain explore improbable regions of the state space. The theorem ensures that a stochastic-resonance noise benefit exists for states that obey a vector-norm inequality. Such noise leads to faster convergence because the noise reduces the norm components. A corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality. This leads to a noise-benefit algorithm that requires knowledge of the steady state. An alternative blind algorithm uses only past state information to achieve a weaker noise benefit. Simulations illustrate the predicted noise benefits in three well-known Markov models. The first model is a two-parameter Ehrenfest diffusion model that shows how noise benefits can occur in the class of birth-death processes. The second model is a Wright-Fisher model of genotype drift in population genetics. The third model is a chemical reaction network of zeolite crystallization. A fourth simulation shows a convergence rate increase of 64% for states that satisfy the theorem and an increase of 53% for states that satisfy the corollary. A final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles. Noise benefits tend to be sharpest in Markov models that do not converge quickly and that do not have strong absorbing states.
Robust Dynamics and Control of a Partially Observed Markov Chain
International Nuclear Information System (INIS)
Elliott, R. J.; Malcolm, W. P.; Moore, J. P.
2007-01-01
In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721-734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear).Clark's method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established
The Consensus String Problem and the Complexity of Comparing Hidden Markov Models
DEFF Research Database (Denmark)
Lyngsø, Rune Bang; Pedersen, Christian Nørgaard Storm
2002-01-01
The basic theory of hidden Markov models was developed and applied to problems in speech recognition in the late 1960s, and has since then been applied to numerous problems, e.g. biological sequence analysis. Most applications of hidden Markov models are based on efficient algorithms for computing...... the probability of generating a given string, or computing the most likely path generating a given string. In this paper we consider the problem of computing the most likely string, or consensus string, generated by a given model, and its implications on the complexity of comparing hidden Markov models. We show...... that computing the consensus string, and approximating its probability within any constant factor, is NP-hard, and that the same holds for the closely related labeling problem for class hidden Markov models. Furthermore, we establish the NP-hardness of comparing two hidden Markov models under the L∞- and L1...
MARKOV CHAIN PORTFOLIO LIQUIDITY OPTIMIZATION MODEL
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Eder Oliveira Abensur
2014-05-01
Full Text Available The international financial crisis of September 2008 and May 2010 showed the importance of liquidity as an attribute to be considered in portfolio decisions. This study proposes an optimization model based on available public data, using Markov chain and Genetic Algorithms concepts as it considers the classic duality of risk versus return and incorporating liquidity costs. The work intends to propose a multi-criterion non-linear optimization model using liquidity based on a Markov chain. The non-linear model was tested using Genetic Algorithms with twenty five Brazilian stocks from 2007 to 2009. The results suggest that this is an innovative development methodology and useful for developing an efficient and realistic financial portfolio, as it considers many attributes such as risk, return and liquidity.
An interlacing theorem for reversible Markov chains
International Nuclear Information System (INIS)
Grone, Robert; Salamon, Peter; Hoffmann, Karl Heinz
2008-01-01
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
An interlacing theorem for reversible Markov chains
Energy Technology Data Exchange (ETDEWEB)
Grone, Robert; Salamon, Peter [Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720 (United States); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet Chemnitz, D-09107 Chemnitz (Germany)
2008-05-30
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
Handbook of Markov chain Monte Carlo
Brooks, Steve
2011-01-01
""Handbook of Markov Chain Monte Carlo"" brings together the major advances that have occurred in recent years while incorporating enough introductory material for new users of MCMC. Along with thorough coverage of the theoretical foundations and algorithmic and computational methodology, this comprehensive handbook includes substantial realistic case studies from a variety of disciplines. These case studies demonstrate the application of MCMC methods and serve as a series of templates for the construction, implementation, and choice of MCMC methodology.
Second Order Optimality in Markov Decision Chains
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2017-01-01
Roč. 53, č. 6 (2017), s. 1086-1099 ISSN 0023-5954 R&D Projects: GA ČR GA15-10331S Institutional support: RVO:67985556 Keywords : Markov decision chains * second order optimality * optimalilty conditions for transient, discounted and average models * policy and value iterations Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 0.379, year: 2016 http://library.utia.cas.cz/separaty/2017/E/sladky-0485146.pdf
Modelling of cyclical stratigraphy using Markov chains
Energy Technology Data Exchange (ETDEWEB)
Kulatilake, P.H.S.W.
1987-07-01
State-of-the-art on modelling of cyclical stratigraphy using first-order Markov chains is reviewed. Shortcomings of the presently available procedures are identified. A procedure which eliminates all the identified shortcomings is presented. Required statistical tests to perform this modelling are given in detail. An example (the Oficina formation in eastern Venezuela) is given to illustrate the presented procedure. 12 refs., 3 tabs. 1 fig.
Temperature scaling method for Markov chains.
Crosby, Lonnie D; Windus, Theresa L
2009-01-22
The use of ab initio potentials in Monte Carlo simulations aimed at investigating the nucleation kinetics of water clusters is complicated by the computational expense of the potential energy determinations. Furthermore, the common desire to investigate the temperature dependence of kinetic properties leads to an urgent need to reduce the expense of performing simulations at many different temperatures. A method is detailed that allows a Markov chain (obtained via Monte Carlo) at one temperature to be scaled to other temperatures of interest without the need to perform additional large simulations. This Markov chain temperature-scaling (TeS) can be generally applied to simulations geared for numerous applications. This paper shows the quality of results which can be obtained by TeS and the possible quantities which may be extracted from scaled Markov chains. Results are obtained for a 1-D analytical potential for which the exact solutions are known. Also, this method is applied to water clusters consisting of between 2 and 5 monomers, using Dynamical Nucleation Theory to determine the evaporation rate constant for monomer loss. Although ab initio potentials are not utilized in this paper, the benefit of this method is made apparent by using the Dang-Chang polarizable classical potential for water to obtain statistical properties at various temperatures.
A Duration Hidden Markov Model for the Identification of Regimes in Stock Market Returns
DEFF Research Database (Denmark)
Ntantamis, Christos
This paper introduces a Duration Hidden Markov Model to model bull and bear market regime switches in the stock market; the duration of each state of the Markov Chain is a random variable that depends on a set of exogenous variables. The model not only allows the endogenous determination...... of the different regimes and but also estimates the effect of the explanatory variables on the regimes' durations. The model is estimated here on NYSE returns using the short-term interest rate and the interest rate spread as exogenous variables. The bull market regime is assigned to the identified state...... with the higher mean and lower variance; bull market duration is found to be negatively dependent on short-term interest rates and positively on the interest rate spread, while bear market duration depends positively the short-term interest rate and negatively on the interest rate spread....
Enhanced Map-Matching Algorithm with a Hidden Markov Model for Mobile Phone Positioning
Directory of Open Access Journals (Sweden)
An Luo
2017-10-01
Full Text Available Numerous map-matching techniques have been developed to improve positioning, using Global Positioning System (GPS data and other sensors. However, most existing map-matching algorithms process GPS data with high sampling rates, to achieve a higher correct rate and strong universality. This paper introduces a novel map-matching algorithm based on a hidden Markov model (HMM for GPS positioning and mobile phone positioning with a low sampling rate. The HMM is a statistical model well known for providing solutions to temporal recognition applications such as text and speech recognition. In this work, the hidden Markov chain model was built to establish a map-matching process, using the geometric data, the topologies matrix of road links in road network and refined quad-tree data structure. HMM-based map-matching exploits the Viterbi algorithm to find the optimized road link sequence. The sequence consists of hidden states in the HMM model. The HMM-based map-matching algorithm is validated on a vehicle trajectory using GPS and mobile phone data. The results show a significant improvement in mobile phone positioning and high and low sampling of GPS data.
Modeling promoter grammars with evolving hidden Markov models
DEFF Research Database (Denmark)
Won, Kyoung-Jae; Sandelin, Albin; Marstrand, Troels Torben
2008-01-01
MOTIVATION: Describing and modeling biological features of eukaryotic promoters remains an important and challenging problem within computational biology. The promoters of higher eukaryotes in particular display a wide variation in regulatory features, which are difficult to model. Often several...... factors are involved in the regulation of a set of co-regulated genes. If so, promoters can be modeled with connected regulatory features, where the network of connections is characteristic for a particular mode of regulation. RESULTS: With the goal of automatically deciphering such regulatory structures......, we present a method that iteratively evolves an ensemble of regulatory grammars using a hidden Markov Model (HMM) architecture composed of interconnected blocks representing transcription factor binding sites (TFBSs) and background regions of promoter sequences. The ensemble approach reduces the risk...
Geolocating fish using Hidden Markov Models and Data Storage Tags
DEFF Research Database (Denmark)
Thygesen, Uffe Høgsbro; Pedersen, Martin Wæver; Madsen, Henrik
2009-01-01
Geolocation of fish based on data from archival tags typically requires a statistical analysis to reduce the effect of measurement errors. In this paper we present a novel technique for this analysis, one based on Hidden Markov Models (HMM's). We assume that the actual path of the fish is generated...... by a biased random walk. The HMM methodology produces, for each time step, the probability that the fish resides in each grid cell. Because there is no Monte Carlo step in our technique, we are able to estimate parameters within the likelihood framework. The method does not require the distribution...... of inference in state-space models of animals. The technique can be applied to geolocation based on light, on tidal patterns, or measurement of other variables that vary with space. We illustrate the method through application to a simulated data set where geolocation relies on depth data exclusively....
Engineering of Algorithms for Hidden Markov models and Tree Distances
DEFF Research Database (Denmark)
Sand, Andreas
Bioinformatics is an interdisciplinary scientific field that combines biology with mathematics, statistics and computer science in an effort to develop computational methods for handling, analyzing and learning from biological data. In the recent decades, the amount of available biological data has...... speed up all the classical algorithms for analyses and training of hidden Markov models. And I show how two particularly important algorithms, the forward algorithm and the Viterbi algorithm, can be accelerated through a reformulation of the algorithms and a somewhat more complicated parallelization...... contribution to the theoretically fastest set of algorithms presently available to compute two closely related measures of tree distance, the triplet distance and the quartet distance. And I further demonstrate that they are also the fastest algorithms in almost all cases when tested in practice....
Motion Imitation and Recognition using Parametric Hidden Markov Models
DEFF Research Database (Denmark)
Herzog, Dennis; Ude, Ales; Krüger, Volker
2008-01-01
) are important. Only together they convey the whole meaning of an action. Similarly, to imitate a movement, the robot needs to select the proper action and parameterize it, e.g., by the relative position of the object that needs to be grasped. We propose to utilize parametric hidden Markov models (PHMMs), which...... extend the classical HMMs by introducing a joint parameterization of the observation densities, to simultaneously solve the problems of action recognition, parameterization of the observed actions, and action synthesis. The proposed approach was fully implemented on a humanoid robot HOAP-3. To evaluate...... the approach, we focused on reaching and pointing actions. Even though the movements are very similar in appearance, our approach is able to distinguish the two movement types and discover the parameterization, and is thus enabling both, action recognition and action synthesis. Through parameterization we...
A hidden Markov model approach to neuron firing patterns.
Camproux, A C; Saunier, F; Chouvet, G; Thalabard, J C; Thomas, G
1996-11-01
Analysis and characterization of neuronal discharge patterns are of interest to neurophysiologists and neuropharmacologists. In this paper we present a hidden Markov model approach to modeling single neuron electrical activity. Basically the model assumes that each interspike interval corresponds to one of several possible states of the neuron. Fitting the model to experimental series of interspike intervals by maximum likelihood allows estimation of the number of possible underlying neuron states, the probability density functions of interspike intervals corresponding to each state, and the transition probabilities between states. We present an application to the analysis of recordings of a locus coeruleus neuron under three pharmacological conditions. The model distinguishes two states during halothane anesthesia and during recovery from halothane anesthesia, and four states after administration of clonidine. The transition probabilities yield additional insights into the mechanisms of neuron firing.
Understanding eye movements in face recognition using hidden Markov models.
Chuk, Tim; Chan, Antoni B; Hsiao, Janet H
2014-09-16
We use a hidden Markov model (HMM) based approach to analyze eye movement data in face recognition. HMMs are statistical models that are specialized in handling time-series data. We conducted a face recognition task with Asian participants, and model each participant's eye movement pattern with an HMM, which summarized the participant's scan paths in face recognition with both regions of interest and the transition probabilities among them. By clustering these HMMs, we showed that participants' eye movements could be categorized into holistic or analytic patterns, demonstrating significant individual differences even within the same culture. Participants with the analytic pattern had longer response times, but did not differ significantly in recognition accuracy from those with the holistic pattern. We also found that correct and wrong recognitions were associated with distinctive eye movement patterns; the difference between the two patterns lies in the transitions rather than locations of the fixations alone. © 2014 ARVO.
Monotone measures of ergodicity for Markov chains
Directory of Open Access Journals (Sweden)
J. Keilson
1998-01-01
Full Text Available The following paper, first written in 1974, was never published other than as part of an internal research series. Its lack of publication is unrelated to the merits of the paper and the paper is of current importance by virtue of its relation to the relaxation time. A systematic discussion is provided of the approach of a finite Markov chain to ergodicity by proving the monotonicity of an important set of norms, each measures of egodicity, whether or not time reversibility is present. The paper is of particular interest because the discussion of the relaxation time of a finite Markov chain [2] has only been clean for time reversible chains, a small subset of the chains of interest. This restriction is not present here. Indeed, a new relaxation time quoted quantifies the relaxation time for all finite ergodic chains (cf. the discussion of Q1(t below Equation (1.7]. This relaxation time was developed by Keilson with A. Roy in his thesis [6], yet to be published.
Honest Importance Sampling with Multiple Markov Chains.
Tan, Aixin; Doss, Hani; Hobert, James P
2015-01-01
Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable
SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.
Thiede, Erik; VAN Koten, Brian; Weare, Jonathan
For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations.
The Consensus String Problem and the Complexity of Comparing Hidden Markov Models
DEFF Research Database (Denmark)
Lyngsø, Rune Bang; Pedersen, Christian Nørgaard Storm
2002-01-01
The basic theory of hidden Markov models was developed and applied to problems in speech recognition in the late 1960s, and has since then been applied to numerous problems, e.g. biological sequence analysis. Most applications of hidden Markov models are based on efficient algorithms for computing......-norms. We discuss the applicability of the technique used for proving the hardness of comparing two hidden Markov models under the L1-norm to other measures of distance between probability distributions. In particular, we show that it cannot be used for proving NP-hardness of determining the Kullback...
Bayesian tomography by interacting Markov chains
Romary, T.
2017-12-01
In seismic tomography, we seek to determine the velocity of the undergound from noisy first arrival travel time observations. In most situations, this is an ill posed inverse problem that admits several unperfect solutions. Given an a priori distribution over the parameters of the velocity model, the Bayesian formulation allows to state this problem as a probabilistic one, with a solution under the form of a posterior distribution. The posterior distribution is generally high dimensional and may exhibit multimodality. Moreover, as it is known only up to a constant, the only sensible way to addressthis problem is to try to generate simulations from the posterior. The natural tools to perform these simulations are Monte Carlo Markov chains (MCMC). Classical implementations of MCMC algorithms generally suffer from slow mixing: the generated states are slow to enter the stationary regime, that is to fit the observations, and when one mode of the posterior is eventually identified, it may become difficult to visit others. Using a varying temperature parameter relaxing the constraint on the data may help to enter the stationary regime. Besides, the sequential nature of MCMC makes them ill fitted toparallel implementation. Running a large number of chains in parallel may be suboptimal as the information gathered by each chain is not mutualized. Parallel tempering (PT) can be seen as a first attempt to make parallel chains at different temperatures communicate but only exchange information between current states. In this talk, I will show that PT actually belongs to a general class of interacting Markov chains algorithm. I will also show that this class enables to design interacting schemes that can take advantage of the whole history of the chain, by authorizing exchanges toward already visited states. The algorithms will be illustrated with toy examples and an application to first arrival traveltime tomography.
Markov Chain Analysis of Musical Dice Games
Volchenkov, D.; Dawin, J. R.
2012-07-01
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
Vulnerability of networks of interacting Markov chains.
Kocarev, L; Zlatanov, N; Trajanov, D
2010-05-13
The concept of vulnerability is introduced for a model of random, dynamical interactions on networks. In this model, known as the influence model, the nodes are arranged in an arbitrary network, while the evolution of the status at a node is according to an internal Markov chain, but with transition probabilities that depend not only on the current status of that node but also on the statuses of the neighbouring nodes. Vulnerability is treated analytically and numerically for several networks with different topological structures, as well as for two real networks--the network of infrastructures and the EU power grid--identifying the most vulnerable nodes of these networks.
Respondent-driven sampling as Markov chain Monte Carlo.
Goel, Sharad; Salganik, Matthew J
2009-07-30
Respondent-driven sampling (RDS) is a recently introduced, and now widely used, technique for estimating disease prevalence in hidden populations. RDS data are collected through a snowball mechanism, in which current sample members recruit future sample members. In this paper we present RDS as Markov chain Monte Carlo importance sampling, and we examine the effects of community structure and the recruitment procedure on the variance of RDS estimates. Past work has assumed that the variance of RDS estimates is primarily affected by segregation between healthy and infected individuals. We examine an illustrative model to show that this is not necessarily the case, and that bottlenecks anywhere in the networks can substantially affect estimates. We also show that variance is inflated by a common design feature in which the sample members are encouraged to recruit multiple future sample members. The paper concludes with suggestions for implementing and evaluating RDS studies.
A New GMRES(m Method for Markov Chains
Directory of Open Access Journals (Sweden)
Bing-Yuan Pu
2013-01-01
Full Text Available This paper presents a class of new accelerated restarted GMRES method for calculating the stationary probability vector of an irreducible Markov chain. We focus on the mechanism of this new hybrid method by showing how to periodically combine the GMRES and vector extrapolation method into a much efficient one for improving the convergence rate in Markov chain problems. Numerical experiments are carried out to demonstrate the efficiency of our new algorithm on several typical Markov chain problems.
Asymptotic evolution of quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)
2012-07-01
The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.
Approximating Markov Chains: What and why
International Nuclear Information System (INIS)
Pincus, S.
1996-01-01
Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to open-quote open-quote solve,close-quote close-quote or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the attractor, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. copyright 1996 American Institute of Physics
Optical character recognition of handwritten Arabic using hidden Markov models
Aulama, Mohannad M.; Natsheh, Asem M.; Abandah, Gheith A.; Olama, Mohammed M.
2011-04-01
The problem of optical character recognition (OCR) of handwritten Arabic has not received a satisfactory solution yet. In this paper, an Arabic OCR algorithm is developed based on Hidden Markov Models (HMMs) combined with the Viterbi algorithm, which results in an improved and more robust recognition of characters at the sub-word level. Integrating the HMMs represents another step of the overall OCR trends being currently researched in the literature. The proposed approach exploits the structure of characters in the Arabic language in addition to their extracted features to achieve improved recognition rates. Useful statistical information of the Arabic language is initially extracted and then used to estimate the probabilistic parameters of the mathematical HMM. A new custom implementation of the HMM is developed in this study, where the transition matrix is built based on the collected large corpus, and the emission matrix is built based on the results obtained via the extracted character features. The recognition process is triggered using the Viterbi algorithm which employs the most probable sequence of sub-words. The model was implemented to recognize the sub-word unit of Arabic text raising the recognition rate from being linked to the worst recognition rate for any character to the overall structure of the Arabic language. Numerical results show that there is a potentially large recognition improvement by using the proposed algorithms.
Hidden Semi-Markov Models for Predictive Maintenance
Directory of Open Access Journals (Sweden)
Francesco Cartella
2015-01-01
Full Text Available Realistic predictive maintenance approaches are essential for condition monitoring and predictive maintenance of industrial machines. In this work, we propose Hidden Semi-Markov Models (HSMMs with (i no constraints on the state duration density function and (ii being applied to continuous or discrete observation. To deal with such a type of HSMM, we also propose modifications to the learning, inference, and prediction algorithms. Finally, automatic model selection has been made possible using the Akaike Information Criterion. This paper describes the theoretical formalization of the model as well as several experiments performed on simulated and real data with the aim of methodology validation. In all performed experiments, the model is able to correctly estimate the current state and to effectively predict the time to a predefined event with a low overall average absolute error. As a consequence, its applicability to real world settings can be beneficial, especially where in real time the Remaining Useful Lifetime (RUL of the machine is calculated.
A Bayesian Approach for Structural Learning with Hidden Markov Models
Directory of Open Access Journals (Sweden)
Cen Li
2002-01-01
Full Text Available Hidden Markov Models(HMM have proved to be a successful modeling paradigm for dynamic and spatial processes in many domains, such as speech recognition, genomics, and general sequence alignment. Typically, in these applications, the model structures are predefined by domain experts. Therefore, the HMM learning problem focuses on the learning of the parameter values of the model to fit the given data sequences. However, when one considers other domains, such as, economics and physiology, model structure capturing the system dynamic behavior is not available. In order to successfully apply the HMM methodology in these domains, it is important that a mechanism is available for automatically deriving the model structure from the data. This paper presents a HMM learning procedure that simultaneously learns the model structure and the maximum likelihood parameter values of a HMM from data. The HMM model structures are derived based on the Bayesian model selection methodology. In addition, we introduce a new initialization procedure for HMM parameter value estimation based on the K-means clustering method. Experimental results with artificially generated data show the effectiveness of the approach.
Mobile Application Identification based on Hidden Markov Model
Directory of Open Access Journals (Sweden)
Yang Xinyan
2018-01-01
Full Text Available With the increasing number of mobile applications, there has more challenging network management tasks to resolve. Users also face security issues of the mobile Internet application when enjoying the mobile network resources. Identifying applications that correspond to network traffic can help network operators effectively perform network management. The existing mobile application recognition technology presents new challenges in extensibility and applications with encryption protocols. For the existing mobile application recognition technology, there are two problems, they can not recognize the application which using the encryption protocol and their scalability is poor. In this paper, a mobile application identification method based on Hidden Markov Model(HMM is proposed to extract the defined statistical characteristics from different network flows generated when each application starting. According to the time information of different network flows to get the corresponding time series, and then for each application to be identified separately to establish the corresponding HMM model. Then, we use 10 common applications to test the method proposed in this paper. The test results show that the mobile application recognition method proposed in this paper has a high accuracy and good generalization ability.
A Framework for Bioacoustic Vocalization Analysis Using Hidden Markov Models
Directory of Open Access Journals (Sweden)
Ebenezer Out-Nyarko
2009-11-01
Full Text Available Using Hidden Markov Models (HMMs as a recognition framework for automatic classification of animal vocalizations has a number of benefits, including the ability to handle duration variability through nonlinear time alignment, the ability to incorporate complex language or recognition constraints, and easy extendibility to continuous recognition and detection domains. In this work, we apply HMMs to several different species and bioacoustic tasks using generalized spectral features that can be easily adjusted across species and HMM network topologies suited to each task. This experimental work includes a simple call type classification task using one HMM per vocalization for repertoire analysis of Asian elephants, a language-constrained song recognition task using syllable models as base units for ortolan bunting vocalizations, and a stress stimulus differentiation task in poultry vocalizations using a non-sequential model via a one-state HMM with Gaussian mixtures. Results show strong performance across all tasks and illustrate the flexibility of the HMM framework for a variety of species, vocalization types, and analysis tasks.
Forecasting oil price trends using wavelets and hidden Markov models
International Nuclear Information System (INIS)
Souza e Silva, Edmundo G. de; Souza e Silva, Edmundo A. de; Legey, Luiz F.L.
2010-01-01
The crude oil price is influenced by a great number of factors, most of which interact in very complex ways. For this reason, forecasting it through a fundamentalist approach is a difficult task. An alternative is to use time series methodologies, with which the price's past behavior is conveniently analyzed, and used to predict future movements. In this paper, we investigate the usefulness of a nonlinear time series model, known as hidden Markov model (HMM), to predict future crude oil price movements. Using an HMM, we develop a forecasting methodology that consists of, basically, three steps. First, we employ wavelet analysis to remove high frequency price movements, which can be assumed as noise. Then, the HMM is used to forecast the probability distribution of the price return accumulated over the next F days. Finally, from this distribution, we infer future price trends. Our results indicate that the proposed methodology might be a useful decision support tool for agents participating in the crude oil market. (author)
Clustering Multivariate Time Series Using Hidden Markov Models
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Shima Ghassempour
2014-03-01
Full Text Available In this paper we describe an algorithm for clustering multivariate time series with variables taking both categorical and continuous values. Time series of this type are frequent in health care, where they represent the health trajectories of individuals. The problem is challenging because categorical variables make it difficult to define a meaningful distance between trajectories. We propose an approach based on Hidden Markov Models (HMMs, where we first map each trajectory into an HMM, then define a suitable distance between HMMs and finally proceed to cluster the HMMs with a method based on a distance matrix. We test our approach on a simulated, but realistic, data set of 1,255 trajectories of individuals of age 45 and over, on a synthetic validation set with known clustering structure, and on a smaller set of 268 trajectories extracted from the longitudinal Health and Retirement Survey. The proposed method can be implemented quite simply using standard packages in R and Matlab and may be a good candidate for solving the difficult problem of clustering multivariate time series with categorical variables using tools that do not require advanced statistic knowledge, and therefore are accessible to a wide range of researchers.
Modelling and evaluation of surgical performance using hidden Markov models.
Megali, Giuseppe; Sinigaglia, Stefano; Tonet, Oliver; Dario, Paolo
2006-10-01
Minimally invasive surgery has become very widespread in the last ten years. Since surgeons experience difficulties in learning and mastering minimally invasive techniques, the development of training methods is of great importance. While the introduction of virtual reality-based simulators has introduced a new paradigm in surgical training, skill evaluation methods are far from being objective. This paper proposes a method for defining a model of surgical expertise and an objective metric to evaluate performance in laparoscopic surgery. Our approach is based on the processing of kinematic data describing movements of surgical instruments. We use hidden Markov model theory to define an expert model that describes expert surgical gesture. The model is trained on kinematic data related to exercises performed on a surgical simulator by experienced surgeons. Subsequently, we use this expert model as a reference model in the definition of an objective metric to evaluate performance of surgeons with different abilities. Preliminary results show that, using different topologies for the expert model, the method can be efficiently used both for the discrimination between experienced and novice surgeons, and for the quantitative assessment of surgical ability.
Hidden Markov modelling of movement data from fish
DEFF Research Database (Denmark)
Pedersen, Martin Wæver
Movement data from marine animals tagged with electronic tags are becoming increasingly diverse and plentiful. This trend entails a need for statistical methods that are able to filter the observations to extract the ecologically relevant content. This dissertation focuses on the development...... the behaviour of the animal. With the extended model can migratory and resident movement behaviour be related to geographical regions. For population inference multiple individual state-space analyses can be interconnected using mixed effects modelling. This framework provides parameter estimates...... approximated. This furthermore enables accurate probability densities of location to be computed. Finally, the performance of the HMM approach in analysing nonlinear state space models is compared with two alternatives: the AD Model Builder framework and BUGS, which relies on Markov chain Monte Carlo...
438 Optimal Number of States in Hidden Markov Models and its ...
African Journals Online (AJOL)
In this paper, Hidden Markov Model is applied to model human movements as to .... emit either discrete information or a continuous data derived from a Probability .... For each hidden state in the test set, the probability = ... by applying the Kullback-Leibler distance (Juang & Rabiner, 1985) which ..... One Size Does Not Fit.
Compositionality for Markov reward chains with fast and silent transitions
Markovski, J.; Sokolova, A.; Trcka, N.; Vink, de E.P.
2009-01-01
A parallel composition is defined for Markov reward chains with stochastic discontinuity, and with fast and silent transitions. In this setting, compositionality with respect to the relevant aggregation preorders is established. For Markov reward chains with fast transitions the preorders are
First hitting probabilities for semi markov chains and estimation
DEFF Research Database (Denmark)
Georgiadis, Stylianos
2017-01-01
We first consider a stochastic system described by an absorbing semi-Markov chain with finite state space and we introduce the absorption probability to a class of recurrent states. Afterwards, we study the first hitting probability to a subset of states for an irreducible semi-Markov chain...
A Markov Chain Model for Contagion
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Angelos Dassios
2014-11-01
Full Text Available We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the clustering arrival of events, such as jumps, bankruptcies, crises and catastrophes in finance, insurance and economics with both internal contagion risk and external common risk. Key distributional properties, such as the moments and probability generating functions, for this process are derived. Some special cases with explicit results and numerical examples and the motivation for further actuarial applications are also discussed. The model can be considered a generalisation of the dynamic contagion process introduced by Dassios and Zhao (2011.
Multivariate Markov chain modeling for stock markets
Maskawa, Jun-ichi
2003-06-01
We study a multivariate Markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes are coded into the sequences of up and down spins according to their signs. We start with the discussion for small portfolios consisting of two stock issues. The generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation. The resultant form of the joint probability of the stationary state coincides with Gibbs measure assigned to each configuration of spin glass model. Through the analysis of actual portfolios, it has been shown that the synchronization of the direction of the price changes is well described by the model.
Introduction to the numerical solutions of Markov chains
Stewart, Williams J
1994-01-01
A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse - and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here, Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing metho...
Zhao, Zhibiao
2011-06-01
We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise.
Long Memory of Financial Time Series and Hidden Markov Models with Time-Varying Parameters
DEFF Research Database (Denmark)
Nystrup, Peter; Madsen, Henrik; Lindström, Erik
2016-01-01
Hidden Markov models are often used to model daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time-varying behavior have not been thoroughly examined. This paper presents an adaptive...... to reproduce with a hidden Markov model. Capturing the time-varying behavior of the parameters also leads to improved one-step density forecasts. Finally, it is shown that the forecasting performance of the estimated models can be further improved using local smoothing to forecast the parameter variations....
Detecting Seismic Events Using a Supervised Hidden Markov Model
Burks, L.; Forrest, R.; Ray, J.; Young, C.
2017-12-01
We explore the use of supervised hidden Markov models (HMMs) to detect seismic events in streaming seismogram data. Current methods for seismic event detection include simple triggering algorithms, such as STA/LTA and the Z-statistic, which can lead to large numbers of false positives that must be investigated by an analyst. The hypothesis of this study is that more advanced detection methods, such as HMMs, may decreases false positives while maintaining accuracy similar to current methods. We train a binary HMM classifier using 2 weeks of 3-component waveform data from the International Monitoring System (IMS) that was carefully reviewed by an expert analyst to pick all seismic events. Using an ensemble of simple and discrete features, such as the triggering of STA/LTA, the HMM predicts the time at which transition occurs from noise to signal. Compared to the STA/LTA detection algorithm, the HMM detects more true events, but the false positive rate remains unacceptably high. Future work to potentially decrease the false positive rate may include using continuous features, a Gaussian HMM, and multi-class HMMs to distinguish between types of seismic waves (e.g., P-waves and S-waves). Acknowledgement: Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.SAND No: SAND2017-8154 A
Accelerating Information Retrieval from Profile Hidden Markov Model Databases.
Tamimi, Ahmad; Ashhab, Yaqoub; Tamimi, Hashem
2016-01-01
Profile Hidden Markov Model (Profile-HMM) is an efficient statistical approach to represent protein families. Currently, several databases maintain valuable protein sequence information as profile-HMMs. There is an increasing interest to improve the efficiency of searching Profile-HMM databases to detect sequence-profile or profile-profile homology. However, most efforts to enhance searching efficiency have been focusing on improving the alignment algorithms. Although the performance of these algorithms is fairly acceptable, the growing size of these databases, as well as the increasing demand for using batch query searching approach, are strong motivations that call for further enhancement of information retrieval from profile-HMM databases. This work presents a heuristic method to accelerate the current profile-HMM homology searching approaches. The method works by cluster-based remodeling of the database to reduce the search space, rather than focusing on the alignment algorithms. Using different clustering techniques, 4284 TIGRFAMs profiles were clustered based on their similarities. A representative for each cluster was assigned. To enhance sensitivity, we proposed an extended step that allows overlapping among clusters. A validation benchmark of 6000 randomly selected protein sequences was used to query the clustered profiles. To evaluate the efficiency of our approach, speed and recall values were measured and compared with the sequential search approach. Using hierarchical, k-means, and connected component clustering techniques followed by the extended overlapping step, we obtained an average reduction in time of 41%, and an average recall of 96%. Our results demonstrate that representation of profile-HMMs using a clustering-based approach can significantly accelerate data retrieval from profile-HMM databases.
Accelerating Information Retrieval from Profile Hidden Markov Model Databases.
Directory of Open Access Journals (Sweden)
Ahmad Tamimi
Full Text Available Profile Hidden Markov Model (Profile-HMM is an efficient statistical approach to represent protein families. Currently, several databases maintain valuable protein sequence information as profile-HMMs. There is an increasing interest to improve the efficiency of searching Profile-HMM databases to detect sequence-profile or profile-profile homology. However, most efforts to enhance searching efficiency have been focusing on improving the alignment algorithms. Although the performance of these algorithms is fairly acceptable, the growing size of these databases, as well as the increasing demand for using batch query searching approach, are strong motivations that call for further enhancement of information retrieval from profile-HMM databases. This work presents a heuristic method to accelerate the current profile-HMM homology searching approaches. The method works by cluster-based remodeling of the database to reduce the search space, rather than focusing on the alignment algorithms. Using different clustering techniques, 4284 TIGRFAMs profiles were clustered based on their similarities. A representative for each cluster was assigned. To enhance sensitivity, we proposed an extended step that allows overlapping among clusters. A validation benchmark of 6000 randomly selected protein sequences was used to query the clustered profiles. To evaluate the efficiency of our approach, speed and recall values were measured and compared with the sequential search approach. Using hierarchical, k-means, and connected component clustering techniques followed by the extended overlapping step, we obtained an average reduction in time of 41%, and an average recall of 96%. Our results demonstrate that representation of profile-HMMs using a clustering-based approach can significantly accelerate data retrieval from profile-HMM databases.
Long memory of financial time series and hidden Markov models with time-varying parameters
DEFF Research Database (Denmark)
Nystrup, Peter; Madsen, Henrik; Lindström, Erik
Hidden Markov models are often used to capture stylized facts of daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time-varying behavior for the ability to reproduce the stylized...... facts have not been thoroughly examined. This paper presents an adaptive estimation approach that allows for the parameters of the estimated models to be time-varying. It is shown that a two-state Gaussian hidden Markov model with time-varying parameters is able to reproduce the long memory of squared...... daily returns that was previously believed to be the most difficult fact to reproduce with a hidden Markov model. Capturing the time-varying behavior of the parameters also leads to improved one-step predictions....
Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium
Kapfer, Sebastian C.; Krauth, Werner
2017-12-01
We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.
Maximally reliable Markov chains under energy constraints.
Escola, Sean; Eisele, Michael; Miller, Kenneth; Paninski, Liam
2009-07-01
Signal-to-noise ratios in physical systems can be significantly degraded if the outputs of the systems are highly variable. Biological processes for which highly stereotyped signal generations are necessary features appear to have reduced their signal variabilities by employing multiple processing steps. To better understand why this multistep cascade structure might be desirable, we prove that the reliability of a signal generated by a multistate system with no memory (i.e., a Markov chain) is maximal if and only if the system topology is such that the process steps irreversibly through each state, with transition rates chosen such that an equal fraction of the total signal is generated in each state. Furthermore, our result indicates that by increasing the number of states, it is possible to arbitrarily increase the reliability of the system. In a physical system, however, an energy cost is associated with maintaining irreversible transitions, and this cost increases with the number of such transitions (i.e., the number of states). Thus, an infinite-length chain, which would be perfectly reliable, is infeasible. To model the effects of energy demands on the maximally reliable solution, we numerically optimize the topology under two distinct energy functions that penalize either irreversible transitions or incommunicability between states, respectively. In both cases, the solutions are essentially irreversible linear chains, but with upper bounds on the number of states set by the amount of available energy. We therefore conclude that a physical system for which signal reliability is important should employ a linear architecture, with the number of states (and thus the reliability) determined by the intrinsic energy constraints of the system.
Modeling Uncertainty of Directed Movement via Markov Chains
Directory of Open Access Journals (Sweden)
YIN Zhangcai
2015-10-01
Full Text Available Probabilistic time geography (PTG is suggested as an extension of (classical time geography, in order to present the uncertainty of an agent located at the accessible position by probability. This may provide a quantitative basis for most likely finding an agent at a location. In recent years, PTG based on normal distribution or Brown bridge has been proposed, its variance, however, is irrelevant with the agent's speed or divergent with the increase of the speed; so they are difficult to take into account application pertinence and stability. In this paper, a new method is proposed to model PTG based on Markov chain. Firstly, a bidirectional conditions Markov chain is modeled, the limit of which, when the moving speed is large enough, can be regarded as the Brown bridge, thus has the characteristics of digital stability. Then, the directed movement is mapped to Markov chains. The essential part is to build step length, the state space and transfer matrix of Markov chain according to the space and time position of directional movement, movement speed information, to make sure the Markov chain related to the movement speed. Finally, calculating continuously the probability distribution of the directed movement at any time by the Markov chains, it can be get the possibility of an agent located at the accessible position. Experimental results show that, the variance based on Markov chains not only is related to speed, but also is tending towards stability with increasing the agent's maximum speed.
Turner, Sean; Galelli, Stefano; Wilcox, Karen
2015-04-01
Water reservoir systems are often affected by recurring large-scale ocean-atmospheric anomalies, known as teleconnections, that cause prolonged periods of climatological drought. Accurate forecasts of these events -- at lead times in the order of weeks and months -- may enable reservoir operators to take more effective release decisions to improve the performance of their systems. In practice this might mean a more reliable water supply system, a more profitable hydropower plant or a more sustainable environmental release policy. To this end, climate indices, which represent the oscillation of the ocean-atmospheric system, might be gainfully employed within reservoir operating models that adapt the reservoir operation as a function of the climate condition. This study develops a Stochastic Dynamic Programming (SDP) approach that can incorporate climate indices using a Hidden Markov Model. The model simulates the climatic regime as a hidden state following a Markov chain, with the state transitions driven by variation in climatic indices, such as the Southern Oscillation Index. Time series analysis of recorded streamflow data reveals the parameters of separate autoregressive models that describe the inflow to the reservoir under three representative climate states ("normal", "wet", "dry"). These models then define inflow transition probabilities for use in a classic SDP approach. The key advantage of the Hidden Markov Model is that it allows conditioning the operating policy not only on the reservoir storage and the antecedent inflow, but also on the climate condition, thus potentially allowing adaptability to a broader range of climate conditions. In practice, the reservoir operator would effect a water release tailored to a specific climate state based on available teleconnection data and forecasts. The approach is demonstrated on the operation of a realistic, stylised water reservoir with carry-over capacity in South-East Australia. Here teleconnections relating
Sampling rare fluctuations of discrete-time Markov chains
Whitelam, Stephen
2018-03-01
We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.
A Hidden Markov Model Representing the Spatial and Temporal Correlation of Multiple Wind Farms
DEFF Research Database (Denmark)
Fang, Jiakun; Su, Chi; Hu, Weihao
2015-01-01
To accommodate the increasing wind energy with stochastic nature becomes a major issue on power system reliability. This paper proposes a methodology to characterize the spatiotemporal correlation of multiple wind farms. First, a hierarchical clustering method based on self-organizing maps is ado....... The proposed statistical modeling framework is compatible with the sequential power system reliability analysis. A case study on optimal sizing and location of fast-response regulation sources is presented.......To accommodate the increasing wind energy with stochastic nature becomes a major issue on power system reliability. This paper proposes a methodology to characterize the spatiotemporal correlation of multiple wind farms. First, a hierarchical clustering method based on self-organizing maps...... is adopted to categorize the similar output patterns of several wind farms into joint states. Then the hidden Markov model (HMM) is then designed to describe the temporal correlations among these joint states. Unlike the conventional Markov chain model, the accumulated wind power is taken into consideration...
Bayesian posterior distributions without Markov chains.
Cole, Stephen R; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B
2012-03-01
Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.
Logics and Models for Stochastic Analysis Beyond Markov Chains
DEFF Research Database (Denmark)
Zeng, Kebin
, because of the generality of ME distributions, we have to leave the world of Markov chains. To support ME distributions with multiple exits, we introduce a multi-exits ME distribution together with a process algebra MEME to express the systems having the semantics as Markov renewal processes with ME...
Swallowing sound detection using hidden markov modeling of recurrence plot features
International Nuclear Information System (INIS)
Aboofazeli, Mohammad; Moussavi, Zahra
2009-01-01
Automated detection of swallowing sounds in swallowing and breath sound recordings is of importance for monitoring purposes in which the recording durations are long. This paper presents a novel method for swallowing sound detection using hidden Markov modeling of recurrence plot features. Tracheal sound recordings of 15 healthy and nine dysphagic subjects were studied. The multidimensional state space trajectory of each signal was reconstructed using the Taken method of delays. The sequences of three recurrence plot features of the reconstructed trajectories (which have shown discriminating capability between swallowing and breath sounds) were modeled by three hidden Markov models. The Viterbi algorithm was used for swallowing sound detection. The results were validated manually by inspection of the simultaneously recorded airflow signal and spectrogram of the sounds, and also by auditory means. The experimental results suggested that the performance of the proposed method using hidden Markov modeling of recurrence plot features was superior to the previous swallowing sound detection methods.
Swallowing sound detection using hidden markov modeling of recurrence plot features
Energy Technology Data Exchange (ETDEWEB)
Aboofazeli, Mohammad [Faculty of Engineering, Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba, R3T 5V6 (Canada)], E-mail: umaboofa@cc.umanitoba.ca; Moussavi, Zahra [Faculty of Engineering, Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba, R3T 5V6 (Canada)], E-mail: mousavi@ee.umanitoba.ca
2009-01-30
Automated detection of swallowing sounds in swallowing and breath sound recordings is of importance for monitoring purposes in which the recording durations are long. This paper presents a novel method for swallowing sound detection using hidden Markov modeling of recurrence plot features. Tracheal sound recordings of 15 healthy and nine dysphagic subjects were studied. The multidimensional state space trajectory of each signal was reconstructed using the Taken method of delays. The sequences of three recurrence plot features of the reconstructed trajectories (which have shown discriminating capability between swallowing and breath sounds) were modeled by three hidden Markov models. The Viterbi algorithm was used for swallowing sound detection. The results were validated manually by inspection of the simultaneously recorded airflow signal and spectrogram of the sounds, and also by auditory means. The experimental results suggested that the performance of the proposed method using hidden Markov modeling of recurrence plot features was superior to the previous swallowing sound detection methods.
Markov Chain: A Predictive Model for Manpower Planning ...
African Journals Online (AJOL)
ADOWIE PERE
Keywords: Markov Chain, Transition Probability Matrix, Manpower Planning, Recruitment, Promotion, .... movement of the workforce in Jordan productivity .... Planning periods, with T being the horizon, the value of t represents a session.
A simplified parsimonious higher order multivariate Markov chain model
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, a simplified parsimonious higher-order multivariate Markov chain model (SPHOMMCM) is presented. Moreover, parameter estimation method of TPHOMMCM is give. Numerical experiments shows the effectiveness of TPHOMMCM.
A tridiagonal parsimonious higher order multivariate Markov chain model
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, we present a tridiagonal parsimonious higher-order multivariate Markov chain model (TPHOMMCM). Moreover, estimation method of the parameters in TPHOMMCM is give. Numerical experiments illustrate the effectiveness of TPHOMMCM.
Markov chain: a predictive model for manpower planning | Ezugwu ...
African Journals Online (AJOL)
In respect of organizational management, numerous previous studies have ... and to forecast the academic staff structure of the university in the next five years. ... Keywords: Markov Chain, Transition Probability Matrix, Manpower Planning, ...
On almost-periodic points of a topological Markov chain
International Nuclear Information System (INIS)
Bogatyi, Semeon A; Redkozubov, Vadim V
2012-01-01
We prove that a transitive topological Markov chain has almost-periodic points of all D-periods. Moreover, every D-period is realized by continuously many distinct minimal sets. We give a simple constructive proof of the result which asserts that any transitive topological Markov chain has periodic points of almost all periods, and study the structure of the finite set of positive integers that are not periods.
Switching Markov chains for a holistic modeling of SIS unavailability
International Nuclear Information System (INIS)
Mechri, Walid; Simon, Christophe; BenOthman, Kamel
2015-01-01
This paper proposes a holistic approach to model the Safety Instrumented Systems (SIS). The model is based on Switching Markov Chain and integrates several parameters like Common Cause Failure, Imperfect Proof testing, partial proof testing, etc. The basic concepts of Switching Markov Chain applied to reliability analysis are introduced and a model to compute the unavailability for a case study is presented. The proposed Switching Markov Chain allows us to assess the effect of each parameter on the SIS performance. The proposed method ensures the relevance of the results. - Highlights: • A holistic approach to model the unavailability safety systems using Switching Markov chains. • The model integrates several parameters like probability of failure due to the test, the probability of not detecting a failure in a test. • The basic concepts of the Switching Markov Chains are introduced and applied to compute the unavailability for safety systems. • The proposed Switching Markov Chain allows assessing the effect of each parameter on the chemical reactor performance
Prognostics for Steam Generator Tube Rupture using Markov Chain model
International Nuclear Information System (INIS)
Kim, Gibeom; Heo, Gyunyoung; Kim, Hyeonmin
2016-01-01
This paper will describe the prognostics method for evaluating and forecasting the ageing effect and demonstrate the procedure of prognostics for the Steam Generator Tube Rupture (SGTR) accident. Authors will propose the data-driven method so called MCMC (Markov Chain Monte Carlo) which is preferred to the physical-model method in terms of flexibility and availability. Degradation data is represented as growth of burst probability over time. Markov chain model is performed based on transition probability of state. And the state must be discrete variable. Therefore, burst probability that is continuous variable have to be changed into discrete variable to apply Markov chain model to the degradation data. The Markov chain model which is one of prognostics methods was described and the pilot demonstration for a SGTR accident was performed as a case study. The Markov chain model is strong since it is possible to be performed without physical models as long as enough data are available. However, in the case of the discrete Markov chain used in this study, there must be loss of information while the given data is discretized and assigned to the finite number of states. In this process, original information might not be reflected on prediction sufficiently. This should be noted as the limitation of discrete models. Now we will be studying on other prognostics methods such as GPM (General Path Model) which is also data-driven method as well as the particle filer which belongs to physical-model method and conducting comparison analysis
Probability distributions for Markov chain based quantum walks
Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.
2018-01-01
We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.
Energy Technology Data Exchange (ETDEWEB)
Frank, T D [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)
2008-07-18
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
International Nuclear Information System (INIS)
Frank, T D
2008-01-01
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
Automated generation of partial Markov chain from high level descriptions
International Nuclear Information System (INIS)
Brameret, P.-A.; Rauzy, A.; Roussel, J.-M.
2015-01-01
We propose an algorithm to generate partial Markov chains from high level implicit descriptions, namely AltaRica models. This algorithm relies on two components. First, a variation on Dijkstra's algorithm to compute shortest paths in a graph. Second, the definition of a notion of distance to select which states must be kept and which can be safely discarded. The proposed method solves two problems at once. First, it avoids a manual construction of Markov chains, which is both tedious and error prone. Second, up the price of acceptable approximations, it makes it possible to push back dramatically the exponential blow-up of the size of the resulting chains. We report experimental results that show the efficiency of the proposed approach. - Highlights: • We generate Markov chains from a higher level safety modeling language (AltaRica). • We use a variation on Dijkstra's algorithm to generate partial Markov chains. • Hence we solve two problems: the first problem is the tedious manual construction of Markov chains. • The second problem is the blow-up of the size of the chains, at the cost of decent approximations. • The experimental results highlight the efficiency of the method
Quantile Forecasting for Credit Risk Management Using Possibly Mis-specified Hidden Markov Models
Banachewicz, K.P.; Lucas, A.
2008-01-01
Recent models for credit risk management make use of hidden Markov models (HMMs). HMMs are used to forecast quantiles of corporate default rates. Little research has been done on the quality of such forecasts if the underlying HMM is potentially misspecified. In this paper, we focus on
Automatic categorization of web pages and user clustering with mixtures of hidden Markov models
Ypma, A.; Heskes, T.M.; Zaiane, O.R.; Srivastav, J.
2003-01-01
We propose mixtures of hidden Markov models for modelling clickstreams of web surfers. Hence, the page categorization is learned from the data without the need for a (possibly cumbersome) manual categorization. We provide an EM algorithm for training a mixture of HMMs and show that additional static
Fast sampling from a Hidden Markov Model posterior for large data
DEFF Research Database (Denmark)
Bonnevie, Rasmus; Hansen, Lars Kai
2014-01-01
Hidden Markov Models are of interest in a broad set of applications including modern data driven systems involving very large data sets. However, approximate inference methods based on Bayesian averaging are precluded in such applications as each sampling step requires a full sweep over the data...
Asymptotic behavior of Bayes estimators for hidden Markov models with application to ion channels
de Gunst, M.C.M.; Shcherbakova, O.V.
2008-01-01
In this paper we study the asymptotic behavior of Bayes estimators for hidden Markov models as the number of observations goes to infinity. The theorem that we prove is similar to the Bernstein-von Mises theorem on the asymptotic behavior of the posterior distribution for the case of independent
Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R
DEFF Research Database (Denmark)
O'Connell, Jarad Michael; Højsgaard, Søren
2011-01-01
models only allow a geometrically distributed sojourn time in a given state, while hidden semi-Markov models extend this by allowing an arbitrary sojourn distribution. We demonstrate the software with simulation examples and an application involving the modelling of the ovarian cycle of dairy cows...
Efficient tests for equivalence of hidden Markov processes and quantum random walks
U. Faigle; A. Schönhuth (Alexander)
2011-01-01
htmlabstractWhile two hidden Markov process (HMP) resp.~quantum random walk (QRW) parametrizations can differ from one another, the stochastic processes arising from them can be equivalent. Here a polynomial-time algorithm is presented which can determine equivalence of two HMP parametrizations
Exact Sampling and Decoding in High-Order Hidden Markov Models
Carter, S.; Dymetman, M.; Bouchard, G.
2012-01-01
We present a method for exact optimization and sampling from high order Hidden Markov Models (HMMs), which are generally handled by approximation techniques. Motivated by adaptive rejection sampling and heuristic search, we propose a strategy based on sequentially refining a lower-order language
Segmentation of laser range radar images using hidden Markov field models
International Nuclear Information System (INIS)
Pucar, P.
1993-01-01
Segmentation of images in the context of model based stochastic techniques is connected with high, very often unpracticle computational complexity. The objective with this thesis is to take the models used in model based image processing, simplify and use them in suboptimal, but not computationally demanding algorithms. Algorithms that are essentially one-dimensional, and their extensions to two dimensions are given. The model used in this thesis is the well known hidden Markov model. Estimation of the number of hidden states from observed data is a problem that is addressed. The state order estimation problem is of general interest and is not specifically connected to image processing. An investigation of three state order estimation techniques for hidden Markov models is given. 76 refs
Martingales and Markov chains solved exercises and elements of theory
Baldi, Paolo; Priouret, Pierre
2002-01-01
CONDITIONAL EXPECTATIONSIntroductionDefinition and First PropertiesConditional Expectations and Conditional LawsExercisesSolutionsSTOCHASTIC PROCESSESGeneral FactsStopping TimesExercisesSolutionsMARTINGALESFirst DefinitionsFirst PropertiesThe Stopping TheoremMaximal InequalitiesSquare Integral MartingalesConvergence TheoremsRegular MartingalesExercisesProblemsSolutionsMARKOV CHAINSTransition Matrices, Markov ChainsConstruction and ExistenceComputations on the Canonical ChainPotential OperatorsPassage ProblemsRecurrence, TransienceRecurrent Irreducible ChainsPeriodicityExercisesProblemsSolution
Some remarks about the thermodynamics of discrete finite Markov chains
Energy Technology Data Exchange (ETDEWEB)
Siboni, S. [Trento Univ. (Italy). Facolta` di Ingegneria, Dip. di Ingegneria dei Materiali
1998-08-01
The Author propose a simple way to define a Hamiltonian for aperiodic Markov chains and to apply these chains in a thermodynamical context. The basic thermodynamic functions are correspondingly calculated. A quite intriguing and nontrivial application to stochastic automata is also pointed out.
Fracture Mechanical Markov Chain Crack Growth Model
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
1991-01-01
propagation process can be described by a discrete space Markov theory. The model is applicable to deterministic as well as to random loading. Once the model parameters for a given material have been determined, the results can be used for any structure as soon as the geometrical function is known....
Markov chain of distances between parked cars
International Nuclear Information System (INIS)
Seba, Petr
2008-01-01
We describe the distribution of distances between parked cars as a solution of certain Markov processes and show that its solution is obtained with the help of a distributional fixed point equation. Under certain conditions the process is solved explicitly. The resulting probability density is compared with the actual parking data measured in the city. (fast track communication)
Hidden Markov model for improved ultrasound-based presence detection
Jaramillo Garcia, P.A.; Linnartz, J.P.M.G.
2015-01-01
Adaptive lighting systems typically use a presence detector to save energy by switching off lights in unoccupied rooms. However, it is highly annoying when lights are erroneously turned off while a user is present (false negative, FN). This paper focuses on the estimation of presence, using a Hidden
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Valor, A.; Caleyo, F.; Alfonso, L.; Velázquez, J. C.; Hallen, J. M.
2013-01-01
The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure ...
Identification of temporal patterns in the seismicity of Sumatra using Poisson Hidden Markov models
Directory of Open Access Journals (Sweden)
Katerina Orfanogiannaki
2014-05-01
Full Text Available On 26 December 2004 and 28 March 2005 two large earthquakes occurred between the Indo-Australian and the southeastern Eurasian plates with moment magnitudes Mw=9.1 and Mw=8.6, respectively. Complete data (mb≥4.2 of the post-1993 time interval have been used to apply Poisson Hidden Markov models (PHMMs for identifying temporal patterns in the time series of the two earthquake sequences. Each time series consists of earthquake counts, in given and constant time units, in the regions determined by the aftershock zones of the two mainshocks. In PHMMs each count is generated by one of m different Poisson processes that are called states. The series of states is unobserved and is in fact a Markov chain. The model incorporates a varying seismicity rate, it assigns a different rate to each state and it detects the changes on the rate over time. In PHMMs unobserved factors, related to the local properties of the region are considered affecting the earthquake occurrence rate. Estimation and interpretation of the unobserved sequence of states that underlie the data contribute to better understanding of the geophysical processes that take place in the region. We applied PHMMs to the time series of the two mainshocks and we estimated the unobserved sequences of states that underlie the data. The results obtained showed that the region of the 26 December 2004 earthquake was in state of low seismicity during almost the entire observation period. On the contrary, in the region of the 28 March 2005 earthquake the seismic activity is attributed to triggered seismicity, due to stress transfer from the region of the 2004 mainshock.
Markov chains and semi-Markov models in time-to-event analysis.
Abner, Erin L; Charnigo, Richard J; Kryscio, Richard J
2013-10-25
A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields.
Stochastic Dynamics through Hierarchically Embedded Markov Chains.
Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M
2017-02-03
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
Markov Chains For Testing Redundant Software
White, Allan L.; Sjogren, Jon A.
1990-01-01
Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
Markov chain solution of photon multiple scattering through turbid slabs.
Lin, Ying; Northrop, William F; Li, Xuesong
2016-11-14
This work introduces a Markov Chain solution to model photon multiple scattering through turbid slabs via anisotropic scattering process, i.e., Mie scattering. Results show that the proposed Markov Chain model agree with commonly used Monte Carlo simulation for various mediums such as medium with non-uniform phase functions and absorbing medium. The proposed Markov Chain solution method successfully converts the complex multiple scattering problem with practical phase functions into a matrix form and solves transmitted/reflected photon angular distributions by matrix multiplications. Such characteristics would potentially allow practical inversions by matrix manipulation or stochastic algorithms where widely applied stochastic methods such as Monte Carlo simulations usually fail, and thus enable practical diagnostics reconstructions such as medical diagnosis, spray analysis, and atmosphere sciences.
The spectral method and ergodic theorems for general Markov chains
International Nuclear Information System (INIS)
Nagaev, S V
2015-01-01
We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space
An Application of Graph Theory in Markov Chains Reliability Analysis
Directory of Open Access Journals (Sweden)
Pavel Skalny
2014-01-01
Full Text Available The paper presents reliability analysis which was realized for an industrial company. The aim of the paper is to present the usage of discrete time Markov chains and the flow in network approach. Discrete Markov chains a well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. Markov chains are used to describe transitions between the states of the process. The industrial process is described as a graph network. The maximal flow in the network corresponds to the production. The Ford-Fulkerson algorithm is used to quantify the production for each state. The combination of both methods are utilized to quantify the expected value of the amount of manufactured products for the given time period.
Directory of Open Access Journals (Sweden)
Fei Chen
2015-04-01
Full Text Available Gesture recognition is essential for human and robot collaboration. Within an industrial hybrid assembly cell, the performance of such a system significantly affects the safety of human workers. This work presents an approach to recognizing hand gestures accurately during an assembly task while in collaboration with a robot co-worker. We have designed and developed a sensor system for measuring natural human-robot interactions. The position and rotation information of a human worker's hands and fingertips are tracked in 3D space while completing a task. A modified chain-code method is proposed to describe the motion trajectory of the measured hands and fingertips. The Hidden Markov Model (HMM method is adopted to recognize patterns via data streams and identify workers' gesture patterns and assembly intentions. The effectiveness of the proposed system is verified by experimental results. The outcome demonstrates that the proposed system is able to automatically segment the data streams and recognize the gesture patterns thus represented with a reasonable accuracy ratio.
QRS complex detection based on continuous density hidden Markov models using univariate observations
Sotelo, S.; Arenas, W.; Altuve, M.
2018-04-01
In the electrocardiogram (ECG), the detection of QRS complexes is a fundamental step in the ECG signal processing chain since it allows the determination of other characteristics waves of the ECG and provides information about heart rate variability. In this work, an automatic QRS complex detector based on continuous density hidden Markov models (HMM) is proposed. HMM were trained using univariate observation sequences taken either from QRS complexes or their derivatives. The detection approach is based on the log-likelihood comparison of the observation sequence with a fixed threshold. A sliding window was used to obtain the observation sequence to be evaluated by the model. The threshold was optimized by receiver operating characteristic curves. Sensitivity (Sen), specificity (Spc) and F1 score were used to evaluate the detection performance. The approach was validated using ECG recordings from the MIT-BIH Arrhythmia database. A 6-fold cross-validation shows that the best detection performance was achieved with 2 states HMM trained with QRS complexes sequences (Sen = 0.668, Spc = 0.360 and F1 = 0.309). We concluded that these univariate sequences provide enough information to characterize the QRS complex dynamics from HMM. Future works are directed to the use of multivariate observations to increase the detection performance.
Hidden Markov model approach for identifying the modular framework of the protein backbone.
Camproux, A C; Tuffery, P; Chevrolat, J P; Boisvieux, J F; Hazout, S
1999-12-01
The hidden Markov model (HMM) was used to identify recurrent short 3D structural building blocks (SBBs) describing protein backbones, independently of any a priori knowledge. Polypeptide chains are decomposed into a series of short segments defined by their inter-alpha-carbon distances. Basically, the model takes into account the sequentiality of the observed segments and assumes that each one corresponds to one of several possible SBBs. Fitting the model to a database of non-redundant proteins allowed us to decode proteins in terms of 12 distinct SBBs with different roles in protein structure. Some SBBs correspond to classical regular secondary structures. Others correspond to a significant subdivision of their bounding regions previously considered to be a single pattern. The major contribution of the HMM is that this model implicitly takes into account the sequential connections between SBBs and thus describes the most probable pathways by which the blocks are connected to form the framework of the protein structures. Validation of the SBBs code was performed by extracting SBB series repeated in recoding proteins and examining their structural similarities. Preliminary results on the sequence specificity of SBBs suggest promising perspectives for the prediction of SBBs or series of SBBs from the protein sequences.
Dynamic modeling of presence of occupants using inhomogeneous Markov chains
DEFF Research Database (Denmark)
Andersen, Philip Hvidthøft Delff; Iversen, Anne; Madsen, Henrik
2014-01-01
on time of day, and by use of a filter of the observations it is able to capture per-employee sequence dynamics. Simulations using this method are compared with simulations using homogeneous Markov chains and show far better ability to reproduce key properties of the data. The method is based...... on inhomogeneous Markov chains with where the transition probabilities are estimated using generalized linear models with polynomials, B-splines, and a filter of passed observations as inputs. For treating the dispersion of the data series, a hierarchical model structure is used where one model is for low presence...
On a Markov chain roulette-type game
International Nuclear Information System (INIS)
El-Shehawey, M A; El-Shreef, Gh A
2009-01-01
A Markov chain on non-negative integers which arises in a roulette-type game is discussed. The transition probabilities are p 01 = ρ, p Nj = δ Nj , p i,i+W = q, p i,i-1 = p = 1 - q, 1 ≤ W < N, 0 ≤ ρ ≤ 1, N - W < j ≤ N and i = 1, 2, ..., N - W. Using formulae for the determinant of a partitioned matrix, a closed form expression for the solution of the Markov chain roulette-type game is deduced. The present analysis is supported by two mathematical models from tumor growth and war with bargaining
Classification of customer lifetime value models using Markov chain
Permana, Dony; Pasaribu, Udjianna S.; Indratno, Sapto W.; Suprayogi
2017-10-01
A firm’s potential reward in future time from a customer can be determined by customer lifetime value (CLV). There are some mathematic methods to calculate it. One method is using Markov chain stochastic model. Here, a customer is assumed through some states. Transition inter the states follow Markovian properties. If we are given some states for a customer and the relationships inter states, then we can make some Markov models to describe the properties of the customer. As Markov models, CLV is defined as a vector contains CLV for a customer in the first state. In this paper we make a classification of Markov Models to calculate CLV. Start from two states of customer model, we make develop in many states models. The development a model is based on weaknesses in previous model. Some last models can be expected to describe how real characters of customers in a firm.
ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
Directory of Open Access Journals (Sweden)
Mohammad Mirabi
2012-01-01
Full Text Available
ENGLISH ABSTRACT: In this research, a Markov analysis of acceptance sampling plans in a single stage and in two stages is proposed, based on the quality of the items inspected. In a stage of this policy, if the number of defective items in a sample of inspected items is more than the upper threshold, the batch is rejected. However, the batch is accepted if the number of defective items is less than the lower threshold. Nonetheless, when the number of defective items falls between the upper and lower thresholds, the decision-making process continues to inspect the items and collect further samples. The primary objective is to determine the optimal values of the upper and lower thresholds using a Markov process to minimise the total cost associated with a batch acceptance policy. A solution method is presented, along with a numerical demonstration of the application of the proposed methodology.
AFRIKAANSE OPSOMMING: In hierdie navorsing word ’n Markov-ontleding gedoen van aannamemonsternemingsplanne wat plaasvind in ’n enkele stap of in twee stappe na gelang van die kwaliteit van die items wat geïnspekteer word. Indien die eerste monster toon dat die aantal defektiewe items ’n boonste grens oorskry, word die lot afgekeur. Indien die eerste monster toon dat die aantal defektiewe items minder is as ’n onderste grens, word die lot aanvaar. Indien die eerste monster toon dat die aantal defektiewe items in die gebied tussen die boonste en onderste grense lê, word die besluitnemingsproses voortgesit en verdere monsters word geneem. Die primêre doel is om die optimale waardes van die booonste en onderste grense te bepaal deur gebruik te maak van ’n Markov-proses sodat die totale koste verbonde aan die proses geminimiseer kan word. ’n Oplossing word daarna voorgehou tesame met ’n numeriese voorbeeld van die toepassing van die voorgestelde oplossing.
Vaglica, Gabriella; Lillo, Fabrizio; Mantegna, Rosario N.
2010-07-01
Large trades in a financial market are usually split into smaller parts and traded incrementally over extended periods of time. We address these large trades as hidden orders. In order to identify and characterize hidden orders, we fit hidden Markov models to the time series of the sign of the tick-by-tick inventory variation of market members of the Spanish Stock Exchange. Our methodology probabilistically detects trading sequences, which are characterized by a significant majority of buy or sell transactions. We interpret these patches of sequential buying or selling transactions as proxies of the traded hidden orders. We find that the time, volume and number of transaction size distributions of these patches are fat tailed. Long patches are characterized by a large fraction of market orders and a low participation rate, while short patches have a large fraction of limit orders and a high participation rate. We observe the existence of a buy-sell asymmetry in the number, average length, average fraction of market orders and average participation rate of the detected patches. The detected asymmetry is clearly dependent on the local market trend. We also compare the hidden Markov model patches with those obtained with the segmentation method used in Vaglica et al (2008 Phys. Rev. E 77 036110), and we conclude that the former ones can be interpreted as a partition of the latter ones.
Hidden Markov Model of atomic quantum jump dynamics in an optically probed cavity
DEFF Research Database (Denmark)
Gammelmark, S.; Molmer, K.; Alt, W.
2014-01-01
We analyze the quantum jumps of an atom interacting with a cavity field. The strong atom- field interaction makes the cavity transmission depend on the time dependent atomic state, and we present a Hidden Markov Model description of the atomic state dynamics which is conditioned in a Bayesian...... manner on the detected signal. We suggest that small variations in the observed signal may be due to spatial motion of the atom within the cavity, and we represent the atomic system by a number of hidden states to account for both the small variations and the internal state jump dynamics. In our theory...
Influence of credit scoring on the dynamics of Markov chain
Galina, Timofeeva
2015-11-01
Markov processes are widely used to model the dynamics of a credit portfolio and forecast the portfolio risk and profitability. In the Markov chain model the loan portfolio is divided into several groups with different quality, which determined by presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is described by a multistage controlled system. The article outlines mathematical formalization of controls which reflect the actions of the bank's management in order to improve the loan portfolio quality. The most important control is the organization of approval procedure of loan applications. The credit scoring is studied as a control affecting to the dynamic system. Different formalizations of "good" and "bad" consumers are proposed in connection with the Markov chain model.
Learning to Automatically Detect Features for Mobile Robots Using Second-Order Hidden Markov Models
Directory of Open Access Journals (Sweden)
Olivier Aycard
2004-12-01
Full Text Available In this paper, we propose a new method based on Hidden Markov Models to interpret temporal sequences of sensor data from mobile robots to automatically detect features. Hidden Markov Models have been used for a long time in pattern recognition, especially in speech recognition. Their main advantages over other methods (such as neural networks are their ability to model noisy temporal signals of variable length. We show in this paper that this approach is well suited for interpretation of temporal sequences of mobile-robot sensor data. We present two distinct experiments and results: the first one in an indoor environment where a mobile robot learns to detect features like open doors or T-intersections, the second one in an outdoor environment where a different mobile robot has to identify situations like climbing a hill or crossing a rock.
Hidden Markov models for zero-inflated Poisson counts with an application to substance use.
DeSantis, Stacia M; Bandyopadhyay, Dipankar
2011-06-30
Paradigms for substance abuse cue-reactivity research involve pharmacological or stressful stimulation designed to elicit stress and craving responses in cocaine-dependent subjects. It is unclear as to whether stress induced from participation in such studies increases drug-seeking behavior. We propose a 2-state Hidden Markov model to model the number of cocaine abuses per week before and after participation in a stress-and cue-reactivity study. The hypothesized latent state corresponds to 'high' or 'low' use. To account for a preponderance of zeros, we assume a zero-inflated Poisson model for the count data. Transition probabilities depend on the prior week's state, fixed demographic variables, and time-varying covariates. We adopt a Bayesian approach to model fitting, and use the conditional predictive ordinate statistic to demonstrate that the zero-inflated Poisson hidden Markov model outperforms other models for longitudinal count data. Copyright © 2011 John Wiley & Sons, Ltd.
Modeling of IP scanning activities with Hidden Markov Models: Darknet case study
De Santis , Giulia; Lahmadi , Abdelkader; Francois , Jerome; Festor , Olivier
2016-01-01
International audience; We propose a methodology based on Hidden Markov Models (HMMs) to model scanning activities monitored by a darknet. The HMMs of scanning activities are built on the basis of the number of scanned IP addresses within a time window and fitted using mixtures of Poisson distributions. Our methodology is applied on real data traces collected from a darknet and generated by two large scale scanners, ZMap and Shodan. We demonstrated that the built models are able to characteri...
Utilizing Gaze Behavior for Inferring Task Transitions Using Abstract Hidden Markov Models
Directory of Open Access Journals (Sweden)
Daniel Fernando Tello Gamarra
2016-12-01
Full Text Available We demonstrate an improved method for utilizing observed gaze behavior and show that it is useful in inferring hand movement intent during goal directed tasks. The task dynamics and the relationship between hand and gaze behavior are learned using an Abstract Hidden Markov Model (AHMM. We show that the predicted hand movement transitions occur consistently earlier in AHMM models with gaze than those models that do not include gaze observations.
Belief Bisimulation for Hidden Markov Models Logical Characterisation and Decision Algorithm
DEFF Research Database (Denmark)
Jansen, David N.; Nielson, Flemming; Zhang, Lijun
2012-01-01
This paper establishes connections between logical equivalences and bisimulation relations for hidden Markov models (HMM). Both standard and belief state bisimulations are considered. We also present decision algorithms for the bisimilarities. For standard bisimilarity, an extension of the usual...... partition refinement algorithm is enough. Belief bisimilarity, being a relation on the continuous space of belief states, cannot be described directly. Instead, we show how to generate a linear equation system in time cubic in the number of states....
Caveats on Bayesian and hidden-Markov models (v2.8)
Schomaker, Lambert
2016-01-01
This paper describes a number of fundamental and practical problems in the application of hidden-Markov models and Bayes when applied to cursive-script recognition. Several problems, however, will have an effect in other application areas. The most fundamental problem is the propagation of error in the product of probabilities. This is a common and pervasive problem which deserves more attention. On the basis of Monte Carlo modeling, tables for the expected relative error are given. It seems ...
Recombination Processes and Nonlinear Markov Chains.
Pirogov, Sergey; Rybko, Alexander; Kalinina, Anastasia; Gelfand, Mikhail
2016-09-01
Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity between the recombining segments, several studies examined whether this could lead to the emergence of subspecies. Most of them simulated fixed-size Wright-Fisher populations, in which the genetic drift should be taken into account. Here, we use nonlinear Markov processes to describe a bacterial population evolving under mutation and recombination. We consider a population structure as a probability measure on the space of genomes. This approach implies the infinite population size limit, and thus, the genetic drift is not assumed. We prove that under these conditions, the emergence of subspecies is impossible.
A Parallel Solver for Large-Scale Markov Chains
Czech Academy of Sciences Publication Activity Database
Benzi, M.; Tůma, Miroslav
2002-01-01
Roč. 41, - (2002), s. 135-153 ISSN 0168-9274 R&D Projects: GA AV ČR IAA2030801; GA ČR GA101/00/1035 Keywords : parallel preconditioning * iterative methods * discrete Markov chains * generalized inverses * singular matrices * graph partitioning * AINV * Bi-CGSTAB Subject RIV: BA - General Mathematics Impact factor: 0.504, year: 2002
Markov chain model for demersal fish catch analysis in Indonesia
Firdaniza; Gusriani, N.
2018-03-01
As an archipelagic country, Indonesia has considerable potential fishery resources. One of the fish resources that has high economic value is demersal fish. Demersal fish is a fish with a habitat in the muddy seabed. Demersal fish scattered throughout the Indonesian seas. Demersal fish production in each Indonesia’s Fisheries Management Area (FMA) varies each year. In this paper we have discussed the Markov chain model for demersal fish yield analysis throughout all Indonesia’s Fisheries Management Area. Data of demersal fish catch in every FMA in 2005-2014 was obtained from Directorate of Capture Fisheries. From this data a transition probability matrix is determined by the number of transitions from the catch that lie below the median or above the median. The Markov chain model of demersal fish catch data was an ergodic Markov chain model, so that the limiting probability of the Markov chain model can be determined. The predictive value of demersal fishing yields was obtained by calculating the combination of limiting probability with average catch results below the median and above the median. The results showed that for 2018 and long-term demersal fishing results in most of FMA were below the median value.
The How and Why of Interactive Markov Chains
Hermanns, H.; Katoen, Joost P.; de Boer, F.S; Bonsangue, S.H.; Leuschel, M
2010-01-01
This paper reviews the model of interactive Markov chains (IMCs, for short), an extension of labelled transition systems with exponentially delayed transitions. We show that IMCs are closed under parallel composition and hiding, and show how IMCs can be compositionally aggregated prior to analysis
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, P.; van Doorn, E.A.
2001-01-01
The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, Pauline; van Doorn, Erik A.
2002-01-01
he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\\Pi$ is the matrix $D \\equiv \\int_0^{\\infty} (P(t)-\\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a
Exact goodness-of-fit tests for Markov chains.
Besag, J; Mondal, D
2013-06-01
Goodness-of-fit tests are useful in assessing whether a statistical model is consistent with available data. However, the usual χ² asymptotics often fail, either because of the paucity of the data or because a nonstandard test statistic is of interest. In this article, we describe exact goodness-of-fit tests for first- and higher order Markov chains, with particular attention given to time-reversible ones. The tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple Monte Carlo sampling or by Markov chain Monte Carlo. They apply both to single and to multiple sequences and allow a free choice of test statistic. Three examples are given. The first concerns multiple sequences of dry and wet January days for the years 1948-1983 at Snoqualmie Falls, Washington State, and suggests that standard analysis may be misleading. The second one is for a four-state DNA sequence and lends support to the original conclusion that a second-order Markov chain provides an adequate fit to the data. The last one is six-state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first-order reversible Markov chain at 6 picosecond time steps. © 2013, The International Biometric Society.
Complete Axiomatization for the Bisimilarity Distance on Markov Chains
DEFF Research Database (Denmark)
Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand
2016-01-01
In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS...
Adiabatic condition and the quantum hitting time of Markov chains
International Nuclear Information System (INIS)
Krovi, Hari; Ozols, Maris; Roland, Jeremie
2010-01-01
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P ' where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP ' and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.
Exploring Mass Perception with Markov Chain Monte Carlo
Cohen, Andrew L.; Ross, Michael G.
2009-01-01
Several previous studies have examined the ability to judge the relative mass of objects in idealized collisions. With a newly developed technique of psychological Markov chain Monte Carlo sampling (A. N. Sanborn & T. L. Griffiths, 2008), this work explores participants; perceptions of different collision mass ratios. The results reveal…
Model checking conditional CSL for continuous-time Markov chains
DEFF Research Database (Denmark)
Gao, Yang; Xu, Ming; Zhan, Naijun
2013-01-01
In this paper, we consider the model-checking problem of continuous-time Markov chains (CTMCs) with respect to conditional logic. To the end, we extend Continuous Stochastic Logic introduced in Aziz et al. (2000) [1] to Conditional Continuous Stochastic Logic (CCSL) by introducing a conditional...
Power plant reliability calculation with Markov chain models
International Nuclear Information System (INIS)
Senegacnik, A.; Tuma, M.
1998-01-01
In the paper power plant operation is modelled using continuous time Markov chains with discrete state space. The model is used to compute the power plant reliability and the importance and influence of individual states, as well as the transition probabilities between states. For comparison the model is fitted to data for coal and nuclear power plants recorded over several years. (orig.) [de
On the Metric-based Approximate Minimization of Markov Chains
DEFF Research Database (Denmark)
Bacci, Giovanni; Bacci, Giorgio; Larsen, Kim Guldstrand
2018-01-01
In this paper we address the approximate minimization problem of Markov Chains (MCs) from a behavioral metric-based perspective. Specifically, given a finite MC and a positive integer k, we are looking for an MC with at most k states having minimal distance to the original. The metric considered...
Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion
DEFF Research Database (Denmark)
Zunino, Andrea; Lange, Katrine; Melnikova, Yulia
2014-01-01
We present a study on the inversion of seismic reflection data generated from a synthetic reservoir model. Our aim is to invert directly for rock facies and porosity of the target reservoir zone. We solve this inverse problem using a Markov chain Monte Carlo (McMC) method to handle the nonlinear...
Students' Progress throughout Examination Process as a Markov Chain
Hlavatý, Robert; Dömeová, Ludmila
2014-01-01
The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…
Markov chains with quasitoeplitz transition matrix: first zero hitting
Directory of Open Access Journals (Sweden)
Alexander M. Dukhovny
1989-01-01
Full Text Available This paper continues the investigation of Markov Chains with a quasitoeplitz transition matrix. Generating functions of first zero hitting probabilities and mean times are found by the solution of special Riemann boundary value problems on the unit circle. Duality is discussed.
On the Total Variation Distance of Semi-Markov Chains
DEFF Research Database (Denmark)
Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand
2015-01-01
Semi-Markov chains (SMCs) are continuous-time probabilistic transition systems where the residence time on states is governed by generic distributions on the positive real line. This paper shows the tight relation between the total variation distance on SMCs and their model checking problem over...
On the Metric-Based Approximate Minimization of Markov Chains
DEFF Research Database (Denmark)
Bacci, Giovanni; Bacci, Giorgio; Larsen, Kim Guldstrand
2017-01-01
We address the behavioral metric-based approximate minimization problem of Markov Chains (MCs), i.e., given a finite MC and a positive integer k, we are interested in finding a k-state MC of minimal distance to the original. By considering as metric the bisimilarity distance of Desharnais at al...
A theoretical Markov chain model for evaluating correctional ...
African Journals Online (AJOL)
In this paper a stochastic method is applied in the study of the long time effect of confinement in a correctional institution on the behaviour of a person with criminal tendencies. The approach used is Markov chain, which uses past history to predict the state of a system in the future. A model is developed for comparing the ...
When are two Markov chains the same? | Cowen | Quaestiones ...
African Journals Online (AJOL)
Given two one-sided Markov chains, the authors illustrate a procedure for ascertaining whether they are essentially the same. Precisely, they show how one can determine whether they are block-isomorphic. An application to hydrology is investigated with an example. Quaestiones Mathematicae 23(2000), 507–513 ...
Operations and support cost modeling using Markov chains
Unal, Resit
1989-01-01
Systems for future missions will be selected with life cycle costs (LCC) as a primary evaluation criterion. This reflects the current realization that only systems which are considered affordable will be built in the future due to the national budget constaints. Such an environment calls for innovative cost modeling techniques which address all of the phases a space system goes through during its life cycle, namely: design and development, fabrication, operations and support; and retirement. A significant portion of the LCC for reusable systems are generated during the operations and support phase (OS). Typically, OS costs can account for 60 to 80 percent of the total LCC. Clearly, OS costs are wholly determined or at least strongly influenced by decisions made during the design and development phases of the project. As a result OS costs need to be considered and estimated early in the conceptual phase. To be effective, an OS cost estimating model needs to account for actual instead of ideal processes by associating cost elements with probabilities. One approach that may be suitable for OS cost modeling is the use of the Markov Chain Process. Markov chains are an important method of probabilistic analysis for operations research analysts but they are rarely used for life cycle cost analysis. This research effort evaluates the use of Markov Chains in LCC analysis by developing OS cost model for a hypothetical reusable space transportation vehicle (HSTV) and suggests further uses of the Markov Chain process as a design-aid tool.
Markov chain Monte Carlo methods in radiotherapy treatment planning
International Nuclear Information System (INIS)
Hugtenburg, R.P.
2001-01-01
The Markov chain method can be used to incorporate measured data in Monte Carlo based radiotherapy treatment planning. This paper shows that convergence to the measured data, within the target precision, is achievable. Relative output factors for blocked fields and oblique beams are shown to compare well with independent measurements according to the same criterion. (orig.)
A Multilayer Hidden Markov Models-Based Method for Human-Robot Interaction
Directory of Open Access Journals (Sweden)
Chongben Tao
2013-01-01
Full Text Available To achieve Human-Robot Interaction (HRI by using gestures, a continuous gesture recognition approach based on Multilayer Hidden Markov Models (MHMMs is proposed, which consists of two parts. One part is gesture spotting and segment module, the other part is continuous gesture recognition module. Firstly, a Kinect sensor is used to capture 3D acceleration and 3D angular velocity data of hand gestures. And then, a Feed-forward Neural Networks (FNNs and a threshold criterion are used for gesture spotting and segment, respectively. Afterwards, the segmented gesture signals are respectively preprocessed and vector symbolized by a sliding window and a K-means clustering method. Finally, symbolized data are sent into Lower Hidden Markov Models (LHMMs to identify individual gestures, and then, a Bayesian filter with sequential constraints among gestures in Upper Hidden Markov Models (UHMMs is used to correct recognition errors created in LHMMs. Five predefined gestures are used to interact with a Kinect mobile robot in experiments. The experimental results show that the proposed method not only has good effectiveness and accuracy, but also has favorable real-time performance.
Basic problems solving for two-dimensional discrete 3 × 4 order hidden markov model
International Nuclear Information System (INIS)
Wang, Guo-gang; Gan, Zong-liang; Tang, Gui-jin; Cui, Zi-guan; Zhu, Xiu-chang
2016-01-01
A novel model is proposed to overcome the shortages of the classical hypothesis of the two-dimensional discrete hidden Markov model. In the proposed model, the state transition probability depends on not only immediate horizontal and vertical states but also on immediate diagonal state, and the observation symbol probability depends on not only current state but also on immediate horizontal, vertical and diagonal states. This paper defines the structure of the model, and studies the three basic problems of the model, including probability calculation, path backtracking and parameters estimation. By exploiting the idea that the sequences of states on rows or columns of the model can be seen as states of a one-dimensional discrete 1 × 2 order hidden Markov model, several algorithms solving the three questions are theoretically derived. Simulation results further demonstrate the performance of the algorithms. Compared with the two-dimensional discrete hidden Markov model, there are more statistical characteristics in the structure of the proposed model, therefore the proposed model theoretically can more accurately describe some practical problems.
Hidden Markov models and other machine learning approaches in computational molecular biology
Energy Technology Data Exchange (ETDEWEB)
Baldi, P. [California Inst. of Tech., Pasadena, CA (United States)
1995-12-31
This tutorial was one of eight tutorials selected to be presented at the Third International Conference on Intelligent Systems for Molecular Biology which was held in the United Kingdom from July 16 to 19, 1995. Computational tools are increasingly needed to process the massive amounts of data, to organize and classify sequences, to detect weak similarities, to separate coding from non-coding regions, and reconstruct the underlying evolutionary history. The fundamental problem in machine learning is the same as in scientific reasoning in general, as well as statistical modeling: to come up with a good model for the data. In this tutorial four classes of models are reviewed. They are: Hidden Markov models; artificial Neural Networks; Belief Networks; and Stochastic Grammars. When dealing with DNA and protein primary sequences, Hidden Markov models are one of the most flexible and powerful alignments and data base searches. In this tutorial, attention is focused on the theory of Hidden Markov Models, and how to apply them to problems in molecular biology.
Geometry and Dynamics for Markov Chain Monte Carlo
Barp, Alessandro; Briol, Francois-Xavier; Kennedy, Anthony D.; Girolami, Mark
2017-01-01
Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains which can explore probability densities efficiently. The method emerges from physics and geometry and these links have been extensively studied by a series of authors through the last thirty years. However, there is currently a gap between the in...
Transportation and concentration inequalities for bifurcating Markov chains
DEFF Research Database (Denmark)
Penda, S. Valère Bitseki; Escobar-Bach, Mikael; Guillin, Arnaud
2017-01-01
We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful...... concentration inequalities.We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive...
Markov chain analysis of single spin flip Ising simulations
International Nuclear Information System (INIS)
Hennecke, M.
1997-01-01
The Markov processes defined by random and loop-based schemes for single spin flip attempts in Monte Carlo simulations of the 2D Ising model are investigated, by explicitly constructing their transition matrices. Their analysis reveals that loops over all lattice sites using a Metropolis-type single spin flip probability often do not define ergodic Markov chains, and have distorted dynamical properties even if they are ergodic. The transition matrices also enable a comparison of the dynamics of random versus loop spin selection and Glauber versus Metropolis probabilities
Hierarchical Multiple Markov Chain Model for Unsupervised Texture Segmentation
Czech Academy of Sciences Publication Activity Database
Scarpa, G.; Gaetano, R.; Haindl, Michal; Zerubia, J.
2009-01-01
Roč. 18, č. 8 (2009), s. 1830-1843 ISSN 1057-7149 R&D Projects: GA ČR GA102/08/0593 EU Projects: European Commission(XE) 507752 - MUSCLE Institutional research plan: CEZ:AV0Z10750506 Keywords : Classification * texture analysis * segmentation * hierarchical image models * Markov process Subject RIV: BD - Theory of Information Impact factor: 2.848, year: 2009 http://library.utia.cas.cz/separaty/2009/RO/haindl-hierarchical multiple markov chain model for unsupervised texture segmentation.pdf
Markov chain aggregation for agent-based models
Banisch, Sven
2016-01-01
This self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting “micro-chain” including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the upd...
Variable context Markov chains for HIV protease cleavage site prediction.
Oğul, Hasan
2009-06-01
Deciphering the knowledge of HIV protease specificity and developing computational tools for detecting its cleavage sites in protein polypeptide chain are very desirable for designing efficient and specific chemical inhibitors to prevent acquired immunodeficiency syndrome. In this study, we developed a generative model based on a generalization of variable order Markov chains (VOMC) for peptide sequences and adapted the model for prediction of their cleavability by certain proteases. The new method, called variable context Markov chains (VCMC), attempts to identify the context equivalence based on the evolutionary similarities between individual amino acids. It was applied for HIV-1 protease cleavage site prediction problem and shown to outperform existing methods in terms of prediction accuracy on a common dataset. In general, the method is a promising tool for prediction of cleavage sites of all proteases and encouraged to be used for any kind of peptide classification problem as well.
Optimization of Markov chains for a SUSY fitter: Fittino
Energy Technology Data Exchange (ETDEWEB)
Prudent, Xavier [IKTP, Technische Universitaet, Dresden (Germany); Bechtle, Philip [DESY, Hamburg (Germany); Desch, Klaus; Wienemann, Peter [Universitaet Bonn (Germany)
2010-07-01
A Markov chains is a ''random walk'' algorithm which allows an efficient scan of a given profile and the search of the absolute minimum, even when this profil suffers from the presence of many secondary minima. This property makes them particularly suited to the study of Supersymmetry (SUSY) models, where minima have to be found in up-to 18-dimensional space for the general MSSM. Hence the SUSY fitter ''Fittino'' uses a Metropolis*Hastings Markov chain in a frequentist interpretation to study the impact of current low -energy measurements, as well as expected measurements from LHC and ILC, on the SUSY parameter space. The expected properties of an optimal Markov chain should be the independence of final results with respect to the starting point and a fast convergence. These two points can be achieved by optimizing the width of the proposal distribution, that is the ''average step length'' between two links in the chain. We developped an algorithm for the optimization of the proposal width, by modifying iteratively the width so that the rejection rate be around fifty percent. This optimization leads to a starting point independent chain as well as a faster convergence.
Benoit, Julia S; Chan, Wenyaw; Luo, Sheng; Yeh, Hung-Wen; Doody, Rachelle
2016-04-30
Understanding the dynamic disease process is vital in early detection, diagnosis, and measuring progression. Continuous-time Markov chain (CTMC) methods have been used to estimate state-change intensities but challenges arise when stages are potentially misclassified. We present an analytical likelihood approach where the hidden state is modeled as a three-state CTMC model allowing for some observed states to be possibly misclassified. Covariate effects of the hidden process and misclassification probabilities of the hidden state are estimated without information from a 'gold standard' as comparison. Parameter estimates are obtained using a modified expectation-maximization (EM) algorithm, and identifiability of CTMC estimation is addressed. Simulation studies and an application studying Alzheimer's disease caregiver stress-levels are presented. The method was highly sensitive to detecting true misclassification and did not falsely identify error in the absence of misclassification. In conclusion, we have developed a robust longitudinal method for analyzing categorical outcome data when classification of disease severity stage is uncertain and the purpose is to study the process' transition behavior without a gold standard. Copyright © 2016 John Wiley & Sons, Ltd.
Markov chain modelling of pitting corrosion in underground pipelines
Energy Technology Data Exchange (ETDEWEB)
Caleyo, F. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)], E-mail: fcaleyo@gmail.com; Velazquez, J.C. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico); Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 La Habana (Cuba); Hallen, J.M. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)
2009-09-15
A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.
Markov chain modelling of pitting corrosion in underground pipelines
International Nuclear Information System (INIS)
Caleyo, F.; Velazquez, J.C.; Valor, A.; Hallen, J.M.
2009-01-01
A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.
a Probability Model for Drought Prediction Using Fusion of Markov Chain and SAX Methods
Jouybari-Moghaddam, Y.; Saradjian, M. R.; Forati, A. M.
2017-09-01
Drought is one of the most powerful natural disasters which are affected on different aspects of the environment. Most of the time this phenomenon is immense in the arid and semi-arid area. Monitoring and prediction the severity of the drought can be useful in the management of the natural disaster caused by drought. Many indices were used in predicting droughts such as SPI, VCI, and TVX. In this paper, based on three data sets (rainfall, NDVI, and land surface temperature) which are acquired from MODIS satellite imagery, time series of SPI, VCI, and TVX in time limited between winters 2000 to summer 2015 for the east region of Isfahan province were created. Using these indices and fusion of symbolic aggregation approximation and hidden Markov chain drought was predicted for fall 2015. For this purpose, at first, each time series was transformed into the set of quality data based on the state of drought (5 group) by using SAX algorithm then the probability matrix for the future state was created by using Markov hidden chain. The fall drought severity was predicted by fusion the probability matrix and state of drought severity in summer 2015. The prediction based on the likelihood for each state of drought includes severe drought, middle drought, normal drought, severe wet and middle wet. The analysis and experimental result from proposed algorithm show that the product of this algorithm is acceptable and the proposed algorithm is appropriate and efficient for predicting drought using remote sensor data.
Algebraic decay in self-similar Markov chains
International Nuclear Information System (INIS)
Hanson, J.D.; Cary, J.R.; Meiss, J.D.
1985-01-01
A continuous-time Markov chain is used to model motion in the neighborhood of a critical invariant circle for a Hamiltonian map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. For the case of a noble frequency, the chain is self-similar and the nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to the critical noble circle, the decay proceeds as t/sup -4.05/
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
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A. Valor
2013-01-01
Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.
Two-Stage Hidden Markov Model in Gesture Recognition for Human Robot Interaction
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Nhan Nguyen-Duc-Thanh
2012-07-01
Full Text Available Hidden Markov Model (HMM is very rich in mathematical structure and hence can form the theoretical basis for use in a wide range of applications including gesture representation. Most research in this field, however, uses only HMM for recognizing simple gestures, while HMM can definitely be applied for whole gesture meaning recognition. This is very effectively applicable in Human-Robot Interaction (HRI. In this paper, we introduce an approach for HRI in which not only the human can naturally control the robot by hand gesture, but also the robot can recognize what kind of task it is executing. The main idea behind this method is the 2-stages Hidden Markov Model. The 1st HMM is to recognize the prime command-like gestures. Based on the sequence of prime gestures that are recognized from the 1st stage and which represent the whole action, the 2nd HMM plays a role in task recognition. Another contribution of this paper is that we use the output Mixed Gaussian distribution in HMM to improve the recognition rate. In the experiment, we also complete a comparison of the different number of hidden states and mixture components to obtain the optimal one, and compare to other methods to evaluate this performance.
Detection of bursts in extracellular spike trains using hidden semi-Markov point process models.
Tokdar, Surya; Xi, Peiyi; Kelly, Ryan C; Kass, Robert E
2010-08-01
Neurons in vitro and in vivo have epochs of bursting or "up state" activity during which firing rates are dramatically elevated. Various methods of detecting bursts in extracellular spike trains have appeared in the literature, the most widely used apparently being Poisson Surprise (PS). A natural description of the phenomenon assumes (1) there are two hidden states, which we label "burst" and "non-burst," (2) the neuron evolves stochastically, switching at random between these two states, and (3) within each state the spike train follows a time-homogeneous point process. If in (2) the transitions from non-burst to burst and burst to non-burst states are memoryless, this becomes a hidden Markov model (HMM). For HMMs, the state transitions follow exponential distributions, and are highly irregular. Because observed bursting may in some cases be fairly regular-exhibiting inter-burst intervals with small variation-we relaxed this assumption. When more general probability distributions are used to describe the state transitions the two-state point process model becomes a hidden semi-Markov model (HSMM). We developed an efficient Bayesian computational scheme to fit HSMMs to spike train data. Numerical simulations indicate the method can perform well, sometimes yielding very different results than those based on PS.
Geometric allocation approaches in Markov chain Monte Carlo
International Nuclear Information System (INIS)
Todo, S; Suwa, H
2013-01-01
The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the selection of candidate states, the optimization of transition kernel, algorithm for choosing a configuration according to the transition probabilities. We show that the unconventional approaches based on the geometric allocation of probabilities or weights can improve the dynamics and scaling of the Monte Carlo simulation in several aspects. Particularly, the approach using the irreversible kernel can reduce or sometimes completely eliminate the rejection of trial move in the Markov chain. We also discuss how the space-time interchange technique together with Walker's method of aliases can reduce the computational time especially for the case where the number of candidates is large, such as models with long-range interactions
Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains
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Erik Van der Straeten
2009-11-01
Full Text Available In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use one-dimensional classical spin systems to illustrate the theoretical ideas. The examples studied in this paper are: the Ising model, the Potts model and the Blume-Emery-Griffiths model.
The computation of stationary distributions of Markov chains through perturbations
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Jeffery J. Hunter
1991-01-01
Full Text Available An algorithmic procedure for the determination of the stationary distribution of a finite, m-state, irreducible Markov chain, that does not require the use of methods for solving systems of linear equations, is presented. The technique is based upon a succession of m, rank one, perturbations of the trivial doubly stochastic matrix whose known steady state vector is updated at each stage to yield the required stationary probability vector.
R Package clickstream: Analyzing Clickstream Data with Markov Chains
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Michael Scholz
2016-10-01
Full Text Available Clickstream analysis is a useful tool for investigating consumer behavior, market research and software testing. I present the clickstream package which provides functionality for reading, clustering, analyzing and writing clickstreams in R. The package allows for a modeling of lists of clickstreams as zero-, first- and higher-order Markov chains. I illustrate the application of clickstream for a list of representative clickstreams from an online store.
Markov Chain Models for Stochastic Behavior in Resonance Overlap Regions
McCarthy, Morgan; Quillen, Alice
2018-01-01
We aim to predict lifetimes of particles in chaotic zoneswhere resonances overlap. A continuous-time Markov chain model isconstructed using mean motion resonance libration timescales toestimate transition times between resonances. The model is applied todiffusion in the co-rotation region of a planet. For particles begunat low eccentricity, the model is effective for early diffusion, butnot at later time when particles experience close encounters to the planet.
Parallel algorithms for simulating continuous time Markov chains
Nicol, David M.; Heidelberger, Philip
1992-01-01
We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.
MARKOV CHAIN MODELING OF PERFORMANCE DEGRADATION OF PHOTOVOLTAIC SYSTEM
E. Suresh Kumar; Asis Sarkar; Dhiren kumar Behera
2012-01-01
Modern probability theory studies chance processes for which theknowledge of previous outcomes influence predictions for future experiments. In principle, when a sequence of chance experiments, all of the past outcomes could influence the predictions for the next experiment. In Markov chain type of chance, the outcome of a given experiment can affect the outcome of the next experiment. The system state changes with time and the state X and time t are two random variables. Each of these variab...
Finding metastabilities in reversible Markov chains based on incomplete sampling
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Fackeldey Konstantin
2017-01-01
Full Text Available In order to fully characterize the state-transition behaviour of finite Markov chains one needs to provide the corresponding transition matrix P. In many applications such as molecular simulation and drug design, the entries of the transition matrix P are estimated by generating realizations of the Markov chain and determining the one-step conditional probability Pij for a transition from one state i to state j. This sampling can be computational very demanding. Therefore, it is a good idea to reduce the sampling effort. The main purpose of this paper is to design a sampling strategy, which provides a partial sampling of only a subset of the rows of such a matrix P. Our proposed approach fits very well to stochastic processes stemming from simulation of molecular systems or random walks on graphs and it is different from the matrix completion approaches which try to approximate the transition matrix by using a low-rank-assumption. It will be shown how Markov chains can be analyzed on the basis of a partial sampling. More precisely. First, we will estimate the stationary distribution from a partially given matrix P. Second, we will estimate the infinitesimal generator Q of P on the basis of this stationary distribution. Third, from the generator we will compute the leading invariant subspace, which should be identical to the leading invariant subspace of P. Forth, we will apply Robust Perron Cluster Analysis (PCCA+ in order to identify metastabilities using this subspace.
''adding'' algorithm for the Markov chain formalism for radiation transfer
International Nuclear Information System (INIS)
Esposito, L.W.
1979-01-01
The Markov chain radiative transfer method of Esposito and House has been shown to be both efficient and accurate for calculation of the diffuse reflection from a homogeneous scattering planetary atmosphere. The use of a new algorithm similar to the ''adding'' formula of Hansen and Travis extends the application of this formalism to an arbitrarily deep atmosphere. The basic idea for this algorithm is to consider a preceding calculation as a single state of a new Markov chain. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. The time required for the algorithm is comparable to that for a doubling calculation for a homogeneous atmosphere, but for a non-homogeneous atmosphere the new method is considerably faster than the standard ''adding'' routine. As with he standard ''adding'' method, the information on the internal radiation field is lost during the calculation. This method retains the advantage of the earlier Markov chain method that the time required is relatively insensitive to the number of illumination angles or observation angles for which the diffuse reflection is calculated. A technical write-up giving fuller details of the algorithm and a sample code are available from the author
Quantitative risk stratification in Markov chains with limiting conditional distributions.
Chan, David C; Pollett, Philip K; Weinstein, Milton C
2009-01-01
Many clinical decisions require patient risk stratification. The authors introduce the concept of limiting conditional distributions, which describe the equilibrium proportion of surviving patients occupying each disease state in a Markov chain with death. Such distributions can quantitatively describe risk stratification. The authors first establish conditions for the existence of a positive limiting conditional distribution in a general Markov chain and describe a framework for risk stratification using the limiting conditional distribution. They then apply their framework to a clinical example of a treatment indicated for high-risk patients, first to infer the risk of patients selected for treatment in clinical trials and then to predict the outcomes of expanding treatment to other populations of risk. For the general chain, a positive limiting conditional distribution exists only if patients in the earliest state have the lowest combined risk of progression or death. The authors show that in their general framework, outcomes and population risk are interchangeable. For the clinical example, they estimate that previous clinical trials have selected the upper quintile of patient risk for this treatment, but they also show that expanded treatment would weakly dominate this degree of targeted treatment, and universal treatment may be cost-effective. Limiting conditional distributions exist in most Markov models of progressive diseases and are well suited to represent risk stratification quantitatively. This framework can characterize patient risk in clinical trials and predict outcomes for other populations of risk.
Epigenetic change detection and pattern recognition via Bayesian hierarchical hidden Markov models.
Wang, Xinlei; Zang, Miao; Xiao, Guanghua
2013-06-15
Epigenetics is the study of changes to the genome that can switch genes on or off and determine which proteins are transcribed without altering the DNA sequence. Recently, epigenetic changes have been linked to the development and progression of disease such as psychiatric disorders. High-throughput epigenetic experiments have enabled researchers to measure genome-wide epigenetic profiles and yield data consisting of intensity ratios of immunoprecipitation versus reference samples. The intensity ratios can provide a view of genomic regions where protein binding occur under one experimental condition and further allow us to detect epigenetic alterations through comparison between two different conditions. However, such experiments can be expensive, with only a few replicates available. Moreover, epigenetic data are often spatially correlated with high noise levels. In this paper, we develop a Bayesian hierarchical model, combined with hidden Markov processes with four states for modeling spatial dependence, to detect genomic sites with epigenetic changes from two-sample experiments with paired internal control. One attractive feature of the proposed method is that the four states of the hidden Markov process have well-defined biological meanings and allow us to directly call the change patterns based on the corresponding posterior probabilities. In contrast, none of existing methods can offer this advantage. In addition, the proposed method offers great power in statistical inference by spatial smoothing (via hidden Markov modeling) and information pooling (via hierarchical modeling). Both simulation studies and real data analysis in a cocaine addiction study illustrate the reliability and success of this method. Copyright © 2012 John Wiley & Sons, Ltd.
Algebraic decay in self-similar Markov chains
International Nuclear Information System (INIS)
Hanson, J.D.; Cary, J.R.; Meiss, J.D.
1984-10-01
A continuous time Markov chain is used to model motion in the neighborhood of a critical noble invariant circle in an area-preserving map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. The nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to Hamiltonian systems the decay proceeds as t -4 05
Large deviations for Markov chains in the positive quadrant
Energy Technology Data Exchange (ETDEWEB)
Borovkov, A A; Mogul' skii, A A [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2001-10-31
The paper deals with so-called N-partially space-homogeneous time-homogeneous Markov chains X(y,n), n=0,1,2,..., X(y,0)=y, in the positive quadrant. These Markov chains are characterized by the following property of the transition probabilities P(y,A)=P(X(y,1) element of A): for some N{>=}0 the measure P(y,dx) depends only on x{sub 2}, y{sub 2}, and x{sub 1}-y{sub 1} in the domain x{sub 1}>N, y{sub 1}>N, and only on x{sub 1}, y{sub 1}, and x{sub 2}-y{sub 2} in the domain x{sub 2}>N, y{sub 2}>N. For such chains the asymptotic behaviour is found for a fixed set B as s{yields}{infinity}, |x|{yields}{infinity}, and n{yields}{infinity}. Some other conditions on the growth of parameters are also considered, for example, |x-y|{yields}{infinity}, |y|{yields}{infinity}. A study is made of the structure of the most probable trajectories, which give the main contribution to this asymptotics, and a number of other results pertaining to the topic are established. Similar results are obtained for the narrower class of 0-partially homogeneous ergodic chains under less restrictive moment conditions on the transition probabilities P(y,dx). Moreover, exact asymptotic expressions for the probabilities P(X(0,n) element of x+B) are found for 0-partially homogeneous ergodic chains under some additional conditions. The interest in partially homogeneous Markov chains in positive octants is due to the mathematical aspects (new and interesting problems arise in the framework of general large deviation theory) as well as applied issues, for such chains prove to be quite accurate mathematical models for numerous basic types of queueing and communication networks such as the widely known Jackson networks, polling systems, or communication networks associated with the ALOHA algorithm. There is a vast literature dealing with the analysis of these objects. The present paper is an attempt to find the extent to which an asymptotic analysis is possible for Markov chains of this type in their general
International Nuclear Information System (INIS)
Miao, Qiang; Huang, Hong Zhong; Fan, Xianfeng
2007-01-01
Condition classification is an important step in machinery fault detection, which is a problem of pattern recognition. Currently, there are a lot of techniques in this area and the purpose of this paper is to investigate two popular recognition techniques, namely hidden Markov model and support vector machine. At the beginning, we briefly introduced the procedure of feature extraction and the theoretical background of this paper. The comparison experiment was conducted for gearbox fault detection and the analysis results from this work showed that support vector machine has better classification performance in this area
Hidden Markov Model-based Pedestrian Navigation System using MEMS Inertial Sensors
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Zhang Yingjun
2015-02-01
Full Text Available In this paper, a foot-mounted pedestrian navigation system using MEMS inertial sensors is implemented, where the zero-velocity detection is abstracted into a hidden Markov model with 4 states and 15 observations. Moreover, an observations extraction algorithm has been developed to extract observations from sensor outputs; sample sets are used to train and optimize the model parameters by the Baum-Welch algorithm. Finally, a navigation system is developed, and the performance of the pedestrian navigation system is evaluated using indoor and outdoor field tests, and the results show that position error is less than 3% of total distance travelled.
Memetic Approaches for Optimizing Hidden Markov Models: A Case Study in Time Series Prediction
Bui, Lam Thu; Barlow, Michael
We propose a methodology for employing memetics (local search) within the framework of evolutionary algorithms to optimize parameters of hidden markov models. With this proposal, the rate and frequency of using local search are automatically changed over time either at a population or individual level. At the population level, we allow the rate of using local search to decay over time to zero (at the final generation). At the individual level, each individual is equipped with information of when it will do local search and for how long. This information evolves over time alongside the main elements of the chromosome representing the individual.
Inferring animal densities from tracking data using Markov chains.
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Hal Whitehead
Full Text Available The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.
Inferring animal densities from tracking data using Markov chains.
Whitehead, Hal; Jonsen, Ian D
2013-01-01
The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.
Study on the Evolution of Weights on the Market of Competitive Products using Markov Chains
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Daniel Mihai Amariei
2016-10-01
Full Text Available In this paper aims the application through the Markov Process mode, within the software product WinQSB, Markov chain in the establishment of the development on the market of five brands of athletic shoes.
Chen, Pei; Liu, Rui; Li, Yongjun; Chen, Luonan
2016-07-15
Identifying the critical state or pre-transition state just before the occurrence of a phase transition is a challenging task, because the state of the system may show little apparent change before this critical transition during the gradual parameter variations. Such dynamics of phase transition is generally composed of three stages, i.e. before-transition state, pre-transition state and after-transition state, which can be considered as three different Markov processes. By exploring the rich dynamical information provided by high-throughput data, we present a novel computational method, i.e. hidden Markov model (HMM) based approach, to detect the switching point of the two Markov processes from the before-transition state (a stationary Markov process) to the pre-transition state (a time-varying Markov process), thereby identifying the pre-transition state or early-warning signals of the phase transition. To validate the effectiveness, we apply this method to detect the signals of the imminent phase transitions of complex systems based on the simulated datasets, and further identify the pre-transition states as well as their critical modules for three real datasets, i.e. the acute lung injury triggered by phosgene inhalation, MCF-7 human breast cancer caused by heregulin and HCV-induced dysplasia and hepatocellular carcinoma. Both functional and pathway enrichment analyses validate the computational results. The source code and some supporting files are available at https://github.com/rabbitpei/HMM_based-method lnchen@sibs.ac.cn or liyj@scut.edu.cn Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
A Markov chain model for CANDU feeder pipe degradation
International Nuclear Information System (INIS)
Datla, S.; Dinnie, K.; Usmani, A.; Yuan, X.-X.
2008-01-01
There is need for risk based approach to manage feeder pipe degradation to ensure safe operation by minimizing the nuclear safety risk. The current lack of understanding of some fundamental degradation mechanisms will result in uncertainty in predicting the rupture frequency. There are still concerns caused by uncertainties in the inspection techniques and engineering evaluations which should be addressed in the current procedures. A probabilistic approach is therefore useful in quantifying the risk and also it provides a tool for risk based decision making. This paper discusses the application of Markov chain model for feeder pipes in order to predict and manage the risks associated with the existing and future aging-related feeder degradation mechanisms. The major challenge in the approach is the lack of service data in characterizing the transition probabilities of the Markov model. The paper also discusses various approaches in estimating plant specific degradation rates. (author)
Caching and interpolated likelihoods: accelerating cosmological Monte Carlo Markov chains
Energy Technology Data Exchange (ETDEWEB)
Bouland, Adam; Easther, Richard; Rosenfeld, Katherine, E-mail: adam.bouland@aya.yale.edu, E-mail: richard.easther@yale.edu, E-mail: krosenfeld@cfa.harvard.edu [Department of Physics, Yale University, New Haven CT 06520 (United States)
2011-05-01
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free parameters and computationally expensive to evaluate. We generate a high-order interpolating polynomial for the log-likelihood using the first points gathered by the Markov chains as a training set. This polynomial then accurately computes the majority of the likelihoods needed in the latter parts of the chains. We implement a simple version of this algorithm as a patch (InterpMC) to CosmoMC and show that it accelerates parameter estimatation by a factor of between two and four for well-converged chains. The current code is primarily intended as a ''proof of concept'', and we argue that there is considerable room for further performance gains. Unlike other approaches to accelerating parameter fits, we make no use of precomputed training sets or special choices of variables, and InterpMC is almost entirely transparent to the user.
Extreme event statistics in a drifting Markov chain
Kindermann, Farina; Hohmann, Michael; Lausch, Tobias; Mayer, Daniel; Schmidt, Felix; Widera, Artur
2017-07-01
We analyze extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one-dimensional periodic potential. Based on more than 500 individual atomic traces we verify the applicability of the Sparre Andersen theorem to our system despite the presence of a drift. We present detailed analysis of four different rare-event statistics for our system: the distributions of extreme values, of record values, of extreme value occurrence in the chain, and of the number of records in the chain. We observe that, for our data, the shape of the extreme event distributions is dominated by the underlying exponential distance distribution extracted from the atomic traces. Furthermore, we find that even small drifts influence the statistics of extreme events and record values, which is supported by numerical simulations, and we identify cases in which the drift can be determined without information about the underlying random variable distributions. Our results facilitate the use of extreme event statistics as a signal for small drifts in correlated trajectories.
Caching and interpolated likelihoods: accelerating cosmological Monte Carlo Markov chains
International Nuclear Information System (INIS)
Bouland, Adam; Easther, Richard; Rosenfeld, Katherine
2011-01-01
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free parameters and computationally expensive to evaluate. We generate a high-order interpolating polynomial for the log-likelihood using the first points gathered by the Markov chains as a training set. This polynomial then accurately computes the majority of the likelihoods needed in the latter parts of the chains. We implement a simple version of this algorithm as a patch (InterpMC) to CosmoMC and show that it accelerates parameter estimatation by a factor of between two and four for well-converged chains. The current code is primarily intended as a ''proof of concept'', and we argue that there is considerable room for further performance gains. Unlike other approaches to accelerating parameter fits, we make no use of precomputed training sets or special choices of variables, and InterpMC is almost entirely transparent to the user
DNA motif alignment by evolving a population of Markov chains.
Bi, Chengpeng
2009-01-30
Deciphering cis-regulatory elements or de novo motif-finding in genomes still remains elusive although much algorithmic effort has been expended. The Markov chain Monte Carlo (MCMC) method such as Gibbs motif samplers has been widely employed to solve the de novo motif-finding problem through sequence local alignment. Nonetheless, the MCMC-based motif samplers still suffer from local maxima like EM. Therefore, as a prerequisite for finding good local alignments, these motif algorithms are often independently run a multitude of times, but without information exchange between different chains. Hence it would be worth a new algorithm design enabling such information exchange. This paper presents a novel motif-finding algorithm by evolving a population of Markov chains with information exchange (PMC), each of which is initialized as a random alignment and run by the Metropolis-Hastings sampler (MHS). It is progressively updated through a series of local alignments stochastically sampled. Explicitly, the PMC motif algorithm performs stochastic sampling as specified by a population-based proposal distribution rather than individual ones, and adaptively evolves the population as a whole towards a global maximum. The alignment information exchange is accomplished by taking advantage of the pooled motif site distributions. A distinct method for running multiple independent Markov chains (IMC) without information exchange, or dubbed as the IMC motif algorithm, is also devised to compare with its PMC counterpart. Experimental studies demonstrate that the performance could be improved if pooled information were used to run a population of motif samplers. The new PMC algorithm was able to improve the convergence and outperformed other popular algorithms tested using simulated and biological motif sequences.
Sun, Wei; Ding, Wei; Yan, Huifang; Duan, Shunli
2018-06-01
Shoe-mounted pedestrian navigation systems based on micro inertial sensors rely on zero velocity updates to correct their positioning errors in time, which effectively makes determining the zero velocity interval play a key role during normal walking. However, as walking gaits are complicated, and vary from person to person, it is difficult to detect walking gaits with a fixed threshold method. This paper proposes a pedestrian gait classification method based on a hidden Markov model. Pedestrian gait data are collected with a micro inertial measurement unit installed at the instep. On the basis of analyzing the characteristics of the pedestrian walk, a single direction angular rate gyro output is used to classify gait features. The angular rate data are modeled into a univariate Gaussian mixture model with three components, and a four-state left–right continuous hidden Markov model (CHMM) is designed to classify the normal walking gait. The model parameters are trained and optimized using the Baum–Welch algorithm and then the sliding window Viterbi algorithm is used to decode the gait. Walking data are collected through eight subjects walking along the same route at three different speeds; the leave-one-subject-out cross validation method is conducted to test the model. Experimental results show that the proposed algorithm can accurately detect different walking gaits of zero velocity interval. The location experiment shows that the precision of CHMM-based pedestrian navigation improved by 40% when compared to the angular rate threshold method.
Robertson, Colin; Sawford, Kate; Gunawardana, Walimunige S. N.; Nelson, Trisalyn A.; Nathoo, Farouk; Stephen, Craig
2011-01-01
Surveillance systems tracking health patterns in animals have potential for early warning of infectious disease in humans, yet there are many challenges that remain before this can be realized. Specifically, there remains the challenge of detecting early warning signals for diseases that are not known or are not part of routine surveillance for named diseases. This paper reports on the development of a hidden Markov model for analysis of frontline veterinary sentinel surveillance data from Sri Lanka. Field veterinarians collected data on syndromes and diagnoses using mobile phones. A model for submission patterns accounts for both sentinel-related and disease-related variability. Models for commonly reported cattle diagnoses were estimated separately. Region-specific weekly average prevalence was estimated for each diagnoses and partitioned into normal and abnormal periods. Visualization of state probabilities was used to indicate areas and times of unusual disease prevalence. The analysis suggests that hidden Markov modelling is a useful approach for surveillance datasets from novel populations and/or having little historical baselines. PMID:21949763
A Hybrid Generalized Hidden Markov Model-Based Condition Monitoring Approach for Rolling Bearings.
Liu, Jie; Hu, Youmin; Wu, Bo; Wang, Yan; Xie, Fengyun
2017-05-18
The operating condition of rolling bearings affects productivity and quality in the rotating machine process. Developing an effective rolling bearing condition monitoring approach is critical to accurately identify the operating condition. In this paper, a hybrid generalized hidden Markov model-based condition monitoring approach for rolling bearings is proposed, where interval valued features are used to efficiently recognize and classify machine states in the machine process. In the proposed method, vibration signals are decomposed into multiple modes with variational mode decomposition (VMD). Parameters of the VMD, in the form of generalized intervals, provide a concise representation for aleatory and epistemic uncertainty and improve the robustness of identification. The multi-scale permutation entropy method is applied to extract state features from the decomposed signals in different operating conditions. Traditional principal component analysis is adopted to reduce feature size and computational cost. With the extracted features' information, the generalized hidden Markov model, based on generalized interval probability, is used to recognize and classify the fault types and fault severity levels. Finally, the experiment results show that the proposed method is effective at recognizing and classifying the fault types and fault severity levels of rolling bearings. This monitoring method is also efficient enough to quantify the two uncertainty components.
A Hybrid Generalized Hidden Markov Model-Based Condition Monitoring Approach for Rolling Bearings
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Jie Liu
2017-05-01
Full Text Available The operating condition of rolling bearings affects productivity and quality in the rotating machine process. Developing an effective rolling bearing condition monitoring approach is critical to accurately identify the operating condition. In this paper, a hybrid generalized hidden Markov model-based condition monitoring approach for rolling bearings is proposed, where interval valued features are used to efficiently recognize and classify machine states in the machine process. In the proposed method, vibration signals are decomposed into multiple modes with variational mode decomposition (VMD. Parameters of the VMD, in the form of generalized intervals, provide a concise representation for aleatory and epistemic uncertainty and improve the robustness of identification. The multi-scale permutation entropy method is applied to extract state features from the decomposed signals in different operating conditions. Traditional principal component analysis is adopted to reduce feature size and computational cost. With the extracted features’ information, the generalized hidden Markov model, based on generalized interval probability, is used to recognize and classify the fault types and fault severity levels. Finally, the experiment results show that the proposed method is effective at recognizing and classifying the fault types and fault severity levels of rolling bearings. This monitoring method is also efficient enough to quantify the two uncertainty components.
Segmenting Continuous Motions with Hidden Semi-markov Models and Gaussian Processes
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Tomoaki Nakamura
2017-12-01
Full Text Available Humans divide perceived continuous information into segments to facilitate recognition. For example, humans can segment speech waves into recognizable morphemes. Analogously, continuous motions are segmented into recognizable unit actions. People can divide continuous information into segments without using explicit segment points. This capacity for unsupervised segmentation is also useful for robots, because it enables them to flexibly learn languages, gestures, and actions. In this paper, we propose a Gaussian process-hidden semi-Markov model (GP-HSMM that can divide continuous time series data into segments in an unsupervised manner. Our proposed method consists of a generative model based on the hidden semi-Markov model (HSMM, the emission distributions of which are Gaussian processes (GPs. Continuous time series data is generated by connecting segments generated by the GP. Segmentation can be achieved by using forward filtering-backward sampling to estimate the model's parameters, including the lengths and classes of the segments. In an experiment using the CMU motion capture dataset, we tested GP-HSMM with motion capture data containing simple exercise motions; the results of this experiment showed that the proposed GP-HSMM was comparable with other methods. We also conducted an experiment using karate motion capture data, which is more complex than exercise motion capture data; in this experiment, the segmentation accuracy of GP-HSMM was 0.92, which outperformed other methods.
Speech-To-Text Conversion STT System Using Hidden Markov Model HMM
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Su Myat Mon
2015-06-01
Full Text Available Abstract Speech is an easiest way to communicate with each other. Speech processing is widely used in many applications like security devices household appliances cellular phones ATM machines and computers. The human computer interface has been developed to communicate or interact conveniently for one who is suffering from some kind of disabilities. Speech-to-Text Conversion STT systems have a lot of benefits for the deaf or dumb people and find their applications in our daily lives. In the same way the aim of the system is to convert the input speech signals into the text output for the deaf or dumb students in the educational fields. This paper presents an approach to extract features by using Mel Frequency Cepstral Coefficients MFCC from the speech signals of isolated spoken words. And Hidden Markov Model HMM method is applied to train and test the audio files to get the recognized spoken word. The speech database is created by using MATLAB.Then the original speech signals are preprocessed and these speech samples are extracted to the feature vectors which are used as the observation sequences of the Hidden Markov Model HMM recognizer. The feature vectors are analyzed in the HMM depending on the number of states.
Hidden markov model for the prediction of transmembrane proteins using MATLAB.
Chaturvedi, Navaneet; Shanker, Sudhanshu; Singh, Vinay Kumar; Sinha, Dhiraj; Pandey, Paras Nath
2011-01-01
Since membranous proteins play a key role in drug targeting therefore transmembrane proteins prediction is active and challenging area of biological sciences. Location based prediction of transmembrane proteins are significant for functional annotation of protein sequences. Hidden markov model based method was widely applied for transmembrane topology prediction. Here we have presented a revised and a better understanding model than an existing one for transmembrane protein prediction. Scripting on MATLAB was built and compiled for parameter estimation of model and applied this model on amino acid sequence to know the transmembrane and its adjacent locations. Estimated model of transmembrane topology was based on TMHMM model architecture. Only 7 super states are defined in the given dataset, which were converted to 96 states on the basis of their length in sequence. Accuracy of the prediction of model was observed about 74 %, is a good enough in the area of transmembrane topology prediction. Therefore we have concluded the hidden markov model plays crucial role in transmembrane helices prediction on MATLAB platform and it could also be useful for drug discovery strategy. The database is available for free at bioinfonavneet@gmail.comvinaysingh@bhu.ac.in.
biomvRhsmm: Genomic Segmentation with Hidden Semi-Markov Model
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Yang Du
2014-01-01
Full Text Available High-throughput technologies like tiling array and next-generation sequencing (NGS generate continuous homogeneous segments or signal peaks in the genome that represent transcripts and transcript variants (transcript mapping and quantification, regions of deletion and amplification (copy number variation, or regions characterized by particular common features like chromatin state or DNA methylation ratio (epigenetic modifications. However, the volume and output of data produced by these technologies present challenges in analysis. Here, a hidden semi-Markov model (HSMM is implemented and tailored to handle multiple genomic profile, to better facilitate genome annotation by assisting in the detection of transcripts, regulatory regions, and copy number variation by holistic microarray or NGS. With support for various data distributions, instead of limiting itself to one specific application, the proposed hidden semi-Markov model is designed to allow modeling options to accommodate different types of genomic data and to serve as a general segmentation engine. By incorporating genomic positions into the sojourn distribution of HSMM, with optional prior learning using annotation or previous studies, the modeling output is more biologically sensible. The proposed model has been compared with several other state-of-the-art segmentation models through simulation benchmarking, which shows that our efficient implementation achieves comparable or better sensitivity and specificity in genomic segmentation.
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Ririn Kusumawati
2016-05-01
In the classification, using Hidden Markov Model, voice signal is analyzed and searched the maximum possible value that can be recognized. The modeling results obtained parameters are used to compare with the sound of Arabic speakers. From the test results' Classification, Hidden Markov Models with Linear Predictive Coding extraction average accuracy of 78.6% for test data sampling frequency of 8,000 Hz, 80.2% for test data sampling frequency of 22050 Hz, 79% for frequencies sampling test data at 44100 Hz.
Mixed Vehicle Flow At Signalized Intersection: Markov Chain Analysis
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Gertsbakh Ilya B.
2015-09-01
Full Text Available We assume that a Poisson flow of vehicles arrives at isolated signalized intersection, and each vehicle, independently of others, represents a random number X of passenger car units (PCU’s. We analyze numerically the stationary distribution of the queue process {Zn}, where Zn is the number of PCU’s in a queue at the beginning of the n-th red phase, n → ∞. We approximate the number Yn of PCU’s arriving during one red-green cycle by a two-parameter Negative Binomial Distribution (NBD. The well-known fact is that {Zn} follow an infinite-state Markov chain. We approximate its stationary distribution using a finite-state Markov chain. We show numerically that there is a strong dependence of the mean queue length E[Zn] in equilibrium on the input distribution of Yn and, in particular, on the ”over dispersion” parameter γ= Var[Yn]/E[Yn]. For Poisson input, γ = 1. γ > 1 indicates presence of heavy-tailed input. In reality it means that a relatively large ”portion” of PCU’s, considerably exceeding the average, may arrive with high probability during one red-green cycle. Empirical formulas are presented for an accurate estimation of mean queue length as a function of load and g of the input flow. Using the Markov chain technique, we analyze the mean ”virtual” delay time for a car which always arrives at the beginning of the red phase.
SDI and Markov Chains for Regional Drought Characteristics
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Chen-Feng Yeh
2015-08-01
Full Text Available In recent years, global climate change has altered precipitation patterns, causing uneven spatial and temporal distribution of precipitation that gradually induces precipitation polarization phenomena. Taiwan is located in the subtropical climate zone, with distinct wet and dry seasons, which makes the polarization phenomenon more obvious; this has also led to a large difference between river flows during the wet and dry seasons, which is significantly influenced by precipitation, resulting in hydrological drought. Therefore, to effectively address the growing issue of water shortages, it is necessary to explore and assess the drought characteristics of river systems. In this study, the drought characteristics of northern Taiwan were studied using the streamflow drought index (SDI and Markov chains. Analysis results showed that the year 2002 was a turning point for drought severity in both the Lanyang River and Yilan River basins; the severity of rain events in the Lanyang River basin increased after 2002, and the severity of drought events in the Yilan River basin exhibited a gradual upward trend. In the study of drought severity, analysis results from periods of three months (November to January and six months (November to April have shown significant drought characteristics. In addition, analysis of drought occurrence probabilities using the method of Markov chains has shown that the occurrence probabilities of drought events are higher in the Lanyang River basin than in the Yilan River basin; particularly for extreme events, the occurrence probability of an extreme drought event is 20.6% during the dry season (November to April in the Lanyang River basin, and 3.4% in the Yilan River basin. This study shows that for analysis of drought/wet occurrence probabilities, the results obtained for the drought frequency and occurrence probability using short-term data with the method of Markov chains can be used to predict the long-term occurrence
Generating intrinsically disordered protein conformational ensembles from a Markov chain
Cukier, Robert I.
2018-03-01
Intrinsically disordered proteins (IDPs) sample a diverse conformational space. They are important to signaling and regulatory pathways in cells. An entropy penalty must be payed when an IDP becomes ordered upon interaction with another protein or a ligand. Thus, the degree of conformational disorder of an IDP is of interest. We create a dichotomic Markov model that can explore entropic features of an IDP. The Markov condition introduces local (neighbor residues in a protein sequence) rotamer dependences that arise from van der Waals and other chemical constraints. A protein sequence of length N is characterized by its (information) entropy and mutual information, MIMC, the latter providing a measure of the dependence among the random variables describing the rotamer probabilities of the residues that comprise the sequence. For a Markov chain, the MIMC is proportional to the pair mutual information MI which depends on the singlet and pair probabilities of neighbor residue rotamer sampling. All 2N sequence states are generated, along with their probabilities, and contrasted with the probabilities under the assumption of independent residues. An efficient method to generate realizations of the chain is also provided. The chain entropy, MIMC, and state probabilities provide the ingredients to distinguish different scenarios using the terminologies: MoRF (molecular recognition feature), not-MoRF, and not-IDP. A MoRF corresponds to large entropy and large MIMC (strong dependence among the residues' rotamer sampling), a not-MoRF corresponds to large entropy but small MIMC, and not-IDP corresponds to low entropy irrespective of the MIMC. We show that MorFs are most appropriate as descriptors of IDPs. They provide a reasonable number of high-population states that reflect the dependences between neighbor residues, thus classifying them as IDPs, yet without very large entropy that might lead to a too high entropy penalty.
LISA data analysis using Markov chain Monte Carlo methods
International Nuclear Information System (INIS)
Cornish, Neil J.; Crowder, Jeff
2005-01-01
The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low-frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground based gravitational wave astronomy. LISA data analysis requires the identification of individual signals from a data stream containing an unknown number of overlapping signals. Because of the signal overlaps, a global fit to all the signals has to be performed in order to avoid biasing the solution. However, performing such a global fit requires the exploration of an enormous parameter space with a dimension upwards of 50 000. Markov Chain Monte Carlo (MCMC) methods offer a very promising solution to the LISA data analysis problem. MCMC algorithms are able to efficiently explore large parameter spaces, simultaneously providing parameter estimates, error analysis, and even model selection. Here we present the first application of MCMC methods to simulated LISA data and demonstrate the great potential of the MCMC approach. Our implementation uses a generalized F-statistic to evaluate the likelihoods, and simulated annealing to speed convergence of the Markov chains. As a final step we supercool the chains to extract maximum likelihood estimates, and estimates of the Bayes factors for competing models. We find that the MCMC approach is able to correctly identify the number of signals present, extract the source parameters, and return error estimates consistent with Fisher information matrix predictions
Memory functions and correlations in additive binary Markov chains
International Nuclear Information System (INIS)
Melnyk, S S; Usatenko, O V; Yampol'skii, V A; Apostolov, S S; Maiselis, Z A
2006-01-01
A theory of additive Markov chains with a long-range memory, proposed earlier in Usatenko et al (2003 Phys. Rev. E 68 061107), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, memory functions and their relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function
Memory functions and correlations in additive binary Markov chains
Energy Technology Data Exchange (ETDEWEB)
Melnyk, S S [A Ya Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov (Ukraine); Usatenko, O V [A Ya Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov (Ukraine); Yampol' skii, V A [A Ya Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov (Ukraine); Apostolov, S S [V N Karazin Kharkov National University, 4 Svoboda Sq., Kharkov 61077 (Ukraine); Maiselis, Z A [V N Karazin Kharkov National University, 4 Svoboda Sq., Kharkov 61077 (Ukraine)
2006-11-17
A theory of additive Markov chains with a long-range memory, proposed earlier in Usatenko et al (2003 Phys. Rev. E 68 061107), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, memory functions and their relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function.
On Construction of Quantum Markov Chains on Cayley trees
International Nuclear Information System (INIS)
Accardi, Luigi; Mukhamedov, Farrukh; Souissi, Abdessatar
2016-01-01
The main aim of the present paper is to provide a new construction of quantum Markov chain (QMC) on arbitrary order Cayley tree. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Note that this construction reminds statistical mechanics models with competing interactions on trees. If one considers one dimensional tree, then the provided construction reduces to well-known one, which was studied by the first author. Our construction will allow to investigate phase transition problem in a quantum setting. (paper)
Markov Chain Modelling for Short-Term NDVI Time Series Forecasting
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Stepčenko Artūrs
2016-12-01
Full Text Available In this paper, the NDVI time series forecasting model has been developed based on the use of discrete time, continuous state Markov chain of suitable order. The normalised difference vegetation index (NDVI is an indicator that describes the amount of chlorophyll (the green mass and shows the relative density and health of vegetation; therefore, it is an important variable for vegetation forecasting. A Markov chain is a stochastic process that consists of a state space. This stochastic process undergoes transitions from one state to another in the state space with some probabilities. A Markov chain forecast model is flexible in accommodating various forecast assumptions and structures. The present paper discusses the considerations and techniques in building a Markov chain forecast model at each step. Continuous state Markov chain model is analytically described. Finally, the application of the proposed Markov chain model is illustrated with reference to a set of NDVI time series data.
Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)
Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.
2018-05-01
A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.
Improvement of Fuzzy Image Contrast Enhancement Using Simulated Ergodic Fuzzy Markov Chains
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Behrouz Fathi-Vajargah
2014-01-01
Full Text Available This paper presents a novel fuzzy enhancement technique using simulated ergodic fuzzy Markov chains for low contrast brain magnetic resonance imaging (MRI. The fuzzy image contrast enhancement is proposed by weighted fuzzy expected value. The membership values are then modified to enhance the image using ergodic fuzzy Markov chains. The qualitative performance of the proposed method is compared to another method in which ergodic fuzzy Markov chains are not considered. The proposed method produces better quality image.
STATISTICAL ANALYSIS OF NOTATIONAL AFL DATA USING CONTINUOUS TIME MARKOV CHAINS
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Denny Meyer
2006-12-01
Full Text Available Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs, with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated
Simulation of daily rainfall through markov chain modeling
International Nuclear Information System (INIS)
Sadiq, N.
2015-01-01
Being an agricultural country, the inhabitants of dry land in cultivated areas mainly rely on the daily rainfall for watering their fields. A stochastic model based on first order Markov Chain was developed to simulate daily rainfall data for Multan, D. I. Khan, Nawabshah, Chilas and Barkhan for the period 1981-2010. Transitional probability matrices of first order Markov Chain was utilized to generate the daily rainfall occurrence while gamma distribution was used to generate the daily rainfall amount. In order to achieve the parametric values of mentioned cities, method of moments is used to estimate the shape and scale parameters which lead to synthetic sequence generation as per gamma distribution. In this study, unconditional and conditional probabilities of wet and dry days in sum with means and standard deviations are considered as the essential parameters for the simulated stochastic generation of daily rainfalls. It has been found that the computerized synthetic rainfall series concurred pretty well with the actual observed rainfall series. (author)
Planning Tunnel Construction Using Markov Chain Monte Carlo (MCMC
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Juan P. Vargas
2015-01-01
Full Text Available Tunnels, drifts, drives, and other types of underground excavation are very common in mining as well as in the construction of roads, railways, dams, and other civil engineering projects. Planning is essential to the success of tunnel excavation, and construction time is one of the most important factors to be taken into account. This paper proposes a simulation algorithm based on a stochastic numerical method, the Markov chain Monte Carlo method, that can provide the best estimate of the opening excavation times for the classic method of drilling and blasting. Taking account of technical considerations that affect the tunnel excavation cycle, the simulation is developed through a computational algorithm. Using the Markov chain Monte Carlo method, the unit operations involved in the underground excavation cycle are identified and assigned probability distributions that, with random number input, make it possible to simulate the total excavation time. The results obtained with this method are compared with a real case of tunneling excavation. By incorporating variability in the planning, it is possible to determine with greater certainty the ranges over which the execution times of the unit operations fluctuate. In addition, the financial risks associated with planning errors can be reduced and the exploitation of resources maximized.
Markov chain aggregation and its applications to combinatorial reaction networks.
Ganguly, Arnab; Petrov, Tatjana; Koeppl, Heinz
2014-09-01
We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.
Saliency Detection via Absorbing Markov Chain With Learnt Transition Probability.
Lihe Zhang; Jianwu Ai; Bowen Jiang; Huchuan Lu; Xiukui Li
2018-02-01
In this paper, we propose a bottom-up saliency model based on absorbing Markov chain (AMC). First, a sparsely connected graph is constructed to capture the local context information of each node. All image boundary nodes and other nodes are, respectively, treated as the absorbing nodes and transient nodes in the absorbing Markov chain. Then, the expected number of times from each transient node to all other transient nodes can be used to represent the saliency value of this node. The absorbed time depends on the weights on the path and their spatial coordinates, which are completely encoded in the transition probability matrix. Considering the importance of this matrix, we adopt different hierarchies of deep features extracted from fully convolutional networks and learn a transition probability matrix, which is called learnt transition probability matrix. Although the performance is significantly promoted, salient objects are not uniformly highlighted very well. To solve this problem, an angular embedding technique is investigated to refine the saliency results. Based on pairwise local orderings, which are produced by the saliency maps of AMC and boundary maps, we rearrange the global orderings (saliency value) of all nodes. Extensive experiments demonstrate that the proposed algorithm outperforms the state-of-the-art methods on six publicly available benchmark data sets.
Data Analysis Recipes: Using Markov Chain Monte Carlo
Hogg, David W.; Foreman-Mackey, Daniel
2018-05-01
Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data. In this primarily pedagogical contribution, we give a brief overview of the most basic MCMC method and some practical advice for the use of MCMC in real inference problems. We give advice on method choice, tuning for performance, methods for initialization, tests of convergence, troubleshooting, and use of the chain output to produce or report parameter estimates with associated uncertainties. We argue that autocorrelation time is the most important test for convergence, as it directly connects to the uncertainty on the sampling estimate of any quantity of interest. We emphasize that sampling is a method for doing integrals; this guides our thinking about how MCMC output is best used. .
Geometry and Dynamics for Markov Chain Monte Carlo
Barp, Alessandro; Briol, François-Xavier; Kennedy, Anthony D.; Girolami, Mark
2018-03-01
Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains which can explore probability densities efficiently. The method emerges from physics and geometry and these links have been extensively studied by a series of authors through the last thirty years. However, there is currently a gap between the intuitions and knowledge of users of the methodology and our deep understanding of these theoretical foundations. The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners and other users of the methodology with only a basic understanding of Monte Carlo methods. This will be complemented with some discussion of the most recent advances in the field which we believe will become increasingly relevant to applied scientists.
Basic problems and solution methods for two-dimensional continuous 3 × 3 order hidden Markov model
International Nuclear Information System (INIS)
Wang, Guo-gang; Tang, Gui-jin; Gan, Zong-liang; Cui, Zi-guan; Zhu, Xiu-chang
2016-01-01
A novel model referred to as two-dimensional continuous 3 × 3 order hidden Markov model is put forward to avoid the disadvantages of the classical hypothesis of two-dimensional continuous hidden Markov model. This paper presents three equivalent definitions of the model, in which the state transition probability relies on not only immediate horizontal and vertical states but also immediate diagonal state, and in which the probability density of the observation relies on not only current state but also immediate horizontal and vertical states. The paper focuses on the three basic problems of the model, namely probability density calculation, parameters estimation and path backtracking. Some algorithms solving the questions are theoretically derived, by exploiting the idea that the sequences of states on rows or columns of the model can be viewed as states of a one-dimensional continuous 1 × 2 order hidden Markov model. Simulation results further demonstrate the performance of the algorithms. Because there are more statistical characteristics in the structure of the proposed new model, it can more accurately describe some practical problems, as compared to two-dimensional continuous hidden Markov model.
Stifter, Cynthia A.; Rovine, Michael
2015-01-01
The focus of the present longitudinal study, to examine mother-infant interaction during the administration of immunizations at 2 and 6?months of age, used hidden Markov modelling, a time series approach that produces latent states to describe how mothers and infants work together to bring the infant to a soothed state. Results revealed a…
Sub-seasonal-to-seasonal Reservoir Inflow Forecast using Bayesian Hierarchical Hidden Markov Model
Mukhopadhyay, S.; Arumugam, S.
2017-12-01
Sub-seasonal-to-seasonal (S2S) (15-90 days) streamflow forecasting is an emerging area of research that provides seamless information for reservoir operation from weather time scales to seasonal time scales. From an operational perspective, sub-seasonal inflow forecasts are highly valuable as these enable water managers to decide short-term releases (15-30 days), while holding water for seasonal needs (e.g., irrigation and municipal supply) and to meet end-of-the-season target storage at a desired level. We propose a Bayesian Hierarchical Hidden Markov Model (BHHMM) to develop S2S inflow forecasts for the Tennessee Valley Area (TVA) reservoir system. Here, the hidden states are predicted by relevant indices that influence the inflows at S2S time scale. The hidden Markov model also captures the both spatial and temporal hierarchy in predictors that operate at S2S time scale with model parameters being estimated as a posterior distribution using a Bayesian framework. We present our work in two steps, namely single site model and multi-site model. For proof of concept, we consider inflows to Douglas Dam, Tennessee, in the single site model. For multisite model we consider reservoirs in the upper Tennessee valley. Streamflow forecasts are issued and updated continuously every day at S2S time scale. We considered precipitation forecasts obtained from NOAA Climate Forecast System (CFSv2) GCM as predictors for developing S2S streamflow forecasts along with relevant indices for predicting hidden states. Spatial dependence of the inflow series of reservoirs are also preserved in the multi-site model. To circumvent the non-normality of the data, we consider the HMM in a Generalized Linear Model setting. Skill of the proposed approach is tested using split sample validation against a traditional multi-site canonical correlation model developed using the same set of predictors. From the posterior distribution of the inflow forecasts, we also highlight different system behavior
Multi-chain Markov chain Monte Carlo methods for computationally expensive models
Huang, M.; Ray, J.; Ren, H.; Hou, Z.; Bao, J.
2017-12-01
Markov chain Monte Carlo (MCMC) methods are used to infer model parameters from observational data. The parameters are inferred as probability densities, thus capturing estimation error due to sparsity of the data, and the shortcomings of the model. Multiple communicating chains executing the MCMC method have the potential to explore the parameter space better, and conceivably accelerate the convergence to the final distribution. We present results from tests conducted with the multi-chain method to show how the acceleration occurs i.e., for loose convergence tolerances, the multiple chains do not make much of a difference. The ensemble of chains also seems to have the ability to accelerate the convergence of a few chains that might start from suboptimal starting points. Finally, we show the performance of the chains in the estimation of O(10) parameters using computationally expensive forward models such as the Community Land Model, where the sampling burden is distributed over multiple chains.
Post processing of optically recognized text via second order hidden Markov model
Poudel, Srijana
In this thesis, we describe a postprocessing system on Optical Character Recognition(OCR) generated text. Second Order Hidden Markov Model (HMM) approach is used to detect and correct the OCR related errors. The reason for choosing the 2nd order HMM is to keep track of the bigrams so that the model can represent the system more accurately. Based on experiments with training data of 159,733 characters and testing of 5,688 characters, the model was able to correct 43.38 % of the errors with a precision of 75.34 %. However, the precision value indicates that the model introduced some new errors, decreasing the correction percentage to 26.4%.
Damage evaluation by a guided wave-hidden Markov model based method
Mei, Hanfei; Yuan, Shenfang; Qiu, Lei; Zhang, Jinjin
2016-02-01
Guided wave based structural health monitoring has shown great potential in aerospace applications. However, one of the key challenges of practical engineering applications is the accurate interpretation of the guided wave signals under time-varying environmental and operational conditions. This paper presents a guided wave-hidden Markov model based method to improve the damage evaluation reliability of real aircraft structures under time-varying conditions. In the proposed approach, an HMM based unweighted moving average trend estimation method, which can capture the trend of damage propagation from the posterior probability obtained by HMM modeling is used to achieve a probabilistic evaluation of the structural damage. To validate the developed method, experiments are performed on a hole-edge crack specimen under fatigue loading condition and a real aircraft wing spar under changing structural boundary conditions. Experimental results show the advantage of the proposed method.
Hidden Markov models for sequence analysis: extension and analysis of the basic method
DEFF Research Database (Denmark)
Hughey, Richard; Krogh, Anders Stærmose
1996-01-01
-maximization training procedure is relatively straight-forward. In this paper,we review the mathematical extensions and heuristics that move the method from the theoreticalto the practical. Then, we experimentally analyze the effectiveness of model regularization,dynamic model modification, and optimization strategies......Hidden Markov models (HMMs) are a highly effective means of modeling a family of unalignedsequences or a common motif within a set of unaligned sequences. The trained HMM can then beused for discrimination or multiple alignment. The basic mathematical description of an HMMand its expectation....... Finally it is demonstrated on the SH2domain how a domain can be found from unaligned sequences using a special model type. Theexperimental work was completed with the aid of the Sequence Alignment and Modeling softwaresuite....
A Self-Adaptive Hidden Markov Model for Emotion Classification in Chinese Microblogs
Directory of Open Access Journals (Sweden)
Li Liu
2015-01-01
we propose a modified version of hidden Markov model (HMM classifier, called self-adaptive HMM, whose parameters are optimized by Particle Swarm Optimization algorithms. Since manually labeling large-scale dataset is difficult, we also employ the entropy to decide whether a new unlabeled tweet shall be contained in the training dataset after being assigned an emotion using our HMM-based approach. In the experiment, we collected about 200,000 Chinese tweets from Sina Weibo. The results show that the F-score of our approach gets 76% on happiness and fear and 65% on anger, surprise, and sadness. In addition, the self-adaptive HMM classifier outperforms Naive Bayes and Support Vector Machine on recognition of happiness, anger, and sadness.
Non-intrusive gesture recognition system combining with face detection based on Hidden Markov Model
Jin, Jing; Wang, Yuanqing; Xu, Liujing; Cao, Liqun; Han, Lei; Zhou, Biye; Li, Minggao
2014-11-01
A non-intrusive gesture recognition human-machine interaction system is proposed in this paper. In order to solve the hand positioning problem which is a difficulty in current algorithms, face detection is used for the pre-processing to narrow the search area and find user's hand quickly and accurately. Hidden Markov Model (HMM) is used for gesture recognition. A certain number of basic gesture units are trained as HMM models. At the same time, an improved 8-direction feature vector is proposed and used to quantify characteristics in order to improve the detection accuracy. The proposed system can be applied in interaction equipments without special training for users, such as household interactive television
Hidden Markov Item Response Theory Models for Responses and Response Times.
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.
A Coupled Hidden Markov Random Field Model for Simultaneous Face Clustering and Tracking in Videos
Wu, Baoyuan
2016-10-25
Face clustering and face tracking are two areas of active research in automatic facial video processing. They, however, have long been studied separately, despite the inherent link between them. In this paper, we propose to perform simultaneous face clustering and face tracking from real world videos. The motivation for the proposed research is that face clustering and face tracking can provide useful information and constraints to each other, thus can bootstrap and improve the performances of each other. To this end, we introduce a Coupled Hidden Markov Random Field (CHMRF) to simultaneously model face clustering, face tracking, and their interactions. We provide an effective algorithm based on constrained clustering and optimal tracking for the joint optimization of cluster labels and face tracking. We demonstrate significant improvements over state-of-the-art results in face clustering and tracking on several videos.
Zhang, Wei; Jiang, Ling; Han, Lei
2018-04-01
Convective storm nowcasting refers to the prediction of the convective weather initiation, development, and decay in a very short term (typically 0 2 h) .Despite marked progress over the past years, severe convective storm nowcasting still remains a challenge. With the boom of machine learning, it has been well applied in various fields, especially convolutional neural network (CNN). In this paper, we build a servere convective weather nowcasting system based on CNN and hidden Markov model (HMM) using reanalysis meteorological data. The goal of convective storm nowcasting is to predict if there is a convective storm in 30min. In this paper, we compress the VDRAS reanalysis data to low-dimensional data by CNN as the observation vector of HMM, then obtain the development trend of strong convective weather in the form of time series. It shows that, our method can extract robust features without any artificial selection of features, and can capture the development trend of strong convective storm.
A Method for Driving Route Predictions Based on Hidden Markov Model
Directory of Open Access Journals (Sweden)
Ning Ye
2015-01-01
Full Text Available We present a driving route prediction method that is based on Hidden Markov Model (HMM. This method can accurately predict a vehicle’s entire route as early in a trip’s lifetime as possible without inputting origins and destinations beforehand. Firstly, we propose the route recommendation system architecture, where route predictions play important role in the system. Secondly, we define a road network model, normalize each of driving routes in the rectangular coordinate system, and build the HMM to make preparation for route predictions using a method of training set extension based on K-means++ and the add-one (Laplace smoothing technique. Thirdly, we present the route prediction algorithm. Finally, the experimental results of the effectiveness of the route predictions that is based on HMM are shown.
Using hidden Markov models to deal with availability bias on line transect surveys.
Borchers, D L; Zucchini, W; Heide-Jørgensen, M P; Cañadas, A; Langrock, R
2013-09-01
We develop estimators for line transect surveys of animals that are stochastically unavailable for detection while within detection range. The detection process is formulated as a hidden Markov model with a binary state-dependent observation model that depends on both perpendicular and forward distances. This provides a parametric method of dealing with availability bias when estimates of availability process parameters are available even if series of availability events themselves are not. We apply the estimators to an aerial and a shipboard survey of whales, and investigate their properties by simulation. They are shown to be more general and more flexible than existing estimators based on parametric models of the availability process. We also find that methods using availability correction factors can be very biased when surveys are not close to being instantaneous, as can estimators that assume temporal independence in availability when there is temporal dependence. © 2013, The International Biometric Society.
Passive acoustic leak detection for sodium cooled fast reactors using hidden Markov models
Energy Technology Data Exchange (ETDEWEB)
Riber Marklund, A. [CEA, Cadarache, DEN/DTN/STCP/LIET, Batiment 202, 13108 St Paul-lez-Durance, (France); Kishore, S. [Fast Reactor Technology Group of IGCAR, (India); Prakash, V. [Vibrations Diagnostics Division, Fast Reactor Technology Group of IGCAR, (India); Rajan, K.K. [Fast Reactor Technology Group and Engineering Services Group of IGCAR, (India)
2015-07-01
Acoustic leak detection for steam generators of sodium fast reactors have been an active research topic since the early 1970's and several methods have been tested over the years. Inspired by its success in the field of automatic speech recognition, we here apply hidden Markov models (HMM) in combination with Gaussian mixture models (GMM) to the problem. To achieve this, we propose a new feature calculation scheme, based on the temporal evolution of the power spectral density (PSD) of the signal. Using acoustic signals recorded during steam/water injection experiments done at the Indira Gandhi Centre for Atomic Research (IGCAR), the proposed method is tested. We perform parametric studies on the HMM+GMM model size and demonstrate that the proposed method a) performs well without a priori knowledge of injection noise, b) can incorporate several noise models and c) has an output distribution that simplifies false alarm rate control. (authors)
Multi-category micro-milling tool wear monitoring with continuous hidden Markov models
Zhu, Kunpeng; Wong, Yoke San; Hong, Geok Soon
2009-02-01
In-process monitoring of tool conditions is important in micro-machining due to the high precision requirement and high tool wear rate. Tool condition monitoring in micro-machining poses new challenges compared to conventional machining. In this paper, a multi-category classification approach is proposed for tool flank wear state identification in micro-milling. Continuous Hidden Markov models (HMMs) are adapted for modeling of the tool wear process in micro-milling, and estimation of the tool wear state given the cutting force features. For a noise-robust approach, the HMM outputs are connected via a medium filter to minimize the tool state before entry into the next state due to high noise level. A detailed study on the selection of HMM structures for tool condition monitoring (TCM) is presented. Case studies on the tool state estimation in the micro-milling of pure copper and steel demonstrate the effectiveness and potential of these methods.
Naive scoring of human sleep based on a hidden Markov model of the electroencephalogram.
Yaghouby, Farid; Modur, Pradeep; Sunderam, Sridhar
2014-01-01
Clinical sleep scoring involves tedious visual review of overnight polysomnograms by a human expert. Many attempts have been made to automate the process by training computer algorithms such as support vector machines and hidden Markov models (HMMs) to replicate human scoring. Such supervised classifiers are typically trained on scored data and then validated on scored out-of-sample data. Here we describe a methodology based on HMMs for scoring an overnight sleep recording without the benefit of a trained initial model. The number of states in the data is not known a priori and is optimized using a Bayes information criterion. When tested on a 22-subject database, this unsupervised classifier agreed well with human scores (mean of Cohen's kappa > 0.7). The HMM also outperformed other unsupervised classifiers (Gaussian mixture models, k-means, and linkage trees), that are capable of naive classification but do not model dynamics, by a significant margin (p < 0.05).
International Nuclear Information System (INIS)
Regentova, E.; Zhang, L.; Veni, G.; Zheng, J.
2007-01-01
A system is designed for detecting microcalcification clusters (MCC) in digital mammograms. The system is intended for computer-aided diagnostic prompting. Further discrimination of MCC as benign or malignant is assumed to be performed by radiologists. Processing of mammograms is based on the statistical modeling by means of wavelet domain hidden markov trees (WHMT). Segmentation is performed by the weighted likelihood evaluation followed by the classification based on spatial filters for a single microcalcification (MC) and a cluster of MC detection. The analysis is carried out on FROC curves for 40 mammograms from the mini-MIAS database and for 100 mammograms with 50 cancerous and 50 benign cases from DDSM database. The designed system is capable to detect 100% of true positive cases in these sets. The rate of false positives is 2.9 per case for mini-MIAS dataset; and 0.01 for the DDSM images. (orig.)
Name segmentation using hidden Markov models and its application in record linkage
Directory of Open Access Journals (Sweden)
Rita de Cassia Braga Gonçalves
2014-10-01
Full Text Available This study aimed to evaluate the use of hidden Markov models (HMM for the segmentation of person names and its influence on record linkage. A HMM was applied to the segmentation of patient’s and mother’s names in the databases of the Mortality Information System (SIM, Information Subsystem for High Complexity Procedures (APAC, and Hospital Information System (AIH. A sample of 200 patients from each database was segmented via HMM, and the results were compared to those from segmentation by the authors. The APAC-SIM and APAC-AIH databases were linked using three different segmentation strategies, one of which used HMM. Conformity of segmentation via HMM varied from 90.5% to 92.5%. The different segmentation strategies yielded similar results in the record linkage process. This study suggests that segmentation of Brazilian names via HMM is no more effective than traditional segmentation approaches in the linkage process.
Hidden Markov model tracking of continuous gravitational waves from young supernova remnants
Sun, L.; Melatos, A.; Suvorova, S.; Moran, W.; Evans, R. J.
2018-02-01
Searches for persistent gravitational radiation from nonpulsating neutron stars in young supernova remnants are computationally challenging because of rapid stellar braking. We describe a practical, efficient, semicoherent search based on a hidden Markov model tracking scheme, solved by the Viterbi algorithm, combined with a maximum likelihood matched filter, the F statistic. The scheme is well suited to analyzing data from advanced detectors like the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). It can track rapid phase evolution from secular stellar braking and stochastic timing noise torques simultaneously without searching second- and higher-order derivatives of the signal frequency, providing an economical alternative to stack-slide-based semicoherent algorithms. One implementation tracks the signal frequency alone. A second implementation tracks the signal frequency and its first time derivative. It improves the sensitivity by a factor of a few upon the first implementation, but the cost increases by 2 to 3 orders of magnitude.
Aucouturier, Jean-Julien; Nonaka, Yulri; Katahira, Kentaro; Okanoya, Kazuo
2011-11-01
The paper describes an application of machine learning techniques to identify expiratory and inspiration phases from the audio recording of human baby cries. Crying episodes were recorded from 14 infants, spanning four vocalization contexts in their first 12 months of age; recordings from three individuals were annotated manually to identify expiratory and inspiratory sounds and used as training examples to segment automatically the recordings of the other 11 individuals. The proposed algorithm uses a hidden Markov model architecture, in which state likelihoods are estimated either with Gaussian mixture models or by converting the classification decisions of a support vector machine. The algorithm yields up to 95% classification precision (86% average), and its ability generalizes over different babies, different ages, and vocalization contexts. The technique offers an opportunity to quantify expiration duration, count the crying rate, and other time-related characteristics of baby crying for screening, diagnosis, and research purposes over large populations of infants.
Bi-dimension decomposed hidden Markov models for multi-person activity recognition
Institute of Scientific and Technical Information of China (English)
Wei-dong ZHANG; Feng CHEN; Wen-li XU
2009-01-01
We present a novel model for recognizing long-term complex activities involving multiple persons. The proposed model, named 'decomposed hidden Markov model' (DHMM), combines spatial decomposition and hierarchical abstraction to capture multi-modal, long-term dependent and multi-scale characteristics of activities. Decomposition in space and time offers conceptual advantages of compaction and clarity, and greatly reduces the size of state space as well as the number of parameters.DHMMs are efficient even when the number of persons is variable. We also introduce an efficient approximation algorithm for inference and parameter estimation. Experiments on multi-person activities and multi-modal individual activities demonstrate that DHMMs are more efficient and reliable than familiar models, such as coupled HMMs, hierarchical HMMs, and multi-observation HMMs.
Time series segmentation: a new approach based on Genetic Algorithm and Hidden Markov Model
Toreti, A.; Kuglitsch, F. G.; Xoplaki, E.; Luterbacher, J.
2009-04-01
The subdivision of a time series into homogeneous segments has been performed using various methods applied to different disciplines. In climatology, for example, it is accompanied by the well-known homogenization problem and the detection of artificial change points. In this context, we present a new method (GAMM) based on Hidden Markov Model (HMM) and Genetic Algorithm (GA), applicable to series of independent observations (and easily adaptable to autoregressive processes). A left-to-right hidden Markov model, estimating the parameters and the best-state sequence, respectively, with the Baum-Welch and Viterbi algorithms, was applied. In order to avoid the well-known dependence of the Baum-Welch algorithm on the initial condition, a Genetic Algorithm was developed. This algorithm is characterized by mutation, elitism and a crossover procedure implemented with some restrictive rules. Moreover the function to be minimized was derived following the approach of Kehagias (2004), i.e. it is the so-called complete log-likelihood. The number of states was determined applying a two-fold cross-validation procedure (Celeux and Durand, 2008). Being aware that the last issue is complex, and it influences all the analysis, a Multi Response Permutation Procedure (MRPP; Mielke et al., 1981) was inserted. It tests the model with K+1 states (where K is the state number of the best model) if its likelihood is close to K-state model. Finally, an evaluation of the GAMM performances, applied as a break detection method in the field of climate time series homogenization, is shown. 1. G. Celeux and J.B. Durand, Comput Stat 2008. 2. A. Kehagias, Stoch Envir Res 2004. 3. P.W. Mielke, K.J. Berry, G.W. Brier, Monthly Wea Rev 1981.
Progression of liver cirrhosis to HCC: an application of hidden Markov model
Directory of Open Access Journals (Sweden)
Serio Gabriella
2011-04-01
Full Text Available Abstract Background Health service databases of administrative type can be a useful tool for the study of progression of a disease, but the data reported in such sources could be affected by misclassifications of some patients' real disease states at the time. Aim of this work was to estimate the transition probabilities through the different degenerative phases of liver cirrhosis using health service databases. Methods We employed a hidden Markov model to determine the transition probabilities between two states, and of misclassification. The covariates inserted in the model were sex, age, the presence of comorbidities correlated with alcohol abuse, the presence of diagnosis codes indicating hepatitis C virus infection, and the Charlson Index. The analysis was conducted in patients presumed to have suffered the onset of cirrhosis in 2000, observing the disease evolution and, if applicable, death up to the end of the year 2006. Results The incidence of hepatocellular carcinoma (HCC in cirrhotic patients was 1.5% per year. The probability of developing HCC is higher in males (OR = 2.217 and patients over 65 (OR = 1.547; over 65-year-olds have a greater probability of death both while still suffering from cirrhosis (OR = 2.379 and if they have developed HCC (OR = 1.410. A more severe casemix affects the transition from HCC to death (OR = 1.714. The probability of misclassifying subjects with HCC as exclusively affected by liver cirrhosis is 14.08%. Conclusions The hidden Markov model allowing for misclassification is well suited to analyses of health service databases, since it is able to capture bias due to the fact that the quality and accuracy of the available information are not always optimal. The probability of evolution of a cirrhotic subject to HCC depends on sex and age class, while hepatitis C virus infection and comorbidities correlated with alcohol abuse do not seem to have an influence.
Irreversible Markov chains in spin models: Topological excitations
Lei, Ze; Krauth, Werner
2018-01-01
We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain dynamics leads to slow decay of vortex-antivortex correlations while spin waves decorrelate very quickly. Using a Fréchet description of the maximum vortex-antivortex distance, we quantify the contributions of topological excitations to the equilibrium correlations, and show that they vary from a dynamical critical exponent z∼ 2 at the critical temperature to z∼ 0 in the limit of zero temperature. We confirm the event-chain algorithm's fast relaxation (corresponding to z = 0) of spin waves in the harmonic approximation to the XY model. Mixing times (describing the approach towards equilibrium from the least favorable initial state) however remain much larger than equilibrium correlation times at low temperatures. We also describe the respective influence of topological monopole-antimonopole excitations and of spin waves on the event-chain dynamics in the three-dimensional Heisenberg model.
A Hidden Markov Model for Urban-Scale Traffic Estimation Using Floating Car Data.
Wang, Xiaomeng; Peng, Ling; Chi, Tianhe; Li, Mengzhu; Yao, Xiaojing; Shao, Jing
2015-01-01
Urban-scale traffic monitoring plays a vital role in reducing traffic congestion. Owing to its low cost and wide coverage, floating car data (FCD) serves as a novel approach to collecting traffic data. However, sparse probe data represents the vast majority of the data available on arterial roads in most urban environments. In order to overcome the problem of data sparseness, this paper proposes a hidden Markov model (HMM)-based traffic estimation model, in which the traffic condition on a road segment is considered as a hidden state that can be estimated according to the conditions of road segments having similar traffic characteristics. An algorithm based on clustering and pattern mining rather than on adjacency relationships is proposed to find clusters with road segments having similar traffic characteristics. A multi-clustering strategy is adopted to achieve a trade-off between clustering accuracy and coverage. Finally, the proposed model is designed and implemented on the basis of a real-time algorithm. Results of experiments based on real FCD confirm the applicability, accuracy, and efficiency of the model. In addition, the results indicate that the model is practicable for traffic estimation on urban arterials and works well even when more than 70% of the probe data are missing.
Hidden Markov event sequence models: toward unsupervised functional MRI brain mapping.
Faisan, Sylvain; Thoraval, Laurent; Armspach, Jean-Paul; Foucher, Jack R; Metz-Lutz, Marie-Noëlle; Heitz, Fabrice
2005-01-01
Most methods used in functional MRI (fMRI) brain mapping require restrictive assumptions about the shape and timing of the fMRI signal in activated voxels. Consequently, fMRI data may be partially and misleadingly characterized, leading to suboptimal or invalid inference. To limit these assumptions and to capture the broad range of possible activation patterns, a novel statistical fMRI brain mapping method is proposed. It relies on hidden semi-Markov event sequence models (HSMESMs), a special class of hidden Markov models (HMMs) dedicated to the modeling and analysis of event-based random processes. Activation detection is formulated in terms of time coupling between (1) the observed sequence of hemodynamic response onset (HRO) events detected in the voxel's fMRI signal and (2) the "hidden" sequence of task-induced neural activation onset (NAO) events underlying the HROs. Both event sequences are modeled within a single HSMESM. The resulting brain activation model is trained to automatically detect neural activity embedded in the input fMRI data set under analysis. The data sets considered in this article are threefold: synthetic epoch-related, real epoch-related (auditory lexical processing task), and real event-related (oddball detection task) fMRI data sets. Synthetic data: Activation detection results demonstrate the superiority of the HSMESM mapping method with respect to a standard implementation of the statistical parametric mapping (SPM) approach. They are also very close, sometimes equivalent, to those obtained with an "ideal" implementation of SPM in which the activation patterns synthesized are reused for analysis. The HSMESM method appears clearly insensitive to timing variations of the hemodynamic response and exhibits low sensitivity to fluctuations of its shape (unsustained activation during task). Real epoch-related data: HSMESM activation detection results compete with those obtained with SPM, without requiring any prior definition of the expected
A Markov Chain Estimator of Multivariate Volatility from High Frequency Data
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume; Lunde, Asger
We introduce a multivariate estimator of financial volatility that is based on the theory of Markov chains. The Markov chain framework takes advantage of the discreteness of high-frequency returns. We study the finite sample properties of the estimation in a simulation study and apply...
The spectral method and the central limit theorem for general Markov chains
Nagaev, S. V.
2017-12-01
We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.
Fast-slow asymptotics for a Markov chain model of fast sodium current
Starý, Tomáš; Biktashev, Vadim N.
2017-09-01
We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.
A note on asymptotic expansions for Markov chains using operator theory
DEFF Research Database (Denmark)
Jensen, J.L.
1987-01-01
We consider asymptotic expansions for sums Sn on the form Sn = fhook0(X0) + fhook(X1, X0) + ... + fhook(Xn, Xn-1), where Xi is a Markov chain. Under different ergodicity conditions on the Markov chain and certain conditional moment conditions on fhook(Xi, Xi-1), a simple representation...
Computing continuous-time Markov chains as transformers of unbounded observables
DEFF Research Database (Denmark)
Danos, Vincent; Heindel, Tobias; Garnier, Ilias
2017-01-01
The paper studies continuous-time Markov chains (CTMCs) as transformers of real-valued functions on their state space, considered as generalised predicates and called observables. Markov chains are assumed to take values in a countable state space S; observables f: S → ℝ may be unbounded...
Kinetics and thermodynamics of first-order Markov chain copolymerization
Energy Technology Data Exchange (ETDEWEB)
Gaspard, P.; Andrieux, D. [Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels (Belgium)
2014-07-28
We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer.
Solution of the Markov chain for the dead time problem
International Nuclear Information System (INIS)
Degweker, S.B.
1997-01-01
A method for solving the equation for the Markov chain, describing the effect of a non-extendible dead time on the statistics of time correlated pulses, is discussed. The equation, which was derived in an earlier paper, describes a non-linear process and is not amenable to exact solution. The present method consists of representing the probability generating function as a factorial cumulant expansion and neglecting factorial cumulants beyond the second. This results in a closed set of non-linear equations for the factorial moments. Stationary solutions of these equations, which are of interest for calculating the count rate, are obtained iteratively. The method is applied to the variable dead time counter technique for estimation of system parameters in passive neutron assay of Pu and reactor noise analysis. Comparisons of results by this method with Monte Carlo calculations are presented. (author)
Markov Chain Monte Carlo Bayesian Learning for Neural Networks
Goodrich, Michael S.
2011-01-01
Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.
Nonequilibrium thermodynamic potentials for continuous-time Markov chains.
Verley, Gatien
2016-01-01
We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.
Distance between configurations in Markov chain Monte Carlo simulations
Fukuma, Masafumi; Matsumoto, Nobuyuki; Umeda, Naoya
2017-12-01
For a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal form for the class of algorithms which generate local moves in the configuration space. We explicitly calculate the distance for the Langevin algorithm, and show that it certainly has desired and expected properties as distance. We further show that the distance for a multimodal distribution gets dramatically reduced from a large value by the introduction of a tempering method. We also argue that, when the original distribution is highly multimodal with large number of degenerate vacua, an anti-de Sitter-like geometry naturally emerges in the extended configuration space.
Application of the Markov chain approximation to the sunspot observations
International Nuclear Information System (INIS)
Onal, M.
1988-01-01
The positions of the 13,588 sunspot groups observed during the cycle of 1950-1960 at the Istanbul University Observatory have been corrected for the effect of differential rotation. The evolution probability of a sunspot group to the other one in the same region have been determined. By using the Markov chain approximation, the types of these groups and their transition probabilities during the following activity cycle (1950-1960), and the concentration of active regions during 1950-1960 have been estimated. The transition probabilities from the observations of the activity cycle 1960-1970 have been compared with the predicted transition probabilities and a good correlation has been noted. 5 refs.; 2 tabs
Exact Markov chains versus diffusion theory for haploid random mating.
Tyvand, Peder A; Thorvaldsen, Steinar
2010-05-01
Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck. 2010 Elsevier Inc. All rights reserved.
HYDRA: a Java library for Markov Chain Monte Carlo
Directory of Open Access Journals (Sweden)
Gregory R. Warnes
2002-03-01
Full Text Available Hydra is an open-source, platform-neutral library for performing Markov Chain Monte Carlo. It implements the logic of standard MCMC samplers within a framework designed to be easy to use, extend, and integrate with other software tools. In this paper, we describe the problem that motivated our work, outline our goals for the Hydra pro ject, and describe the current features of the Hydra library. We then provide a step-by-step example of using Hydra to simulate from a mixture model drawn from cancer genetics, first using a variable-at-a-time Metropolis sampler and then a Normal Kernel Coupler. We conclude with a discussion of future directions for Hydra.
On the multi-level solution algorithm for Markov chains
Energy Technology Data Exchange (ETDEWEB)
Horton, G. [Univ. of Erlangen, Nuernberg (Germany)
1996-12-31
We discuss the recently introduced multi-level algorithm for the steady-state solution of Markov chains. The method is based on the aggregation principle, which is well established in the literature. Recursive application of the aggregation yields a multi-level method which has been shown experimentally to give results significantly faster than the methods currently in use. The algorithm can be reformulated as an algebraic multigrid scheme of Galerkin-full approximation type. The uniqueness of the scheme stems from its solution-dependent prolongation operator which permits significant computational savings in the evaluation of certain terms. This paper describes the modeling of computer systems to derive information on performance, measured typically as job throughput or component utilization, and availability, defined as the proportion of time a system is able to perform a certain function in the presence of component failures and possibly also repairs.
Stochastic model of milk homogenization process using Markov's chain
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A. A. Khvostov
2016-01-01
Full Text Available The process of development of a mathematical model of the process of homogenization of dairy products is considered in the work. The theory of Markov's chains was used in the development of the mathematical model, Markov's chain with discrete states and continuous parameter for which the homogenisation pressure is taken, being the basis for the model structure. Machine realization of the model is implemented in the medium of structural modeling MathWorks Simulink™. Identification of the model parameters was carried out by minimizing the standard deviation calculated from the experimental data for each fraction of dairy products fat phase. As the set of experimental data processing results of the micrographic images of fat globules of whole milk samples distribution which were subjected to homogenization at different pressures were used. Pattern Search method was used as optimization method with the Latin Hypercube search algorithm from Global Optimization Тoolbox library. The accuracy of calculations averaged over all fractions of 0.88% (the relative share of units, the maximum relative error was 3.7% with the homogenization pressure of 30 MPa, which may be due to the very abrupt change in properties from the original milk in the particle size distribution at the beginning of the homogenization process and the lack of experimental data at homogenization pressures of below the specified value. The mathematical model proposed allows to calculate the profile of volume and mass distribution of the fat phase (fat globules in the product, depending on the homogenization pressure and can be used in the laboratory and research of dairy products composition, as well as in the calculation, design and modeling of the process equipment of the dairy industry enterprises.
Simulating reservoir lithologies by an actively conditioned Markov chain model
Feng, Runhai; Luthi, Stefan M.; Gisolf, Dries
2018-06-01
The coupled Markov chain model can be used to simulate reservoir lithologies between wells, by conditioning them on the observed data in the cored wells. However, with this method, only the state at the same depth as the current cell is going to be used for conditioning, which may be a problem if the geological layers are dipping. This will cause the simulated lithological layers to be broken or to become discontinuous across the reservoir. In order to address this problem, an actively conditioned process is proposed here, in which a tolerance angle is predefined. The states contained in the region constrained by the tolerance angle will be employed for conditioning in the horizontal chain first, after which a coupling concept with the vertical chain is implemented. In order to use the same horizontal transition matrix for different future states, the tolerance angle has to be small. This allows the method to work in reservoirs without complex structures caused by depositional processes or tectonic deformations. Directional artefacts in the modeling process are avoided through a careful choice of the simulation path. The tolerance angle and dipping direction of the strata can be obtained from a correlation between wells, or from seismic data, which are available in most hydrocarbon reservoirs, either by interpretation or by inversion that can also assist the construction of a horizontal probability matrix.
Masuyama, Hiroyuki
2014-01-01
In this paper we study the augmented truncation of discrete-time block-monotone Markov chains under geometric drift conditions. We first present a bound for the total variation distance between the stationary distributions of an original Markov chain and its augmented truncation. We also obtain such error bounds for more general cases, where an original Markov chain itself is not necessarily block monotone but is blockwise dominated by a block-monotone Markov chain. Finally,...
An Efficient Algorithm for Modelling Duration in Hidden Markov Models, with a Dramatic Application
DEFF Research Database (Denmark)
Hauberg, Søren; Sloth, Jakob
2008-01-01
For many years, the hidden Markov model (HMM) has been one of the most popular tools for analysing sequential data. One frequently used special case is the left-right model, in which the order of the hidden states is known. If knowledge of the duration of a state is available it is not possible...... to represent it explicitly with an HMM. Methods for modelling duration with HMM's do exist (Rabiner in Proc. IEEE 77(2):257---286, [1989]), but they come at the price of increased computational complexity. Here we present an efficient and robust algorithm for modelling duration in HMM's, and this algorithm...
Use of profile hidden Markov models in viral discovery: current insights
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Reyes A
2017-07-01
Full Text Available Alejandro Reyes,1–3 João Marcelo P Alves,4 Alan Mitchell Durham,5 Arthur Gruber4 1Department of Biological Sciences, Universidad de los Andes, Bogotá, Colombia; 2Department of Pathology and Immunology, Center for Genome Sciences and Systems Biology, Washington University in Saint Louis, St Louis, MO, USA; 3Max Planck Tandem Group in Computational Biology, Universidad de los Andes, Bogotá, Colombia; 4Department of Parasitology, Institute of Biomedical Sciences, 5Department of Computer Science, Institute of Mathematics and Statistics, Universidade de São Paulo, São Paulo, Brazil Abstract: Sequence similarity searches are the bioinformatic cornerstone of molecular sequence analysis for all domains of life. However, large amounts of divergence between organisms, such as those seen among viruses, can significantly hamper analyses. Profile hidden Markov models (profile HMMs are among the most successful approaches for dealing with this problem, which represent an invaluable tool for viral identification efforts. Profile HMMs are statistical models that convert information from a multiple sequence alignment into a set of probability values that reflect position-specific variation levels in all members of evolutionarily related sequences. Since profile HMMs represent a wide spectrum of variation, these models show higher sensitivity than conventional similarity methods such as BLAST for the detection of remote homologs. In recent years, there has been an effort to compile viral sequences from different viral taxonomic groups into integrated databases, such as Prokaryotic Virus Orthlogous Groups (pVOGs and database of profile HMMs (vFam database, which provide functional annotation, multiple sequence alignments, and profile HMMs. Since these databases rely on viral sequences collected from GenBank and RefSeq, they suffer in variable extent from uneven taxonomic sampling, with low sequence representation of many viral groups, which affects the
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Shi Zhiyan
2009-01-01
Full Text Available We study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain and a nonhomogeneous Markov chain indexed by a tree. As corollary, we obtain the property of the harmonic mean of random transition probability for a nonhomogeneous Markov chain.
Hidden Markov model analysis of maternal behavior patterns in inbred and reciprocal hybrid mice.
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Valeria Carola
Full Text Available Individual variation in maternal care in mammals shows a significant heritable component, with the maternal behavior of daughters resembling that of their mothers. In laboratory mice, genetically distinct inbred strains show stable differences in maternal care during the first postnatal week. Moreover, cross fostering and reciprocal breeding studies demonstrate that differences in maternal care between inbred strains persist in the absence of genetic differences, demonstrating a non-genetic or epigenetic contribution to maternal behavior. In this study we applied a mathematical tool, called hidden Markov model (HMM, to analyze the behavior of female mice in the presence of their young. The frequency of several maternal behaviors in mice has been previously described, including nursing/grooming pups and tending to the nest. However, the ordering, clustering, and transitions between these behaviors have not been systematically described and thus a global description of maternal behavior is lacking. Here we used HMM to describe maternal behavior patterns in two genetically distinct mouse strains, C57BL/6 and BALB/c, and their genetically identical reciprocal hybrid female offspring. HMM analysis is a powerful tool to identify patterns of events that cluster in time and to determine transitions between these clusters, or hidden states. For the HMM analysis we defined seven states: arched-backed nursing, blanket nursing, licking/grooming pups, grooming, activity, eating, and sleeping. By quantifying the frequency, duration, composition, and transition probabilities of these states we were able to describe the pattern of maternal behavior in mouse and identify aspects of these patterns that are under genetic and nongenetic inheritance. Differences in these patterns observed in the experimental groups (inbred and hybrid females were detected only after the application of HMM analysis whereas classical statistical methods and analyses were not able to
Energy Technology Data Exchange (ETDEWEB)
Beyreuther, Moritz; Wassermann, Joachim [Department of Earth and Environmental Sciences (Geophys. Observatory), Ludwig Maximilians Universitaet Muenchen, D-80333 (Germany); Carniel, Roberto [Dipartimento di Georisorse e Territorio Universitat Degli Studi di Udine, I-33100 (Italy)], E-mail: roberto.carniel@uniud.it
2008-10-01
A possible interaction of (volcano-) tectonic earthquakes with the continuous seismic noise recorded in the volcanic island of Tenerife was recently suggested, but existing catalogues seem to be far from being self consistent, calling for the development of automatic detection and classification algorithms. In this work we propose the adoption of a methodology based on Hidden Markov Models (HMMs), widely used already in other fields, such as speech classification.
Häme, Yrjö; Angelini, Elsa D.; Hoffman, Eric A.; Barr, R. Graham; Laine, Andrew F.
2014-01-01
The extent of pulmonary emphysema is commonly estimated from CT images by computing the proportional area of voxels below a predefined attenuation threshold. However, the reliability of this approach is limited by several factors that affect the CT intensity distributions in the lung. This work presents a novel method for emphysema quantification, based on parametric modeling of intensity distributions in the lung and a hidden Markov measure field model to segment emphysematous regions. The framework adapts to the characteristics of an image to ensure a robust quantification of emphysema under varying CT imaging protocols and differences in parenchymal intensity distributions due to factors such as inspiration level. Compared to standard approaches, the present model involves a larger number of parameters, most of which can be estimated from data, to handle the variability encountered in lung CT scans. The method was used to quantify emphysema on a cohort of 87 subjects, with repeated CT scans acquired over a time period of 8 years using different imaging protocols. The scans were acquired approximately annually, and the data set included a total of 365 scans. The results show that the emphysema estimates produced by the proposed method have very high intra-subject correlation values. By reducing sensitivity to changes in imaging protocol, the method provides a more robust estimate than standard approaches. In addition, the generated emphysema delineations promise great advantages for regional analysis of emphysema extent and progression, possibly advancing disease subtyping. PMID:24759984
A hidden Markov model approach for determining expression from genomic tiling micro arrays
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Krogh Anders
2006-05-01
Full Text Available Abstract Background Genomic tiling micro arrays have great potential for identifying previously undiscovered coding as well as non-coding transcription. To-date, however, analyses of these data have been performed in an ad hoc fashion. Results We present a probabilistic procedure, ExpressHMM, that adaptively models tiling data prior to predicting expression on genomic sequence. A hidden Markov model (HMM is used to model the distributions of tiling array probe scores in expressed and non-expressed regions. The HMM is trained on sets of probes mapped to regions of annotated expression and non-expression. Subsequently, prediction of transcribed fragments is made on tiled genomic sequence. The prediction is accompanied by an expression probability curve for visual inspection of the supporting evidence. We test ExpressHMM on data from the Cheng et al. (2005 tiling array experiments on ten Human chromosomes 1. Results can be downloaded and viewed from our web site 2. Conclusion The value of adaptive modelling of fluorescence scores prior to categorisation into expressed and non-expressed probes is demonstrated. Our results indicate that our adaptive approach is superior to the previous analysis in terms of nucleotide sensitivity and transfrag specificity.
NLStradamus: a simple Hidden Markov Model for nuclear localization signal prediction
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Provart Nicholas
2009-06-01
Full Text Available Abstract Background Nuclear localization signals (NLSs are stretches of residues within a protein that are important for the regulated nuclear import of the protein. Of the many import pathways that exist in yeast, the best characterized is termed the 'classical' NLS pathway. The classical NLS contains specific patterns of basic residues and computational methods have been designed to predict the location of these motifs on proteins. The consensus sequences, or patterns, for the other import pathways are less well-understood. Results In this paper, we present an analysis of characterized NLSs in yeast, and find, despite the large number of nuclear import pathways, that NLSs seem to show similar patterns of amino acid residues. We test current prediction methods and observe a low true positive rate. We therefore suggest an approach using hidden Markov models (HMMs to predict novel NLSs in proteins. We show that our method is able to consistently find 37% of the NLSs with a low false positive rate and that our method retains its true positive rate outside of the yeast data set used for the training parameters. Conclusion Our implementation of this model, NLStradamus, is made available at: http://www.moseslab.csb.utoronto.ca/NLStradamus/
A classification of marked hijaiyah letters' pronunciation using hidden Markov model
Wisesty, Untari N.; Mubarok, M. Syahrul; Adiwijaya
2017-08-01
Hijaiyah letters are the letters that arrange the words in Al Qur'an consisting of 28 letters. They symbolize the consonant sounds. On the other hand, the vowel sounds are symbolized by harokat/marks. Speech recognition system is a system used to process the sound signal to be data so that it can be recognized by computer. To build the system, some stages are needed i.e characteristics/feature extraction and classification. In this research, LPC and MFCC extraction method, K-Means Quantization vector and Hidden Markov Model classification are used. The data used are the 28 letters and 6 harakat with the total class of 168. After several are testing done, it can be concluded that the system can recognize the pronunciation pattern of marked hijaiyah letter very well in the training data with its highest accuracy of 96.1% using the feature of LPC extraction and 94% using the MFCC. Meanwhile, when testing system is used, the accuracy decreases up to 41%.
A Two-Channel Training Algorithm for Hidden Markov Model and Its Application to Lip Reading
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Foo Say Wei
2005-01-01
Full Text Available Hidden Markov model (HMM has been a popular mathematical approach for sequence classification such as speech recognition since 1980s. In this paper, a novel two-channel training strategy is proposed for discriminative training of HMM. For the proposed training strategy, a novel separable-distance function that measures the difference between a pair of training samples is adopted as the criterion function. The symbol emission matrix of an HMM is split into two channels: a static channel to maintain the validity of the HMM and a dynamic channel that is modified to maximize the separable distance. The parameters of the two-channel HMM are estimated by iterative application of expectation-maximization (EM operations. As an example of the application of the novel approach, a hierarchical speaker-dependent visual speech recognition system is trained using the two-channel HMMs. Results of experiments on identifying a group of confusable visemes indicate that the proposed approach is able to increase the recognition accuracy by an average of 20% compared with the conventional HMMs that are trained with the Baum-Welch estimation.
Cluster-based adaptive power control protocol using Hidden Markov Model for Wireless Sensor Networks
Vinutha, C. B.; Nalini, N.; Nagaraja, M.
2017-06-01
This paper presents strategies for an efficient and dynamic transmission power control technique, in order to reduce packet drop and hence energy consumption of power-hungry sensor nodes operated in highly non-linear channel conditions of Wireless Sensor Networks. Besides, we also focus to prolong network lifetime and scalability by designing cluster-based network structure. Specifically we consider weight-based clustering approach wherein, minimum significant node is chosen as Cluster Head (CH) which is computed stemmed from the factors distance, remaining residual battery power and received signal strength (RSS). Further, transmission power control schemes to fit into dynamic channel conditions are meticulously implemented using Hidden Markov Model (HMM) where probability transition matrix is formulated based on the observed RSS measurements. Typically, CH estimates initial transmission power of its cluster members (CMs) from RSS using HMM and broadcast this value to its CMs for initialising their power value. Further, if CH finds that there are variations in link quality and RSS of the CMs, it again re-computes and optimises the transmission power level of the nodes using HMM to avoid packet loss due noise interference. We have demonstrated our simulation results to prove that our technique efficiently controls the power levels of sensing nodes to save significant quantity of energy for different sized network.
The Use of Hidden Markov Models for Anomaly Detection in Nuclear Core Condition Monitoring
Stephen, Bruce; West, Graeme M.; Galloway, Stuart; McArthur, Stephen D. J.; McDonald, James R.; Towle, Dave
2009-04-01
Unplanned outages can be especially costly for generation companies operating nuclear facilities. Early detection of deviations from expected performance through condition monitoring can allow a more proactive and managed approach to dealing with ageing plant. This paper proposes an anomaly detection framework incorporating the use of the Hidden Markov Model (HMM) to support the analysis of nuclear reactor core condition monitoring data. Fuel Grab Load Trace (FGLT) data gathered within the UK during routine refueling operations has been seen to provide information relating to the condition of the graphite bricks that comprise the core. Although manual analysis of this data is time consuming and requires considerable expertise, this paper demonstrates how techniques such as the HMM can provide analysis support by providing a benchmark model of expected behavior against which future refueling events may be compared. The presence of anomalous behavior in candidate traces is inferred through the underlying statistical foundation of the HMM which gives an observation likelihood averaged along the length of the input sequence. Using this likelihood measure, the engineer can be alerted to anomalous behaviour, indicating data which might require further detailed examination. It is proposed that this data analysis technique is used in conjunction with other intelligent analysis techniques currently employed to analyse FGLT to provide a greater confidence measure in detecting anomalous behaviour from FGLT data.
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Bastien Boussau
2009-06-01
Full Text Available Homologous recombination is a pervasive biological process that affects sequences in all living organisms and viruses. In the presence of recombination, the evolutionary history of an alignment of homologous sequences cannot be properly depicted by a single bifurcating tree: some sites have evolved along a specific phylogenetic tree, others have followed another path. Methods available to analyse recombination in sequences usually involve an analysis of the alignment through sliding-windows, or are particularly demanding in computational resources, and are often limited to nucleotide sequences. In this article, we propose and implement a Mixture Model on trees and a phylogenetic Hidden Markov Model to reveal recombination breakpoints while searching for the various evolutionary histories that are present in an alignment known to have undergone homologous recombination. These models are sufficiently efficient to be applied to dozens of sequences on a single desktop computer, and can handle equivalently nucleotide or protein sequences. We estimate their accuracy on simulated sequences and test them on real data.
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Bastien Boussau
2009-01-01
Full Text Available Homologous recombination is a pervasive biological process that affects sequences in all living organisms and viruses. In the presence of recombination, the evolutionary history of an alignment of homologous sequences cannot be properly depicted by a single bifurcating tree: some sites have evolved along a specific phylogenetic tree, others have followed another path. Methods available to analyse recombination in sequences usually involve an analysis of the alignment through sliding-windows, or are particularly demanding in computational resources, and are often limited to nucleotide sequences. In this article, we propose and implement a Mixture Model on trees and a phylogenetic Hidden Markov Model to reveal recombination breakpoints while searching for the various evolutionary histories that are present in an alignment known to have undergone homologous recombination. These models are sufficiently efficient to be applied to dozens of sequences on a single desktop computer, and can handle equivalently nucleotide or protein sequences. We estimate their accuracy on simulated sequences and test them on real data.
Enhancing Speech Recognition Using Improved Particle Swarm Optimization Based Hidden Markov Model
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Lokesh Selvaraj
2014-01-01
Full Text Available Enhancing speech recognition is the primary intention of this work. In this paper a novel speech recognition method based on vector quantization and improved particle swarm optimization (IPSO is suggested. The suggested methodology contains four stages, namely, (i denoising, (ii feature mining (iii, vector quantization, and (iv IPSO based hidden Markov model (HMM technique (IP-HMM. At first, the speech signals are denoised using median filter. Next, characteristics such as peak, pitch spectrum, Mel frequency Cepstral coefficients (MFCC, mean, standard deviation, and minimum and maximum of the signal are extorted from the denoised signal. Following that, to accomplish the training process, the extracted characteristics are given to genetic algorithm based codebook generation in vector quantization. The initial populations are created by selecting random code vectors from the training set for the codebooks for the genetic algorithm process and IP-HMM helps in doing the recognition. At this point the creativeness will be done in terms of one of the genetic operation crossovers. The proposed speech recognition technique offers 97.14% accuracy.
Spatial Region Estimation for Autonomous CoT Clustering Using Hidden Markov Model
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Joon‐young Jung
2018-02-01
Full Text Available This paper proposes a hierarchical dual filtering (HDF algorithm to estimate the spatial region between a Cloud of Things (CoT gateway and an Internet of Things (IoT device. The accuracy of the spatial region estimation is important for autonomous CoT clustering. We conduct spatial region estimation using a hidden Markov model (HMM with a raw Bluetooth received signal strength indicator (RSSI. However, the accuracy of the region estimation using the validation data is only 53.8%. To increase the accuracy of the spatial region estimation, the HDF algorithm removes the high‐frequency signals hierarchically, and alters the parameters according to whether the IoT device moves. The accuracy of spatial region estimation using a raw RSSI, Kalman filter, and HDF are compared to evaluate the effectiveness of the HDF algorithm. The success rate and root mean square error (RMSE of all regions are 0.538, 0.622, and 0.75, and 0.997, 0.812, and 0.5 when raw RSSI, a Kalman filter, and HDF are used, respectively. The HDF algorithm attains the best results in terms of the success rate and RMSE of spatial region estimation using HMM.
A transition-constrained discrete hidden Markov model for automatic sleep staging
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Pan Shing-Tai
2012-08-01
Full Text Available Abstract Background Approximately one-third of the human lifespan is spent sleeping. To diagnose sleep problems, all-night polysomnographic (PSG recordings including electroencephalograms (EEGs, electrooculograms (EOGs and electromyograms (EMGs, are usually acquired from the patient and scored by a well-trained expert according to Rechtschaffen & Kales (R&K rules. Visual sleep scoring is a time-consuming and subjective process. Therefore, the development of an automatic sleep scoring method is desirable. Method The EEG, EOG and EMG signals from twenty subjects were measured. In addition to selecting sleep characteristics based on the 1968 R&K rules, features utilized in other research were collected. Thirteen features were utilized including temporal and spectrum analyses of the EEG, EOG and EMG signals, and a total of 158 hours of sleep data were recorded. Ten subjects were used to train the Discrete Hidden Markov Model (DHMM, and the remaining ten were tested by the trained DHMM for recognition. Furthermore, the 2-fold cross validation was performed during this experiment. Results Overall agreement between the expert and the results presented is 85.29%. With the exception of S1, the sensitivities of each stage were more than 81%. The most accurate stage was SWS (94.9%, and the least-accurately classified stage was S1 ( Conclusion The results of the experiments demonstrate that the proposed method significantly enhances the recognition rate when compared with prior studies.
Capturing the state transitions of seizure-like events using Hidden Markov models.
Guirgis, Mirna; Serletis, Demitre; Carlen, Peter L; Bardakjian, Berj L
2011-01-01
The purpose of this study was to investigate the number of states present in the progression of a seizure-like event (SLE). Of particular interest is to determine if there are more than two clearly defined states, as this would suggest that there is a distinct state preceding an SLE. Whole-intact hippocampus from C57/BL mice was used to model epileptiform activity induced by the perfusion of a low Mg(2+)/high K(+) solution while extracellular field potentials were recorded from CA3 pyramidal neurons. Hidden Markov models (HMM) were used to model the state transitions of the recorded SLEs by incorporating various features of the Hilbert transform into the training algorithm; specifically, 2- and 3-state HMMs were explored. Although the 2-state model was able to distinguish between SLE and nonSLE behavior, it provided no improvements compared to visual inspection alone. However, the 3-state model was able to capture two distinct nonSLE states that visual inspection failed to discriminate. Moreover, by developing an HMM based system a priori knowledge of the state transitions was not required making this an ideal platform for seizure prediction algorithms.
Reverse engineering a social agent-based hidden markov model--visage.
Chen, Hung-Ching Justin; Goldberg, Mark; Magdon-Ismail, Malik; Wallace, William A
2008-12-01
We present a machine learning approach to discover the agent dynamics that drives the evolution of the social groups in a community. We set up the problem by introducing an agent-based hidden Markov model for the agent dynamics: an agent's actions are determined by micro-laws. Nonetheless, We learn the agent dynamics from the observed communications without knowing state transitions. Our approach is to identify the appropriate micro-laws corresponding to an identification of the appropriate parameters in the model. The model identification problem is then formulated as a mixed optimization problem. To solve the problem, we develop a multistage learning process for determining the group structure, the group evolution, and the micro-laws of a community based on the observed set of communications among actors, without knowing the semantic contents. Finally, to test the quality of our approximations and the feasibility of the approach, we present the results of extensive experiments on synthetic data as well as the results on real communities, such as Enron email and Movie newsgroups. Insight into agent dynamics helps us understand the driving forces behind social evolution.
Adaptive hidden Markov model with anomaly States for price manipulation detection.
Cao, Yi; Li, Yuhua; Coleman, Sonya; Belatreche, Ammar; McGinnity, Thomas Martin
2015-02-01
Price manipulation refers to the activities of those traders who use carefully designed trading behaviors to manually push up or down the underlying equity prices for making profits. With increasing volumes and frequency of trading, price manipulation can be extremely damaging to the proper functioning and integrity of capital markets. The existing literature focuses on either empirical studies of market abuse cases or analysis of particular manipulation types based on certain assumptions. Effective approaches for analyzing and detecting price manipulation in real time are yet to be developed. This paper proposes a novel approach, called adaptive hidden Markov model with anomaly states (AHMMAS) for modeling and detecting price manipulation activities. Together with wavelet transformations and gradients as the feature extraction methods, the AHMMAS model caters to price manipulation detection and basic manipulation type recognition. The evaluation experiments conducted on seven stock tick data from NASDAQ and the London Stock Exchange and 10 simulated stock prices by stochastic differential equation show that the proposed AHMMAS model can effectively detect price manipulation patterns and outperforms the selected benchmark models.
Using Hidden Markov Models to characterise intermittent social behaviour in fish shoals
Bode, Nikolai W. F.; Seitz, Michael J.
2018-02-01
The movement of animals in groups is widespread in nature. Understanding this phenomenon presents an important problem in ecology with many applications that range from conservation to robotics. Underlying all group movements are interactions between individual animals and it is therefore crucial to understand the mechanisms of this social behaviour. To date, despite promising methodological developments, there are few applications to data of practical statistical techniques that inferentially investigate the extent and nature of social interactions in group movement. We address this gap by demonstrating the usefulness of a Hidden Markov Model approach to characterise individual-level social movement in published trajectory data on three-spined stickleback shoals ( Gasterosteus aculeatus) and novel data on guppy shoals ( Poecilia reticulata). With these models, we formally test for speed-mediated social interactions and verify that they are present. We further characterise this inferred social behaviour and find that despite the substantial shoal-level differences in movement dynamics between species, it is qualitatively similar in guppies and sticklebacks. It is intermittent, occurring in varying numbers of individuals at different time points. The speeds of interacting fish follow a bimodal distribution, indicating that they are either stationary or move at a preferred mean speed, and social fish with more social neighbours move at higher speeds, on average. Our findings and methodology present steps towards characterising social behaviour in animal groups.
Identifying bubble collapse in a hydrothermal system using hidden Markov models
Dawson, P.B.; Benitez, M.C.; Lowenstern, J. B.; Chouet, B.A.
2012-01-01
Beginning in July 2003 and lasting through September 2003, the Norris Geyser Basin in Yellowstone National Park exhibited an unusual increase in ground temperature and hydrothermal activity. Using hidden Markov model theory, we identify over five million high-frequency (>15Hz) seismic events observed at a temporary seismic station deployed in the basin in response to the increase in hydrothermal activity. The source of these seismic events is constrained to within ???100 m of the station, and produced ???3500-5500 events per hour with mean durations of ???0.35-0.45s. The seismic event rate, air temperature, hydrologic temperatures, and surficial water flow of the geyser basin exhibited a marked diurnal pattern that was closely associated with solar thermal radiance. We interpret the source of the seismicity to be due to the collapse of small steam bubbles in the hydrothermal system, with the rate of collapse being controlled by surficial temperatures and daytime evaporation rates. copyright 2012 by the American Geophysical Union.
Development of a Fault Monitoring Technique for Wind Turbines Using a Hidden Markov Model.
Shin, Sung-Hwan; Kim, SangRyul; Seo, Yun-Ho
2018-06-02
Regular inspection for the maintenance of the wind turbines is difficult because of their remote locations. For this reason, condition monitoring systems (CMSs) are typically installed to monitor their health condition. The purpose of this study is to propose a fault detection algorithm for the mechanical parts of the wind turbine. To this end, long-term vibration data were collected over two years by a CMS installed on a 3 MW wind turbine. The vibration distribution at a specific rotating speed of main shaft is approximated by the Weibull distribution and its cumulative distribution function is utilized for determining the threshold levels that indicate impending failure of mechanical parts. A Hidden Markov model (HMM) is employed to propose the statistical fault detection algorithm in the time domain and the method whereby the input sequence for HMM is extracted is also introduced by considering the threshold levels and the correlation between the signals. Finally, it was demonstrated that the proposed HMM algorithm achieved a greater than 95% detection success rate by using the long-term signals.
Segmentation of heart sound recordings by a duration-dependent hidden Markov model
International Nuclear Information System (INIS)
Schmidt, S E; Graff, C; Toft, E; Struijk, J J; Holst-Hansen, C
2010-01-01
Digital stethoscopes offer new opportunities for computerized analysis of heart sounds. Segmentation of heart sound recordings into periods related to the first and second heart sound (S1 and S2) is fundamental in the analysis process. However, segmentation of heart sounds recorded with handheld stethoscopes in clinical environments is often complicated by background noise. A duration-dependent hidden Markov model (DHMM) is proposed for robust segmentation of heart sounds. The DHMM identifies the most likely sequence of physiological heart sounds, based on duration of the events, the amplitude of the signal envelope and a predefined model structure. The DHMM model was developed and tested with heart sounds recorded bedside with a commercially available handheld stethoscope from a population of patients referred for coronary arterioangiography. The DHMM identified 890 S1 and S2 sounds out of 901 which corresponds to 98.8% (CI: 97.8–99.3%) sensitivity in 73 test patients and 13 misplaced sounds out of 903 identified sounds which corresponds to 98.6% (CI: 97.6–99.1%) positive predictivity. These results indicate that the DHMM is an appropriate model of the heart cycle and suitable for segmentation of clinically recorded heart sounds
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Md. Rabiul Islam
2014-01-01
Full Text Available The aim of the paper is to propose a feature fusion based Audio-Visual Speaker Identification (AVSI system with varied conditions of illumination environments. Among the different fusion strategies, feature level fusion has been used for the proposed AVSI system where Hidden Markov Model (HMM is used for learning and classification. Since the feature set contains richer information about the raw biometric data than any other levels, integration at feature level is expected to provide better authentication results. In this paper, both Mel Frequency Cepstral Coefficients (MFCCs and Linear Prediction Cepstral Coefficients (LPCCs are combined to get the audio feature vectors and Active Shape Model (ASM based appearance and shape facial features are concatenated to take the visual feature vectors. These combined audio and visual features are used for the feature-fusion. To reduce the dimension of the audio and visual feature vectors, Principal Component Analysis (PCA method is used. The VALID audio-visual database is used to measure the performance of the proposed system where four different illumination levels of lighting conditions are considered. Experimental results focus on the significance of the proposed audio-visual speaker identification system with various combinations of audio and visual features.
Hossen, Jakir; Jacobs, Eddie L.; Chari, Srikant
2015-07-01
Linear pyroelectric array sensors have enabled useful classifications of objects such as humans and animals to be performed with relatively low-cost hardware in border and perimeter security applications. Ongoing research has sought to improve the performance of these sensors through signal processing algorithms. In the research presented here, we introduce the use of hidden Markov tree (HMT) models for object recognition in images generated by linear pyroelectric sensors. HMTs are trained to statistically model the wavelet features of individual objects through an expectation-maximization learning process. Human versus animal classification for a test object is made by evaluating its wavelet features against the trained HMTs using the maximum-likelihood criterion. The classification performance of this approach is compared to two other techniques; a texture, shape, and spectral component features (TSSF) based classifier and a speeded-up robust feature (SURF) classifier. The evaluation indicates that among the three techniques, the wavelet-based HMT model works well, is robust, and has improved classification performance compared to a SURF-based algorithm in equivalent computation time. When compared to the TSSF-based classifier, the HMT model has a slightly degraded performance but almost an order of magnitude improvement in computation time enabling real-time implementation.
Ma, Xiang; Schonfeld, Dan; Khokhar, Ashfaq A
2009-06-01
In this paper, we propose a novel solution to an arbitrary noncausal, multidimensional hidden Markov model (HMM) for image and video classification. First, we show that the noncausal model can be solved by splitting it into multiple causal HMMs and simultaneously solving each causal HMM using a fully synchronous distributed computing framework, therefore referred to as distributed HMMs. Next we present an approximate solution to the multiple causal HMMs that is based on an alternating updating scheme and assumes a realistic sequential computing framework. The parameters of the distributed causal HMMs are estimated by extending the classical 1-D training and classification algorithms to multiple dimensions. The proposed extension to arbitrary causal, multidimensional HMMs allows state transitions that are dependent on all causal neighbors. We, thus, extend three fundamental algorithms to multidimensional causal systems, i.e., 1) expectation-maximization (EM), 2) general forward-backward (GFB), and 3) Viterbi algorithms. In the simulations, we choose to limit ourselves to a noncausal 2-D model whose noncausality is along a single dimension, in order to significantly reduce the computational complexity. Simulation results demonstrate the superior performance, higher accuracy rate, and applicability of the proposed noncausal HMM framework to image and video classification.
Snoring detection using a piezo snoring sensor based on hidden Markov models.
Lee, Hyo-Ki; Lee, Jeon; Kim, Hojoong; Ha, Jin-Young; Lee, Kyoung-Joung
2013-05-01
This study presents a snoring detection method based on hidden Markov models (HMMs) using a piezo snoring sensor. Snoring is a major symptom of obstructive sleep apnea (OSA). In most sleep studies, snoring is detected with a microphone. Since these studies analyze the acoustic properties of snoring, they need to acquire data at high sampling rates, so a large amount of data should be processed. Recently, several sleep studies have monitored snoring using a piezo snoring sensor. However, an automatic method for snoring detection using a piezo snoring sensor has not been reported in the literature. This study proposed the HMM-based method to detect snoring using this sensor, which is attached to the neck. The data from 21 patients with OSA were gathered for training and test sets. The short-time Fourier transform and short-time energy were computed so they could be applied to HMMs. The data were classified as snoring, noise and silence according to their HMMs. As a result, the sensitivity and the positive predictivity values were 93.3% and 99.1% for snoring detection, respectively. The results demonstrated that the method produced simple, portable and user-friendly detection tools that provide an alternative to the microphone-based method.
Snoring detection using a piezo snoring sensor based on hidden Markov models
International Nuclear Information System (INIS)
Lee, Hyo-Ki; Lee, Jeon; Lee, Kyoung-Joung; Kim, Hojoong; Ha, Jin-Young
2013-01-01
This study presents a snoring detection method based on hidden Markov models (HMMs) using a piezo snoring sensor. Snoring is a major symptom of obstructive sleep apnea (OSA). In most sleep studies, snoring is detected with a microphone. Since these studies analyze the acoustic properties of snoring, they need to acquire data at high sampling rates, so a large amount of data should be processed. Recently, several sleep studies have monitored snoring using a piezo snoring sensor. However, an automatic method for snoring detection using a piezo snoring sensor has not been reported in the literature. This study proposed the HMM-based method to detect snoring using this sensor, which is attached to the neck. The data from 21 patients with OSA were gathered for training and test sets. The short-time Fourier transform and short-time energy were computed so they could be applied to HMMs. The data were classified as snoring, noise and silence according to their HMMs. As a result, the sensitivity and the positive predictivity values were 93.3% and 99.1% for snoring detection, respectively. The results demonstrated that the method produced simple, portable and user-friendly detection tools that provide an alternative to the microphone-based method. (note)
Monthly streamflow forecasting based on hidden Markov model and Gaussian Mixture Regression
Liu, Yongqi; Ye, Lei; Qin, Hui; Hong, Xiaofeng; Ye, Jiajun; Yin, Xingli
2018-06-01
Reliable streamflow forecasts can be highly valuable for water resources planning and management. In this study, we combined a hidden Markov model (HMM) and Gaussian Mixture Regression (GMR) for probabilistic monthly streamflow forecasting. The HMM is initialized using a kernelized K-medoids clustering method, and the Baum-Welch algorithm is then executed to learn the model parameters. GMR derives a conditional probability distribution for the predictand given covariate information, including the antecedent flow at a local station and two surrounding stations. The performance of HMM-GMR was verified based on the mean square error and continuous ranked probability score skill scores. The reliability of the forecasts was assessed by examining the uniformity of the probability integral transform values. The results show that HMM-GMR obtained reasonably high skill scores and the uncertainty spread was appropriate. Different HMM states were assumed to be different climate conditions, which would lead to different types of observed values. We demonstrated that the HMM-GMR approach can handle multimodal and heteroscedastic data.
An Analysis and Implementation of the Hidden Markov Model to Technology Stock Prediction
Directory of Open Access Journals (Sweden)
Nguyet Nguyen
2017-11-01
Full Text Available Future stock prices depend on many internal and external factors that are not easy to evaluate. In this paper, we use the Hidden Markov Model, (HMM, to predict a daily stock price of three active trading stocks: Apple, Google, and Facebook, based on their historical data. We first use the Akaike information criterion (AIC and Bayesian information criterion (BIC to choose the numbers of states from HMM. We then use the models to predict close prices of these three stocks using both single observation data and multiple observation data. Finally, we use the predictions as signals for trading these stocks. The criteria tests’ results showed that HMM with two states worked the best among two, three and four states for the three stocks. Our results also demonstrate that the HMM outperformed the naïve method in forecasting stock prices. The results also showed that active traders using HMM got a higher return than using the naïve forecast for Facebook and Google stocks. The stock price prediction method has a significant impact on stock trading and derivative hedging.
Elements of automata theory and the theory of Markov chains. [Self-organizing control systems
Energy Technology Data Exchange (ETDEWEB)
Lind, M
1975-03-01
Selected topics from automata theory and the theory of Markov chains are treated. In particular, finite-memory automata are discussed in detail, and the results are used to formulate an automation model of a class of continuous systems. Stochastic automata are introduced as a natural generalization of the deterministic automaton. Markov chains are shown to be closely related to stochastic automata. Results from Markov chain theory are thereby directly applicable to analysis of stochastic automata. This report provides the theoretical foundation for the investigation in Riso Report No. 315 of a class of self-organizing control systems. (25 figures) (auth)
Estimating Model Probabilities using Thermodynamic Markov Chain Monte Carlo Methods
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.
Asteroid mass estimation using Markov-chain Monte Carlo
Siltala, Lauri; Granvik, Mikael
2017-11-01
Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to an inverse problem in at least 13 dimensions where the aim is to derive the mass of the perturbing asteroid(s) and six orbital elements for both the perturbing asteroid(s) and the test asteroid(s) based on astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations: the very rough 'marching' approximation, in which the asteroids' orbital elements are not fitted, thereby reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-chain Monte Carlo (MCMC) approach. We describe each of these algorithms with particular focus on the MCMC algorithm, and present example results using both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans.
Finding and testing network communities by lumped Markov chains.
Piccardi, Carlo
2011-01-01
Identifying communities (or clusters), namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov chain model of a random walker, a quality measure called "persistence probability" is associated to a cluster, which is then defined as an "α-community" if such a probability is not smaller than α. Consistently, a partition composed of α-communities is an "α-partition." These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired α-level allows one to immediately select the α-partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the quality of each single community. Given its ability in individually assessing each single cluster, this approach can also disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure.
Finding and testing network communities by lumped Markov chains.
Directory of Open Access Journals (Sweden)
Carlo Piccardi
Full Text Available Identifying communities (or clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov chain model of a random walker, a quality measure called "persistence probability" is associated to a cluster, which is then defined as an "α-community" if such a probability is not smaller than α. Consistently, a partition composed of α-communities is an "α-partition." These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired α-level allows one to immediately select the α-partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the quality of each single community. Given its ability in individually assessing each single cluster, this approach can also disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure.
Ensemble bayesian model averaging using markov chain Monte Carlo sampling
Energy Technology Data Exchange (ETDEWEB)
Vrugt, Jasper A [Los Alamos National Laboratory; Diks, Cees G H [NON LANL; Clark, Martyn P [NON LANL
2008-01-01
Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery etal. Mon Weather Rev 133: 1155-1174, 2(05)) has recommended the Expectation-Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed Differential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model stream-flow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.
Threshold partitioning of sparse matrices and applications to Markov chains
Energy Technology Data Exchange (ETDEWEB)
Choi, Hwajeong; Szyld, D.B. [Temple Univ., Philadelphia, PA (United States)
1996-12-31
It is well known that the order of the variables and equations of a large, sparse linear system influences the performance of classical iterative methods. In particular if, after a symmetric permutation, the blocks in the diagonal have more nonzeros, classical block methods have a faster asymptotic rate of convergence. In this paper, different ordering and partitioning algorithms for sparse matrices are presented. They are modifications of PABLO. In the new algorithms, in addition to the location of the nonzeros, the values of the entries are taken into account. The matrix resulting after the symmetric permutation has dense blocks along the diagonal, and small entries in the off-diagonal blocks. Parameters can be easily adjusted to obtain, for example, denser blocks, or blocks with elements of larger magnitude. In particular, when the matrices represent Markov chains, the permuted matrices are well suited for block iterative methods that find the corresponding probability distribution. Applications to three types of methods are explored: (1) Classical block methods, such as Block Gauss Seidel. (2) Preconditioned GMRES, where a block diagonal preconditioner is used. (3) Iterative aggregation method (also called aggregation/disaggregation) where the partition obtained from the ordering algorithm with certain parameters is used as an aggregation scheme. In all three cases, experiments are presented which illustrate the performance of the methods with the new orderings. The complexity of the new algorithms is linear in the number of nonzeros and the order of the matrix, and thus adding little computational effort to the overall solution.
Descriptive and predictive evaluation of high resolution Markov chain precipitation models
DEFF Research Database (Denmark)
Sørup, Hjalte Jomo Danielsen; Madsen, Henrik; Arnbjerg-Nielsen, Karsten
2012-01-01
A time series of tipping bucket recordings of very high temporal and volumetric resolution precipitation is modelled using Markov chain models. Both first and second‐order Markov models as well as seasonal and diurnal models are investigated and evaluated using likelihood based techniques. The fi...
Markov chain Monte Carlo with the Integrated Nested Laplace Approximation
Gómez-Rubio, Virgilio
2017-10-06
The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with
Markov chain Monte Carlo with the Integrated Nested Laplace Approximation
Gó mez-Rubio, Virgilio; Rue, Haavard
2017-01-01
The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with
Technical manual for basic version of the Markov chain nest productivity model (MCnest)
The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...
Applying Markov Chains for NDVI Time Series Forecasting of Latvian Regions
Directory of Open Access Journals (Sweden)
Stepchenko Arthur
2015-12-01
Full Text Available Time series of earth observation based estimates of vegetation inform about variations in vegetation at the scale of Latvia. A vegetation index is an indicator that describes the amount of chlorophyll (the green mass and shows the relative density and health of vegetation. NDVI index is an important variable for vegetation forecasting and management of various problems, such as climate change monitoring, energy usage monitoring, managing the consumption of natural resources, agricultural productivity monitoring, drought monitoring and forest fire detection. In this paper, we make a one-step-ahead prediction of 7-daily time series of NDVI index using Markov chains. The choice of a Markov chain is due to the fact that a Markov chain is a sequence of random variables where each variable is located in some state. And a Markov chain contains probabilities of moving from one state to other.
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.
User’s manual for basic version of MCnest Markov chain nest productivity model
The Markov Chain Nest Productivity Model (or MCnest) integrates existing toxicity information from three standardized avian toxicity tests with information on species life history and the timing of pesticide applications relative to the timing of avian breeding seasons to quantit...
Wang, Hui; Wellmann, Florian; Verweij, Elizabeth; von Hebel, Christian; van der Kruk, Jan
2017-04-01
Lateral and vertical spatial heterogeneity of subsurface properties such as soil texture and structure influences the available water and resource supply for crop growth. High-resolution mapping of subsurface structures using non-invasive geo-referenced geophysical measurements, like electromagnetic induction (EMI), enables a characterization of 3D soil structures, which have shown correlations to remote sensing information of the crop states. The benefit of EMI is that it can return 3D subsurface information, however the spatial dimensions are limited due to the labor intensive measurement procedure. Although active and passive sensors mounted on air- or space-borne platforms return 2D images, they have much larger spatial dimensions. Combining both approaches provides us with a potential pathway to extend the detailed 3D geophysical information to a larger area by using remote sensing information. In this study, we aim at extracting and providing insights into the spatial and statistical correlation of the geophysical and remote sensing observations of the soil/vegetation continuum system. To this end, two key points need to be addressed: 1) how to detect and recognize the geometric patterns (i.e., spatial heterogeneity) from multiple data sets, and 2) how to quantitatively describe the statistical correlation between remote sensing information and geophysical measurements. In the current study, the spatial domain is restricted to shallow depths up to 3 meters, and the geostatistical database contains normalized difference vegetation index (NDVI) derived from RapidEye satellite images and apparent electrical conductivities (ECa) measured from multi-receiver EMI sensors for nine depths of exploration ranging from 0-2.7 m. The integrated data sets are mapped into both the physical space (i.e. the spatial domain) and feature space (i.e. a two-dimensional space framed by the NDVI and the ECa data). Hidden Markov Random Fields (HMRF) are employed to model the
Rakhimberdiev, Eldar; Winkler, David W; Bridge, Eli; Seavy, Nathaniel E; Sheldon, Daniel; Piersma, Theunis; Saveliev, Anatoly
2015-01-01
Solar archival tags (henceforth called geolocators) are tracking devices deployed on animals to reconstruct their long-distance movements on the basis of locations inferred post hoc with reference to the geographical and seasonal variations in the timing and speeds of sunrise and sunset. The increased use of geolocators has created a need for analytical tools to produce accurate and objective estimates of migration routes that are explicit in their uncertainty about the position estimates. We developed a hidden Markov chain model for the analysis of geolocator data. This model estimates tracks for animals with complex migratory behaviour by combining: (1) a shading-insensitive, template-fit physical model, (2) an uncorrelated random walk movement model that includes migratory and sedentary behavioural states, and (3) spatially explicit behavioural masks. The model is implemented in a specially developed open source R package FLightR. We used the particle filter (PF) algorithm to provide relatively fast model posterior computation. We illustrate our modelling approach with analysis of simulated data for stationary tags and of real tracks of both a tree swallow Tachycineta bicolor migrating along the east and a golden-crowned sparrow Zonotrichia atricapilla migrating along the west coast of North America. We provide a model that increases accuracy in analyses of noisy data and movements of animals with complicated migration behaviour. It provides posterior distributions for the positions of animals, their behavioural states (e.g., migrating or sedentary), and distance and direction of movement. Our approach allows biologists to estimate locations of animals with complex migratory behaviour based on raw light data. This model advances the current methods for estimating migration tracks from solar geolocation, and will benefit a fast-growing number of tracking studies with this technology.
Maximum Kolmogorov-Sinai Entropy Versus Minimum Mixing Time in Markov Chains
Mihelich, M.; Dubrulle, B.; Paillard, D.; Kral, Q.; Faranda, D.
2018-01-01
We establish a link between the maximization of Kolmogorov Sinai entropy (KSE) and the minimization of the mixing time for general Markov chains. Since the maximisation of KSE is analytical and easier to compute in general than mixing time, this link provides a new faster method to approximate the minimum mixing time dynamics. It could be interesting in computer sciences and statistical physics, for computations that use random walks on graphs that can be represented as Markov chains.
A sufficiency property arising from the characterization of extremes of Markov chains
Bortot, Paola; Coles, Stuart
2000-01-01
At extreme levels, it is known that for a particular choice of marginal distribution, transitions of a Markov chain behave like a random walk. For a broad class of Markov chains, we give a characterization for the step length density of the limiting random walk, which leads to an interesting sufficiency property. This representation also leads us to propose a new technique for kernel density estimation for this class of models.
Asteroid mass estimation with Markov-chain Monte Carlo
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.
Robust filtering and prediction for systems with embedded finite-state Markov-Chain dynamics
International Nuclear Information System (INIS)
Pate, E.B.
1986-01-01
This research developed new methodologies for the design of robust near-optimal filters/predictors for a class of system models that exhibit embedded finite-state Markov-chain dynamics. These methodologies are developed through the concepts and methods of stochastic model building (including time-series analysis), game theory, decision theory, and filtering/prediction for linear dynamic systems. The methodology is based on the relationship between the robustness of a class of time-series models and quantization which is applied to the time series as part of the model identification process. This relationship is exploited by utilizing the concept of an equivalence, through invariance of spectra, between the class of Markov-chain models and the class of autoregressive moving average (ARMA) models. This spectral equivalence permits a straightforward implementation of the desirable robust properties of the Markov-chain approximation in a class of models which may be applied in linear-recursive form in a linear Kalman filter/predictor structure. The linear filter/predictor structure is shown to provide asymptotically optimal estimates of states which represent one or more integrations of the Markov-chain state. The development of a new saddle-point theorem for a game based on the Markov-chain model structure gives rise to a technique for determining a worst case Markov-chain process, upon which a robust filter/predictor design if based
Modeling Strategic Use of Human Computer Interfaces with Novel Hidden Markov Models
Directory of Open Access Journals (Sweden)
Laura Jane Mariano
2015-07-01
Full Text Available Immersive software tools are virtual environments designed to give their users an augmented view of real-world data and ways of manipulating that data. As virtual environments, every action users make while interacting with these tools can be carefully logged, as can the state of the software and the information it presents to the user, giving these actions context. This data provides a high-resolution lens through which dynamic cognitive and behavioral processes can be viewed. In this report, we describe new methods for the analysis and interpretation of such data, utilizing a novel implementation of the Beta Process Hidden Markov Model (BP-HMM for analysis of software activity logs. We further report the results of a preliminary study designed to establish the validity of our modeling approach. A group of 20 participants were asked to play a simple computer game, instrumented to log every interaction with the interface. Participants had no previous experience with the game’s functionality or rules, so the activity logs collected during their naïve interactions capture patterns of exploratory behavior and skill acquisition as they attempted to learn the rules of the game. Pre- and post-task questionnaires probed for self-reported styles of problem solving, as well as task engagement, difficulty, and workload. We jointly modeled the activity log sequences collected from all participants using the BP-HMM approach, identifying a global library of activity patterns representative of the collective behavior of all the participants. Analyses show systematic relationships between both pre- and post-task questionnaires, self-reported approaches to analytic problem solving, and metrics extracted from the BP-HMM decomposition. Overall, we find that this novel approach to decomposing unstructured behavioral data within software environments provides a sensible means for understanding how users learn to integrate software functionality for strategic
Score-based prediction of genomic islands in prokaryotic genomes using hidden Markov models
Directory of Open Access Journals (Sweden)
Surovcik Katharina
2006-03-01
Full Text Available Abstract Background Horizontal gene transfer (HGT is considered a strong evolutionary force shaping the content of microbial genomes in a substantial manner. It is the difference in speed enabling the rapid adaptation to changing environmental demands that distinguishes HGT from gene genesis, duplications or mutations. For a precise characterization, algorithms are needed that identify transfer events with high reliability. Frequently, the transferred pieces of DNA have a considerable length, comprise several genes and are called genomic islands (GIs or more specifically pathogenicity or symbiotic islands. Results We have implemented the program SIGI-HMM that predicts GIs and the putative donor of each individual alien gene. It is based on the analysis of codon usage (CU of each individual gene of a genome under study. CU of each gene is compared against a carefully selected set of CU tables representing microbial donors or highly expressed genes. Multiple tests are used to identify putatively alien genes, to predict putative donors and to mask putatively highly expressed genes. Thus, we determine the states and emission probabilities of an inhomogeneous hidden Markov model working on gene level. For the transition probabilities, we draw upon classical test theory with the intention of integrating a sensitivity controller in a consistent manner. SIGI-HMM was written in JAVA and is publicly available. It accepts as input any file created according to the EMBL-format. It generates output in the common GFF format readable for genome browsers. Benchmark tests showed that the output of SIGI-HMM is in agreement with known findings. Its predictions were both consistent with annotated GIs and with predictions generated by different methods. Conclusion SIGI-HMM is a sensitive tool for the identification of GIs in microbial genomes. It allows to interactively analyze genomes in detail and to generate or to test hypotheses about the origin of acquired
A first approach to Arrhythmogenic Cardiomyopathy detection through ECG and Hidden Markov Models
Energy Technology Data Exchange (ETDEWEB)
Jimenez-Serrano, S.; Sanz Sanchez, J.; Martínez Hinarejos, C.D.; Igual Muñoz, B.; Millet Roig, J.; Zorio Grima, Z.; Castells, F.
2016-07-01
Arrhythmogenic Cardiomyopathy (ACM) is a heritable cardiac disease causing sudden cardiac death in young people. Its clinical diagnosis includes major and minor criteria based on alterations of the electrocardiogram (ECG). The aim of this study is to evaluate Hidden Markov Models (HMM) in order to assess its possible potential of classification among subjects affected by ACM and those relatives who do not suffer the disease through 12-lead ECG recordings. Database consists of 12-lead ECG recordings from 32 patients diagnosed with ACM, and 37 relatives of those affected, but without gene mutation. Using the HTK toolkit and a hold-out strategy in order to train and evaluate a set of HMM models, we performed a grid search through the number of states and Gaussians across these HMM models. Results show that two different HMM models achieved the best balance between sensibility and specificity. The first one needed 35 states and 2 Gaussians and its performance was 0.7 and 0.8 in sensibility and specificity respectively. The second one achieved a sensibility and specificity values of 0.8 and 0.7 respectively with 50 states and 4 Gaussians. The results of this study show that HMM models can achieve an acceptable level of sensibility and specificity in the classification among ECG registers between those affected by ACM and the control group. All the above suggest that this approach could help to detect the disease in a non-invasive way, especially within the context of family screening, improving sensitivity in detection by ECG. (Author)
Protein secondary structure prediction for a single-sequence using hidden semi-Markov models
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Borodovsky Mark
2006-03-01
Full Text Available Abstract Background The accuracy of protein secondary structure prediction has been improving steadily towards the 88% estimated theoretical limit. There are two types of prediction algorithms: Single-sequence prediction algorithms imply that information about other (homologous proteins is not available, while algorithms of the second type imply that information about homologous proteins is available, and use it intensively. The single-sequence algorithms could make an important contribution to studies of proteins with no detected homologs, however the accuracy of protein secondary structure prediction from a single-sequence is not as high as when the additional evolutionary information is present. Results In this paper, we further refine and extend the hidden semi-Markov model (HSMM initially considered in the BSPSS algorithm. We introduce an improved residue dependency model by considering the patterns of statistically significant amino acid correlation at structural segment borders. We also derive models that specialize on different sections of the dependency structure and incorporate them into HSMM. In addition, we implement an iterative training method to refine estimates of HSMM parameters. The three-state-per-residue accuracy and other accuracy measures of the new method, IPSSP, are shown to be comparable or better than ones for BSPSS as well as for PSIPRED, tested under the single-sequence condition. Conclusions We have shown that new dependency models and training methods bring further improvements to single-sequence protein secondary structure prediction. The results are obtained under cross-validation conditions using a dataset with no pair of sequences having significant sequence similarity. As new sequences are added to the database it is possible to augment the dependency structure and obtain even higher accuracy. Current and future advances should contribute to the improvement of function prediction for orphan proteins inscrutable
Dang, Shilpa; Chaudhury, Santanu; Lall, Brejesh; Roy, Prasun Kumar
2017-02-15
Effective connectivity (EC) analysis of neuronal groups using fMRI delivers insights about functional-integration. However, fMRI signal has low-temporal resolution due to down-sampling and indirectly measures underlying neuronal activity. The aim is to address above issues for more reliable EC estimates. This paper proposes use of autoregressive hidden Markov model with missing data (AR-HMM-md) in dynamically multi-linked (DML) framework for learning EC using multiple fMRI time series. In our recent work (Dang et al., 2016), we have shown how AR-HMM-md for modelling single fMRI time series outperforms the existing methods. AR-HMM-md models unobserved neuronal activity and lost data over time as variables and estimates their values by joint optimization given fMRI observation sequence. The effectiveness in learning EC is shown using simulated experiments. Also the effects of sampling and noise are studied on EC. Moreover, classification-experiments are performed for Attention-Deficit/Hyperactivity Disorder subjects and age-matched controls for performance evaluation of real data. Using Bayesian model selection, we see that the proposed model converged to higher log-likelihood and demonstrated that group-classification can be performed with higher cross-validation accuracy of above 94% using distinctive network EC which characterizes patients vs. The full data EC obtained from DML-AR-HMM-md is more consistent with previous literature than the classical multivariate Granger causality method. The proposed architecture leads to reliable estimates of EC than the existing latent models. This framework overcomes the disadvantage of low-temporal resolution and improves cross-validation accuracy significantly due to presence of missing data variables and autoregressive process. Copyright © 2016 Elsevier B.V. All rights reserved.
A Prediction Mechanism of Energy Consumption in Residential Buildings Using Hidden Markov Model
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Israr Ullah
2018-02-01
Full Text Available Internet of Things (IoT is considered as one of the future disruptive technologies, which has the potential to bring positive change in human lifestyle and uplift living standards. Many IoT-based applications have been designed in various fields, e.g., security, health, education, manufacturing, transportation, etc. IoT has transformed conventional homes into Smart homes. By attaching small IoT devices to various appliances, we cannot only monitor but also control indoor environment as per user demand. Intelligent IoT devices can also be used for optimal energy utilization by operating the associated equipment only when it is needed. In this paper, we have proposed a Hidden Markov Model based algorithm to predict energy consumption in Korean residential buildings using data collected through smart meters. We have used energy consumption data collected from four multi-storied buildings located in Seoul, South Korea for model validation and results analysis. Proposed model prediction results are compared with three well-known prediction algorithms i.e., Support Vector Machine (SVM, Artificial Neural Network (ANN and Classification and Regression Trees (CART. Comparative analysis shows that our proposed model achieves 2.96 % better than ANN results in terms of root mean square error metric, 6.09 % better than SVM and 9.03 % better than CART results. To further establish and validate prediction results of our proposed model, we have performed temporal granularity analysis. For this purpose, we have evaluated our proposed model for hourly, daily and weekly data aggregation. Prediction accuracy in terms of root mean square error metric for hourly, daily and weekly data is 2.62, 1.54 and 0.46, respectively. This shows that our model prediction accuracy improves for coarse grain data. Higher prediction accuracy gives us confidence to further explore its application in building control systems for achieving better energy efficiency.
Efficient view based 3-D object retrieval using Hidden Markov Model
Jain, Yogendra Kumar; Singh, Roshan Kumar
2013-12-01
Recent research effort has been dedicated to view based 3-D object retrieval, because of highly discriminative property of 3-D object and has multi view representation. The state-of-art method is highly depending on their own camera array setting for capturing views of 3-D object and use complex Zernike descriptor, HAC for representative view selection which limit their practical application and make it inefficient for retrieval. Therefore, an efficient and effective algorithm is required for 3-D Object Retrieval. In order to move toward a general framework for efficient 3-D object retrieval which is independent of camera array setting and avoidance of representative view selection, we propose an Efficient View Based 3-D Object Retrieval (EVBOR) method using Hidden Markov Model (HMM). In this framework, each object is represented by independent set of view, which means views are captured from any direction without any camera array restriction. In this, views are clustered (including query view) to generate the view cluster, which is then used to build the query model with HMM. In our proposed method, HMM is used in twofold: in the training (i.e. HMM estimate) and in the retrieval (i.e. HMM decode). The query model is trained by using these view clusters. The EVBOR query model is worked on the basis of query model combining with HMM. The proposed approach remove statically camera array setting for view capturing and can be apply for any 3-D object database to retrieve 3-D object efficiently and effectively. Experimental results demonstrate that the proposed scheme has shown better performance than existing methods. [Figure not available: see fulltext.
Hidden Markov modeling of frequency-following responses to Mandarin lexical tones.
Llanos, Fernando; Xie, Zilong; Chandrasekaran, Bharath
2017-11-01
The frequency-following response (FFR) is a scalp-recorded electrophysiological potential reflecting phase-locked activity from neural ensembles in the auditory system. The FFR is often used to assess the robustness of subcortical pitch processing. Due to low signal-to-noise ratio at the single-trial level, FFRs are typically averaged across thousands of stimulus repetitions. Prior work using this approach has shown that subcortical encoding of linguistically-relevant pitch patterns is modulated by long-term language experience. We examine the extent to which a machine learning approach using hidden Markov modeling (HMM) can be utilized to decode Mandarin tone-categories from scalp-record electrophysiolgical activity. We then assess the extent to which the HMM can capture biologically-relevant effects (language experience-driven plasticity). To this end, we recorded FFRs to four Mandarin tones from 14 adult native speakers of Chinese and 14 of native English. We trained a HMM to decode tone categories from the FFRs with varying size of averages. Tone categories were decoded with above-chance accuracies using HMM. The HMM derived metric (decoding accuracy) revealed a robust effect of language experience, such that FFRs from native Chinese speakers yielded greater accuracies than native English speakers. Critically, the language experience-driven plasticity was captured with average sizes significantly smaller than those used in the extant literature. Our results demonstrate the feasibility of HMM in assessing the robustness of neural pitch. Machine-learning approaches can complement extant analytical methods that capture auditory function and could reduce the number of trials needed to capture biological phenomena. Copyright © 2017 Elsevier B.V. All rights reserved.
Development of a brain MRI-based hidden Markov model for dementia recognition.
Chen, Ying; Pham, Tuan D
2013-01-01
Dementia is an age-related cognitive decline which is indicated by an early degeneration of cortical and sub-cortical structures. Characterizing those morphological changes can help to understand the disease development and contribute to disease early prediction and prevention. But modeling that can best capture brain structural variability and can be valid in both disease classification and interpretation is extremely challenging. The current study aimed to establish a computational approach for modeling the magnetic resonance imaging (MRI)-based structural complexity of the brain using the framework of hidden Markov models (HMMs) for dementia recognition. Regularity dimension and semi-variogram were used to extract structural features of the brains, and vector quantization method was applied to convert extracted feature vectors to prototype vectors. The output VQ indices were then utilized to estimate parameters for HMMs. To validate its accuracy and robustness, experiments were carried out on individuals who were characterized as non-demented and mild Alzheimer's diseased. Four HMMs were constructed based on the cohort of non-demented young, middle-aged, elder and demented elder subjects separately. Classification was carried out using a data set including both non-demented and demented individuals with a wide age range. The proposed HMMs have succeeded in recognition of individual who has mild Alzheimer's disease and achieved a better classification accuracy compared to other related works using different classifiers. Results have shown the ability of the proposed modeling for recognition of early dementia. The findings from this research will allow individual classification to support the early diagnosis and prediction of dementia. By using the brain MRI-based HMMs developed in our proposed research, it will be more efficient, robust and can be easily used by clinicians as a computer-aid tool for validating imaging bio-markers for early prediction of dementia.
Mining adverse drug reactions from online healthcare forums using hidden Markov model.
Sampathkumar, Hariprasad; Chen, Xue-wen; Luo, Bo
2014-10-23
Adverse Drug Reactions are one of the leading causes of injury or death among patients undergoing medical treatments. Not all Adverse Drug Reactions are identified before a drug is made available in the market. Current post-marketing drug surveillance methods, which are based purely on voluntary spontaneous reports, are unable to provide the early indications necessary to prevent the occurrence of such injuries or fatalities. The objective of this research is to extract reports of adverse drug side-effects from messages in online healthcare forums and use them as early indicators to assist in post-marketing drug surveillance. We treat the task of extracting adverse side-effects of drugs from healthcare forum messages as a sequence labeling problem and present a Hidden Markov Model(HMM) based Text Mining system that can be used to classify a message as containing drug side-effect information and then extract the adverse side-effect mentions from it. A manually annotated dataset from http://www.medications.com is used in the training and validation of the HMM based Text Mining system. A 10-fold cross-validation on the manually annotated dataset yielded on average an F-Score of 0.76 from the HMM Classifier, in comparison to 0.575 from the Baseline classifier. Without the Plain Text Filter component as a part of the Text Processing module, the F-Score of the HMM Classifier was reduced to 0.378 on average, while absence of the HTML Filter component was found to have no impact. Reducing the Drug names dictionary size by half, on average reduced the F-Score of the HMM Classifier to 0.359, while a similar reduction to the side-effects dictionary yielded an F-Score of 0.651 on average. Adverse side-effects mined from http://www.medications.com and http://www.steadyhealth.com were found to match the Adverse Drug Reactions on the Drug Package Labels of several drugs. In addition, some novel adverse side-effects, which can be potential Adverse Drug Reactions, were also
Profile hidden Markov models for the detection of viruses within metagenomic sequence data.
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Peter Skewes-Cox
Full Text Available Rapid, sensitive, and specific virus detection is an important component of clinical diagnostics. Massively parallel sequencing enables new diagnostic opportunities that complement traditional serological and PCR based techniques. While massively parallel sequencing promises the benefits of being more comprehensive and less biased than traditional approaches, it presents new analytical challenges, especially with respect to detection of pathogen sequences in metagenomic contexts. To a first approximation, the initial detection of viruses can be achieved simply through alignment of sequence reads or assembled contigs to a reference database of pathogen genomes with tools such as BLAST. However, recognition of highly divergent viral sequences is problematic, and may be further complicated by the inherently high mutation rates of some viral types, especially RNA viruses. In these cases, increased sensitivity may be achieved by leveraging position-specific information during the alignment process. Here, we constructed HMMER3-compatible profile hidden Markov models (profile HMMs from all the virally annotated proteins in RefSeq in an automated fashion using a custom-built bioinformatic pipeline. We then tested the ability of these viral profile HMMs ("vFams" to accurately classify sequences as viral or non-viral. Cross-validation experiments with full-length gene sequences showed that the vFams were able to recall 91% of left-out viral test sequences without erroneously classifying any non-viral sequences into viral protein clusters. Thorough reanalysis of previously published metagenomic datasets with a set of the best-performing vFams showed that they were more sensitive than BLAST for detecting sequences originating from more distant relatives of known viruses. To facilitate the use of the vFams for rapid detection of remote viral homologs in metagenomic data, we provide two sets of vFams, comprising more than 4,000 vFams each, in the HMMER3
Online scenario labeling using a hidden Markov model for assessment of nuclear plant state
International Nuclear Information System (INIS)
Zamalieva, Daniya; Yilmaz, Alper; Aldemir, Tunc
2013-01-01
By taking into account both aleatory and epistemic uncertainties within the same probabilistic framework, dynamic event trees (DETs) provide more comprehensive and systematic coverage of possible scenarios following an initiating event compared to conventional event trees. When DET generation algorithms are applied to complex realistic systems, extremely large amounts of data can be produced due to both the large number of scenarios generated following a single initiating event and the large number of data channels that represent these scenarios. In addition, the computational time required for the simulation of each scenario can be very large (e.g. about 24 h of serial run simulation time for a 4 h station blackout scenario). Since scenarios leading to system failure are more of interest, a method is proposed for online labeling of scenarios as failure or non-failure. The algorithm first trains a Hidden Markov Model, which represents the behavior of non-failure scenarios, using a training set from previous simulations. Then, the maximum likelihoods of sample failure and non-failure scenarios fitting this model are computed. These values are used to determine the timestamp at which the labeling of a certain scenario should be performed. Finally, during the succeeding timestamps, the likelihood of each scenario fitting the learned model is computed, and a dynamic thresholding based on the previously calculated likelihood values is applied. The scenarios whose likelihood is higher than the threshold are labeled as non-failure. The proposed algorithm can further delay the non-failure scenarios or discontinue them in order to redirect the computational resources toward the failure scenarios, and reduce computational time and complexity. Experiments using RELAP5/3D model of a fast reactor utilizing an Reactor Vessel Auxiliary Cooling System (RVACS) passive decay heat removal system and dynamic analysis of a station blackout (SBO) event show that the proposed method is
Decomposition of conditional probability for high-order symbolic Markov chains
Melnik, S. S.; Usatenko, O. V.
2017-07-01
The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.
Quasi-stationary distributions for reducible absorbing Markov chains in discrete time
van Doorn, Erik A.; Pollett, P.K.
2009-01-01
We consider discrete-time Markov chains with one coffin state and a finite set $S$ of transient states, and are interested in the limiting behaviour of such a chain as time $n \\to \\infty,$ conditional on survival up to $n$. It is known that, when $S$ is irreducible, the limiting conditional
Directory of Open Access Journals (Sweden)
Roberto Carrillo Aguilar
2007-04-01
Full Text Available Este trabajo da a conocer el sistema de desarrollo de software para el diseño y manipulación de modelos ocultos de Markov, denominado HTK. Actualmente, la técnica de modelos ocultos de Markov es la herramienta más efectiva para implementar sistemas reconocedores del habla. HTK está orientado principalmente a ese aspecto. Su arquitectura es robusta y autosuficiente. Permite: la entrada lógica y natural desde un micrófono, dispone de módulos para la conversión A/D, preprocesado y parametrización de la información, posee herramientas para definir y manipular modelos ocultos de Markov, tiene librerías para entrenamiento y manipulación de los modelos ocultos de Markov ya definidos, considera funciones para definir la gramática, y además: Una serie de herramientas adicionales permiten lograr el objetivo final de obtener una hipotética transcripción del habla (conversión voz - texto.This paper presents HTK, a software development platform for the design and management of Hidden Markov Models. Nowadays, the Hidden Markov Models technique is the more effective one to implement voice recognition systems. HTK is mainly oriented to this application. Its architecture is robust and self-sufficient. It allows a natural input from a microphone, it has modules for A/D conversion, it allows pre-processing and parameterization of information, it possesses tools to define and manage the Hidden Markov Models, libraries for training and use the already defined Hidden Markov Models. It has functions to define the grammar and it has additional tools to reach the final objective, to obtain an hypothetical transcription of the talking (voice to text translation.
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Bao Wang
2014-01-01
Full Text Available We study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for countable Markov chains indexed by an infinite tree with uniformly bounded degree, which extends the corresponding results of countable Markov chains indexed by a Cayley tree and generalizes the relative results of finite Markov chains indexed by a uniformly bounded tree.
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.
A Probabilistic Short-Term Water Demand Forecasting Model Based on the Markov Chain
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Francesca Gagliardi
2017-07-01
Full Text Available This paper proposes a short-term water demand forecasting method based on the use of the Markov chain. This method provides estimates of future demands by calculating probabilities that the future demand value will fall within pre-assigned intervals covering the expected total variability. More specifically, two models based on homogeneous and non-homogeneous Markov chains were developed and presented. These models, together with two benchmark models (based on artificial neural network and naïve methods, were applied to three real-life case studies for the purpose of forecasting the respective water demands from 1 to 24 h ahead. The results obtained show that the model based on a homogeneous Markov chain provides more accurate short-term forecasts than the one based on a non-homogeneous Markov chain, which is in line with the artificial neural network model. Both Markov chain models enable probabilistic information regarding the stochastic demand forecast to be easily obtained.
Reliability analysis and prediction of mixed mode load using Markov Chain Model
International Nuclear Information System (INIS)
Nikabdullah, N.; Singh, S. S. K.; Alebrahim, R.; Azizi, M. A.; K, Elwaleed A.; Noorani, M. S. M.
2014-01-01
The aim of this paper is to present the reliability analysis and prediction of mixed mode loading by using a simple two state Markov Chain Model for an automotive crankshaft. The reliability analysis and prediction for any automotive component or structure is important for analyzing and measuring the failure to increase the design life, eliminate or reduce the likelihood of failures and safety risk. The mechanical failures of the crankshaft are due of high bending and torsion stress concentration from high cycle and low rotating bending and torsional stress. The Markov Chain was used to model the two states based on the probability of failure due to bending and torsion stress. In most investigations it revealed that bending stress is much serve than torsional stress, therefore the probability criteria for the bending state would be higher compared to the torsion state. A statistical comparison between the developed Markov Chain Model and field data was done to observe the percentage of error. The reliability analysis and prediction was derived and illustrated from the Markov Chain Model were shown in the Weibull probability and cumulative distribution function, hazard rate and reliability curve and the bathtub curve. It can be concluded that Markov Chain Model has the ability to generate near similar data with minimal percentage of error and for a practical application; the proposed model provides a good accuracy in determining the reliability for the crankshaft under mixed mode loading
Yang, Sejung; Lee, Byung-Uk
2015-01-01
In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach. PMID:26352138
Zhang, Yue; Berhane, Kiros
2014-01-01
Questionnaire-based health status outcomes are often prone to misclassification. When studying the effect of risk factors on such outcomes, ignoring any potential misclassification may lead to biased effect estimates. Analytical challenges posed by these misclassified outcomes are further complicated when simultaneously exploring factors for both the misclassification and health processes in a multi-level setting. To address these challenges, we propose a fully Bayesian Mixed Hidden Markov Model (BMHMM) for handling differential misclassification in categorical outcomes in a multi-level setting. The BMHMM generalizes the traditional Hidden Markov Model (HMM) by introducing random effects into three sets of HMM parameters for joint estimation of the prevalence, transition and misclassification probabilities. This formulation not only allows joint estimation of all three sets of parameters, but also accounts for cluster level heterogeneity based on a multi-level model structure. Using this novel approach, both the true health status prevalence and the transition probabilities between the health states during follow-up are modeled as functions of covariates. The observed, possibly misclassified, health states are related to the true, but unobserved, health states and covariates. Results from simulation studies are presented to validate the estimation procedure, to show the computational efficiency due to the Bayesian approach and also to illustrate the gains from the proposed method compared to existing methods that ignore outcome misclassification and cluster level heterogeneity. We apply the proposed method to examine the risk factors for both asthma transition and misclassification in the Southern California Children's Health Study (CHS). PMID:24254432
Stifter, Cynthia A; Rovine, Michael
2015-01-01
The focus of the present longitudinal study, to examine mother-infant interaction during the administration of immunizations at two and six months of age, used hidden Markov modeling, a time series approach that produces latent states to describe how mothers and infants work together to bring the infant to a soothed state. Results revealed a 4-state model for the dyadic responses to a two-month inoculation whereas a 6-state model best described the dyadic process at six months. Two of the states at two months and three of the states at six months suggested a progression from high intensity crying to no crying with parents using vestibular and auditory soothing methods. The use of feeding and/or pacifying to soothe the infant characterized one two-month state and two six-month states. These data indicate that with maturation and experience, the mother-infant dyad is becoming more organized around the soothing interaction. Using hidden Markov modeling to describe individual differences, as well as normative processes, is also presented and discussed.
Pattern statistics on Markov chains and sensitivity to parameter estimation
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Nuel Grégory
2006-10-01
Full Text Available Abstract 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.
Prediction degradation trend of nuclear equipment based on GM (1, 1)-Markov chain
International Nuclear Information System (INIS)
Zhang Liming; Zhao Xinwen; Cai Qi; Wu Guangjiang
2010-01-01
The degradation trend prediction results are important references for nuclear equipment in-service inspection and maintenance plan. But it is difficult to predict the nuclear equipment degradation trend accurately by the traditional statistical probability due to the small samples, lack of degradation data and the wavy degradation locus. Therefore, a method of equipment degradation trend prediction based on GM (1, l)-Markov chain was proposed in this paper. The method which makes use of the advantages of both GM (1, 1) method and Markov chain could improve the prediction precision of nuclear equipment degradation trend. The paper collected degradation data as samples and accurately predicted the degradation trend of canned motor pump. Compared with the prediction results by GM (1, 1) method, the prediction precision by GM (1, l)-Markov chain is more accurate. (authors)
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
Use of Markov chains for forecasting labor requirements in black coal mines
Energy Technology Data Exchange (ETDEWEB)
Penar, L.; Przybyla, H.
1987-01-01
Increasing mining depth, deterioration of mining conditions and technology development are causes of changes in labor requirements. In mines with stable coal output these changes in most cases are of a qualitative character, in mines with an increasing or decreasing coal output they are of a quantitative character. Methods for forecasting personnel needs, in particular professional requirements, are discussed. Quantitative and qualitative changes are accurately described by heterogenous Markov chains. A structure consisting of interdependent variables is the subject of a forecast. Changes that occur within the structure of time units is the subject of investigations. For a homogenous Markov chain probabilities of a transition from the i-state to the j-state are determined (the probabilities being time independent). For a heterogenous Markov chain probabilities of a transition from the i-state to the j-state are non-conditioned. The method was developed for the ODRA 1325 computers. 8 refs.
Counting of oligomers in sequences generated by markov chains for DNA motif discovery.
Shan, Gao; Zheng, Wei-Mou
2009-02-01
By means of the technique of the imbedded Markov chain, an efficient algorithm is proposed to exactly calculate first, second moments of word counts and the probability for a word to occur at least once in random texts generated by a Markov chain. A generating function is introduced directly from the imbedded Markov chain to derive asymptotic approximations for the problem. Two Z-scores, one based on the number of sequences with hits and the other on the total number of word hits in a set of sequences, are examined for discovery of motifs on a set of promoter sequences extracted from A. thaliana genome. Source code is available at http://www.itp.ac.cn/zheng/oligo.c.
Adjoint sensitivity analysis of dynamic reliability models based on Markov chains - I: Theory
International Nuclear Information System (INIS)
Cacuci, D. G.; Cacuci, D. G.; Ionescu-Bujor, M.
2008-01-01
The development of the adjoint sensitivity analysis procedure (ASAP) for generic dynamic reliability models based on Markov chains is presented, together with applications of this procedure to the analysis of several systems of increasing complexity. The general theory is presented in Part I of this work and is accompanied by a paradigm application to the dynamic reliability analysis of a simple binary component, namely a pump functioning on an 'up/down' cycle until it fails irreparably. This paradigm example admits a closed form analytical solution, which permits a clear illustration of the main characteristics of the ASAP for Markov chains. In particular, it is shown that the ASAP for Markov chains presents outstanding computational advantages over other procedures currently in use for sensitivity and uncertainty analysis of the dynamic reliability of large-scale systems. This conclusion is further underscored by the large-scale applications presented in Part II. (authors)
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.
Adjoint sensitivity analysis of dynamic reliability models based on Markov chains - I: Theory
Energy Technology Data Exchange (ETDEWEB)
Cacuci, D. G. [Commiss Energy Atom, Direct Energy Nucl, Saclay, (France); Cacuci, D. G. [Univ Karlsruhe, Inst Nucl Technol and Reactor Safety, D-76021 Karlsruhe, (Germany); Ionescu-Bujor, M. [Forschungszentrum Karlsruhe, Fus Program, D-76021 Karlsruhe, (Germany)
2008-07-01
The development of the adjoint sensitivity analysis procedure (ASAP) for generic dynamic reliability models based on Markov chains is presented, together with applications of this procedure to the analysis of several systems of increasing complexity. The general theory is presented in Part I of this work and is accompanied by a paradigm application to the dynamic reliability analysis of a simple binary component, namely a pump functioning on an 'up/down' cycle until it fails irreparably. This paradigm example admits a closed form analytical solution, which permits a clear illustration of the main characteristics of the ASAP for Markov chains. In particular, it is shown that the ASAP for Markov chains presents outstanding computational advantages over other procedures currently in use for sensitivity and uncertainty analysis of the dynamic reliability of large-scale systems. This conclusion is further underscored by the large-scale applications presented in Part II. (authors)
Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains
Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes
2018-03-01
We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.
Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique
International Nuclear Information System (INIS)
Destainville, N
2003-01-01
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium
Markov Chain Model with Catastrophe to Determine Mean Time to Default of Credit Risky Assets
Dharmaraja, Selvamuthu; Pasricha, Puneet; Tardelli, Paola
2017-11-01
This article deals with the problem of probabilistic prediction of the time distance to default for a firm. To model the credit risk, the dynamics of an asset is described as a function of a homogeneous discrete time Markov chain subject to a catastrophe, the default. The behaviour of the Markov chain is investigated and the mean time to the default is expressed in a closed form. The methodology to estimate the parameters is given. Numerical results are provided to illustrate the applicability of the proposed model on real data and their analysis is discussed.
Directory of Open Access Journals (Sweden)
Nikola Trčka
2009-12-01
Full Text Available We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we consider Markov reward chains which are standardly presented in real matrix theory. By interpreting the obtained matrix conditions for bisimulations in this setting, we automatically obtain the definitions of strong, weak, and branching bisimulation for Markov reward chains. The obtained strong and weak bisimulations are shown to coincide with some existing notions, while the obtained branching bisimulation is new, but its usefulness is questionable.
Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique
Energy Technology Data Exchange (ETDEWEB)
Destainville, N [Laboratoire de Physique Theorique - IRSAMC, CNRS/Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 04 (France)
2003-04-04
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium.
A Cost-Effective Smoothed Multigrid with Modified Neighborhood-Based Aggregation for Markov Chains
Directory of Open Access Journals (Sweden)
Zhao-Li Shen
2015-01-01
Full Text Available Smoothed aggregation multigrid method is considered for computing stationary distributions of Markov chains. A judgement which determines whether to implement the whole aggregation procedure is proposed. Through this strategy, a large amount of time in the aggregation procedure is saved without affecting the convergence behavior. Besides this, we explain the shortage and irrationality of the Neighborhood-Based aggregation which is commonly used in multigrid methods. Then a modified version is presented to remedy and improve it. Numerical experiments on some typical Markov chain problems are reported to illustrate the performance of these methods.
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
Cofré, Rodrigo; Maldonado, Cesar
2018-01-01
We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.
A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains
DEFF Research Database (Denmark)
Bacci, Giovanni; Bacci, Giorgio; Larsen, Kim Guldstrand
2017-01-01
In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS...... an axiom for dealing with the Kantorovich distance between probability distributions. The axiomatization is then used to propose a metric extension of a Kleene's style representation theorem for finite labelled Markov chains, that was proposed (in a more general coalgebraic fashion) by Silva et al. (Inf...
2nd International Workshop on the Numerical Solution of Markov Chains
1995-01-01
Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.
Stochastic modeling of pitting corrosion in underground pipelines using Markov chains
Energy Technology Data Exchange (ETDEWEB)
Velazquez, J.C.; Caleyo, F.; Hallen, J.M.; Araujo, J.E. [Instituto Politecnico Nacional (IPN), Mexico D.F. (Mexico). Escuela Superior de Ingenieria Quimica e Industrias Extractivas (ESIQIE); Valor, A. [Universidad de La Habana, La Habana (Cuba)
2009-07-01
A non-homogenous, linear growth (pure birth) Markov process, with discrete states in continuous time, has been used to model external pitting corrosion in underground pipelines. The transition probability function for the pit depth is obtained from the analytical solution of the forward Kolmogorov equations for this process. The parameters of the transition probability function between depth states can be identified from the observed time evolution of the mean of the pit depth distribution. Monte Carlo simulations were used to predict the time evolution of the mean value of the pit depth distribution in soils with different physicochemical characteristics. The simulated distributions have been used to create an empirical Markov-chain-based stochastic model for predicting the evolution of pitting corrosion from the observed properties of the soil in contact with the pipeline. Real- life case studies, involving simulated and measured pit depth distributions are presented to illustrate the application of the proposed Markov chains model. (author)
Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation
Minasny, B.; Vrugt, J.A.; McBratney, A.B.
2011-01-01
This paper demonstrates for the first time the use of Markov Chain Monte Carlo (MCMC) simulation for parameter inference in model-based soil geostatistics. We implemented the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm to jointly summarize the posterior
Avian life history profiles for use in the Markov chain nest productivity model (MCnest)
The Markov Chain nest productivity model, or MCnest, quantitatively estimates the effects of pesticides or other toxic chemicals on annual reproductive success of avian species (Bennett and Etterson 2013, Etterson and Bennett 2013). The Basic Version of MCnest was developed as a...
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...
On dynamic selection of households for direct marketing based on Markov chain models with memory
Otter, Pieter W.
A simple, dynamic selection procedure is proposed, based on conditional, expected profits using Markov chain models with memory. The method is easy to apply, only frequencies and mean values have to be calculated or estimated. The method is empirically illustrated using a data set from a charitable
Learning Bayesian network classifiers for credit scoring using Markov Chain Monte Carlo search
Baesens, B.; Egmont-Petersen, M.; Castelo, R.; Vanthienen, J.
2001-01-01
In this paper, we will evaluate the power and usefulness of Bayesian network classifiers for credit scoring. Various types of Bayesian network classifiers will be evaluated and contrasted including unrestricted Bayesian network classifiers learnt using Markov Chain Monte Carlo (MCMC) search.
Trcka, N.; Andova, S.; McIver, A.; D'Argenio, P.; Cuijpers, P.J.L.; Markovski, J.; Morgan, C.; Núñez, M.
2009-01-01
We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we consider Markov reward chains which are
User's Manual MCnest - Markov Chain Nest Productivity Model Version 2.0
The Markov chain nest productivity model, or MCnest, is a set of algorithms for integrating the results of avian toxicity tests with reproductive life-history data to project the relative magnitude of chemical effects on avian reproduction. The mathematical foundation of MCnest i...
Triangular M/G/1-type and tree-like QBD Markov chains
Van Houdt, B.; Leeuwaarden, van J.S.H.
2009-01-01
In applying matrix-analytic methods to M/G/1-type and tree-like QBD Markov chains, it is crucial to determine the solution to a (set of) nonlinear matrix equation(s). This is usually done via iterative methods. We consider the highly structured subclass of triangular M/G/1-type and tree-like QBD
Tokunaga and Horton self-similarity for level set trees of Markov chains
International Nuclear Information System (INIS)
Zaliapin, Ilia; Kovchegov, Yevgeniy
2012-01-01
Highlights: ► Self-similar properties of the level set trees for Markov chains are studied. ► Tokunaga and Horton self-similarity are established for symmetric Markov chains and regular Brownian motion. ► Strong, distributional self-similarity is established for symmetric Markov chains with exponential jumps. ► It is conjectured that fractional Brownian motions are Tokunaga self-similar. - Abstract: The Horton and Tokunaga branching laws provide a convenient framework for studying self-similarity in random trees. The Horton self-similarity is a weaker property that addresses the principal branching in a tree; it is a counterpart of the power-law size distribution for elements of a branching system. The stronger Tokunaga self-similarity addresses so-called side branching. The Horton and Tokunaga self-similarity have been empirically established in numerous observed and modeled systems, and proven for two paradigmatic models: the critical Galton–Watson branching process with finite progeny and the finite-tree representation of a regular Brownian excursion. This study establishes the Tokunaga and Horton self-similarity for a tree representation of a finite symmetric homogeneous Markov chain. We also extend the concept of Horton and Tokunaga self-similarity to infinite trees and establish self-similarity for an infinite-tree representation of a regular Brownian motion. We conjecture that fractional Brownian motions are also Tokunaga and Horton self-similar, with self-similarity parameters depending on the Hurst exponent.
Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas behind the Algorithm
Stewart, Wayne; Stewart, Sepideh
2014-01-01
For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…
Markov chain Monte Carlo methods for statistical analysis of RF photonic devices
DEFF Research Database (Denmark)
Piels, Molly; Zibar, Darko
2016-01-01
uncertainty is shown to give unsatisfactory and incorrect results due to the nonlinear relationship between the circuit parameters and the measured data. Markov chain Monte Carlo methods are shown to provide superior results, both for individual devices and for assessing within-die variation...
A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis
Edwards, Michael C.
2010-01-01
Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…
ON TESTING OF CRYPTOGRAPHYC GENERATORS OUTPUT SEQUENCES USING MARKOV CHAINS OF CONDITIONAL ORDER
Directory of Open Access Journals (Sweden)
M. V. Maltsev
2013-01-01
Full Text Available The paper deals with the Markov chain of conditional order, which is used for statisticaltesting of cryptographic generators. Statistical estimations of model parameters are given. Consistency of the order estimator is proved. Results of computer experiments are presented.
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.
Markov Chain model for the stochastic behaviors of wind-direction data
International Nuclear Information System (INIS)
Masseran, Nurulkamal
2015-01-01
Highlights: • I develop a Markov chain model to describe about the stochastic and probabilistic behaviors of wind direction data. • I describe some of the theoretical arguments regarding the Markov chain model in term of wind direction data. • I suggest a limiting probabilities approach to determine a dominant directions of wind blow. - Abstract: Analyzing the behaviors of wind direction can complement knowledge concerning wind speed and help researchers draw conclusions regarding wind energy potential. Knowledge of the wind’s direction enables the wind turbine to be positioned in such a way as to maximize the total amount of captured energy and optimize the wind farm’s performance. In this paper, first-order and higher-order Markov chain models are proposed to describe the probabilistic behaviors of wind-direction data. A case study is conducted using data from Mersing, Malaysia. The wind-direction data are classified according to an eight-state Markov chain based on natural geographical directions. The model’s parameters are estimated using the maximum likelihood method and the linear programming formulation. Several theoretical arguments regarding the model are also discussed. Finally, limiting probabilities are used to determine a long-run proportion of the wind directions generated. The results explain the dominant direction for Mersing’s wind in terms of probability metrics
Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees
Directory of Open Access Journals (Sweden)
Weicai Peng
2016-02-01
Full Text Available Abstract In this paper, a kind of infinite, local finite tree T, named a controlled tree, is introduced. Some strong limit properties, such as the strong law of large numbers and the asymptotic equipartition property, for nonhomogeneous Markov chains indexed by T, are established. The outcomes are the generalizations of some well-known results.
CSL Model Checking Algorithms for Infinite-state Structured Markov chains
Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Raskin, J.-F.; Thiagarajan, P.S.
2007-01-01
Jackson queueing networks (JQNs) are a very general class of queueing networks that find their application in a variety of settings. The state space of the continuous-time Markov chain (CTMC) that underlies such a JQN, is highly structured, however, of infinite size in as many dimensions as there
Vrugt, J.A.; Braak, ter C.J.F.; Clark, M.P.; Hyman, J.M.; Robinson, B.A.
2008-01-01
There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled
Yuan, Y.; Meng, Y.; Chen, Y. X.; Jiang, C.; Yue, A. Z.
2018-04-01
In this study, we proposed a method to map urban encroachment onto farmland using satellite image time series (SITS) based on the hierarchical hidden Markov model (HHMM). In this method, the farmland change process is decomposed into three hierarchical levels, i.e., the land cover level, the vegetation phenology level, and the SITS level. Then a three-level HHMM is constructed to model the multi-level semantic structure of farmland change process. Once the HHMM is established, a change from farmland to built-up could be detected by inferring the underlying state sequence that is most likely to generate the input time series. The performance of the method is evaluated on MODIS time series in Beijing. Results on both simulated and real datasets demonstrate that our method improves the change detection accuracy compared with the HMM-based method.
A Hybrid of Deep Network and Hidden Markov Model for MCI Identification with Resting-State fMRI.
Suk, Heung-Il; Lee, Seong-Whan; Shen, Dinggang
2015-10-01
In this paper, we propose a novel method for modelling functional dynamics in resting-state fMRI (rs-fMRI) for Mild Cognitive Impairment (MCI) identification. Specifically, we devise a hybrid architecture by combining Deep Auto-Encoder (DAE) and Hidden Markov Model (HMM). The roles of DAE and HMM are, respectively, to discover hierarchical non-linear relations among features, by which we transform the original features into a lower dimension space, and to model dynamic characteristics inherent in rs-fMRI, i.e. , internal state changes. By building a generative model with HMMs for each class individually, we estimate the data likelihood of a test subject as MCI or normal healthy control, based on which we identify the clinical label. In our experiments, we achieved the maximal accuracy of 81.08% with the proposed method, outperforming state-of-the-art methods in the literature.
Energy Technology Data Exchange (ETDEWEB)
Quintero Oliveros, Anggi [Dipartimento di Georisorse e Territorio, Universita di Udine (Italy); Departamento de Ciencias de La Tierra, Universidad Simon Bolivar, Caracas (Venezuela); Carniel, Roberto [Dipartimento di Georisorse e Territorio, Universita di Udine (Italy)], E-mail: roberto.carniel@uniud.it; Tarraga, Marta [Departamento de Volcanologia, Museo Nacional de Ciencias Naturales, CSIC, Madrid (Spain); Aspinall, Willy [Aspinall and Associates, 5 Woodside Close, Beaconsfield, Bucks (United Kingdom)
2008-08-15
The Teide-Pico Viejo volcanic complex situated in Tenerife Island (Canary Islands, Spain) has recently shown signs of unrest, long after its last eruptive episode at Chinyero in 1909, and the last explosive episode which happened at Montana Blanca, 2000 years ago. In this paper we study the seismicity of the Teide-Pico Viejo complex recorded between May and December 2004, in order to show the applicability of tools such as Hidden Markov Models and Bayesian Belief Networks which can be used to build a structure for evaluating the probability of given eruptive or volcano-related scenarios. The results support the existence of a bidirectional relationship between volcano-tectonic events and the background seismic noise - in particular its frequency content. This in turn suggests that the two phenomena can be related to one unique process influencing their generation.
Yau, C; Papaspiliopoulos, O; Roberts, G O; Holmes, C
2011-01-01
We consider the development of Bayesian Nonparametric methods for product partition models such as Hidden Markov Models and change point models. Our approach uses a Mixture of Dirichlet Process (MDP) model for the unknown sampling distribution (likelihood) for the observations arising in each state and a computationally efficient data augmentation scheme to aid inference. The method uses novel MCMC methodology which combines recent retrospective sampling methods with the use of slice sampler variables. The methodology is computationally efficient, both in terms of MCMC mixing properties, and robustness to the length of the time series being investigated. Moreover, the method is easy to implement requiring little or no user-interaction. We apply our methodology to the analysis of genomic copy number variation.
International Nuclear Information System (INIS)
Quintero Oliveros, Anggi; Carniel, Roberto; Tarraga, Marta; Aspinall, Willy
2008-01-01
The Teide-Pico Viejo volcanic complex situated in Tenerife Island (Canary Islands, Spain) has recently shown signs of unrest, long after its last eruptive episode at Chinyero in 1909, and the last explosive episode which happened at Montana Blanca, 2000 years ago. In this paper we study the seismicity of the Teide-Pico Viejo complex recorded between May and December 2004, in order to show the applicability of tools such as Hidden Markov Models and Bayesian Belief Networks which can be used to build a structure for evaluating the probability of given eruptive or volcano-related scenarios. The results support the existence of a bidirectional relationship between volcano-tectonic events and the background seismic noise - in particular its frequency content. This in turn suggests that the two phenomena can be related to one unique process influencing their generation
Camproux, A C; Tufféry, P
2005-08-05
Understanding and predicting protein structures depend on the complexity and the accuracy of the models used to represent them. We have recently set up a Hidden Markov Model to optimally compress protein three-dimensional conformations into a one-dimensional series of letters of a structural alphabet. Such a model learns simultaneously the shape of representative structural letters describing the local conformation and the logic of their connections, i.e. the transition matrix between the letters. Here, we move one step further and report some evidence that such a model of protein local architecture also captures some accurate amino acid features. All the letters have specific and distinct amino acid distributions. Moreover, we show that words of amino acids can have significant propensities for some letters. Perspectives point towards the prediction of the series of letters describing the structure of a protein from its amino acid sequence.
Evolution of probability measures by cellular automata on algebraic topological Markov chains
Directory of Open Access Journals (Sweden)
ALEJANDRO MAASS
2003-01-01
Full Text Available In this paper we review some recent results on the evolution of probability measures under cellular automata acting on a fullshift. In particular we discuss the crucial role of the attractiveness of maximal measures. We enlarge the context of the results of a previous study of topological Markov chains that are Abelian groups; the shift map is an automorphism of this group. This is carried out by studying the dynamics of Markov measures by a particular additive cellular automata. Many of these topics were within the focus of Francisco Varela's mathematical interests.
The Fracture Mechanical Markov Chain Fatigue Model Compared with Empirical Data
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
The applicability of the FMF-model (Fracture Mechanical Markov Chain Fatigue Model) introduced in Gansted, L., R. Brincker and L. Pilegaard Hansen (1991) is tested by simulations and compared with empirical data. Two sets of data have been used, the Virkler data (aluminium alloy) and data...... established at the Laboratory of Structural Engineering at Aalborg University, the AUC-data, (mild steel). The model, which is based on the assumption, that the crack propagation process can be described by a discrete Space Markov theory, is applicable to constant as well as random loading. It is shown...
From Brownian Dynamics to Markov Chain: An Ion Channel Example
Chen, Wan
2014-02-27
A discrete rate theory for multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model, one can determine the Markovian transition rates. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed. © 2014 Society for Industrial and Applied Mathematics.
International Nuclear Information System (INIS)
Kim, Joo Yeon; Jang, Han Ki; Jang, Sol Ah; Park, Tae Jin
2014-01-01
There is a question that the simulation actually leads to draws from its target distribution and the most basic one is whether such Markov chains can always be constructed and all chain values sampled from them. The problem to be solved is the determination of how large this iteration should be to achieve the target distribution. This problem can be answered as convergence monitoring. In this paper, two widely used methods, such as autocorrelation and potential scale reduction factor (PSRF) in MCMC are characterized. There is no general agreement on the subject of the convergence. Although it is generally agreed that running n parallel chains in practice is computationally inefficient and unnecessary, running multiple parallel chains is generally applied for the convergence monitoring due to easy implementation. The main debate is the number of parallel chains needed. If the convergence properties of the chain are well understood then clearly a single chain suffices. Therefore, autocorrelation using single chain and multiple parallel ones are tried and their results then compared with each other in this study. And, the following question is answered from the two convergence results: Have the Markov chain realizations for achieved the target distribution?
RESEARCH ABSORBING STATES OF THE SYSTEM USING MARKOV CHAINS AND FUNDAMENTAL MATRIX
Directory of Open Access Journals (Sweden)
Тетяна Мефодіївна ОЛЕХ
2016-02-01
Full Text Available The article discusses the use Markov chains to research models that reflect the essential properties of systems, including methods of measuring the parameters of projects and assess their effectiveness. In the study carried out by its decomposition system for certain discrete state and create a diagram of transitions between these states. Specificity displays various objects Markov homogeneous chains with discrete states and discrete time determined by the method of calculation of transition probabilities. A model of success criteria for absorbing state system that is universal for all projects. A breakdown of passages to the matrix submatrices. The variation elements under matrix Q n with growth linked to the definition of important quantitative characteristics of absorbing circuits: 1 the probability of achieving the status of absorbing any given; 2 the mean number of steps needed to achieve the absorbing state; 3 the mean time that the system spends in each state to hit irreversible system in absorbing state. Built fundamental matrix that allowed calculating the different characteristics of the system. Considered fundamental matrix for supposedly modeled absorbing Markov chain, which gives the forecast for the behavior of the system in the future regardless of the absolute value of the time elapsed from the starting point. This property illustrates the fundamental matrix Markov process that characterizes it as a process without aftereffect.
Directory of Open Access Journals (Sweden)
Pradeepa Yahampath
2008-03-01
Full Text Available Speech coding techniques capable of generating encoded representations which are robust against channel losses play an important role in enabling reliable voice communication over packet networks and mobile wireless systems. In this paper, we investigate the use of multiple description index assignments (MDIAs for loss-tolerant transmission of line spectral frequency (LSF coefficients, typically generated by state-of-the-art speech coders. We propose a simulated annealing-based approach for optimizing MDIAs for Markov-model-based decoders which exploit inter- and intraframe correlations in LSF coefficients to reconstruct the quantized LSFs from coded bit streams corrupted by channel losses. Experimental results are presented which compare the performance of a number of novel LSF transmission schemes. These results clearly demonstrate that Markov-model-based decoders, when used in conjunction with optimized MDIA, can yield average spectral distortion much lower than that produced by methods such as interleaving/interpolation, commonly used to combat the packet losses.
Directory of Open Access Journals (Sweden)
Rondeau Paul
2008-01-01
Full Text Available Speech coding techniques capable of generating encoded representations which are robust against channel losses play an important role in enabling reliable voice communication over packet networks and mobile wireless systems. In this paper, we investigate the use of multiple description index assignments (MDIAs for loss-tolerant transmission of line spectral frequency (LSF coefficients, typically generated by state-of-the-art speech coders. We propose a simulated annealing-based approach for optimizing MDIAs for Markov-model-based decoders which exploit inter- and intraframe correlations in LSF coefficients to reconstruct the quantized LSFs from coded bit streams corrupted by channel losses. Experimental results are presented which compare the performance of a number of novel LSF transmission schemes. These results clearly demonstrate that Markov-model-based decoders, when used in conjunction with optimized MDIA, can yield average spectral distortion much lower than that produced by methods such as interleaving/interpolation, commonly used to combat the packet losses.
Energy Technology Data Exchange (ETDEWEB)
Adaro, Jorge; Cesari, Daniela; Lema, Alba; Galimberti, Pablo [Universidad Nacional de Rio Cuarto (Argentina). Facultad de Ingenieria]. E-mail: aadaro@ing.unrc.edu.ar
2000-07-01
The objective of the present work is to adopt a methodology that allows to generate sequences of values of global solar radiation. It is carried out a preliminary study on the generation of radiation sequence a concept of Chains of Markov. For it is analyzed it the readiness of data and it is investigated about the possibility of using such a methodology calculating values of indexes of clarity previously. With data of available radiation and provided the National Meteorological Service for Rio Cuarto, the preliminary study is carried out the preliminary study looking for to validated the pattern to the effects of being able to transfer the use of the methodology in other regions. (author)
Singer, Philipp; Helic, Denis; Taraghi, Behnam; Strohmaier, Markus
2014-01-01
One of the most frequently used models for understanding human navigation on the Web is the Markov chain model, where Web pages are represented as states and hyperlinks as probabilities of navigating from one page to another. Predominantly, human navigation on the Web has been thought to satisfy the memoryless Markov property stating that the next page a user visits only depends on her current page and not on previously visited ones. This idea has found its way in numerous applications such as Google's PageRank algorithm and others. Recently, new studies suggested that human navigation may better be modeled using higher order Markov chain models, i.e., the next page depends on a longer history of past clicks. Yet, this finding is preliminary and does not account for the higher complexity of higher order Markov chain models which is why the memoryless model is still widely used. In this work we thoroughly present a diverse array of advanced inference methods for determining the appropriate Markov chain order. We highlight strengths and weaknesses of each method and apply them for investigating memory and structure of human navigation on the Web. Our experiments reveal that the complexity of higher order models grows faster than their utility, and thus we confirm that the memoryless model represents a quite practical model for human navigation on a page level. However, when we expand our analysis to a topical level, where we abstract away from specific page transitions to transitions between topics, we find that the memoryless assumption is violated and specific regularities can be observed. We report results from experiments with two types of navigational datasets (goal-oriented vs. free form) and observe interesting structural differences that make a strong argument for more contextual studies of human navigation in future work.
Directory of Open Access Journals (Sweden)
Philipp Singer
Full Text Available One of the most frequently used models for understanding human navigation on the Web is the Markov chain model, where Web pages are represented as states and hyperlinks as probabilities of navigating from one page to another. Predominantly, human navigation on the Web has been thought to satisfy the memoryless Markov property stating that the next page a user visits only depends on her current page and not on previously visited ones. This idea has found its way in numerous applications such as Google's PageRank algorithm and others. Recently, new studies suggested that human navigation may better be modeled using higher order Markov chain models, i.e., the next page depends on a longer history of past clicks. Yet, this finding is preliminary and does not account for the higher complexity of higher order Markov chain models which is why the memoryless model is still widely used. In this work we thoroughly present a diverse array of advanced inference methods for determining the appropriate Markov chain order. We highlight strengths and weaknesses of each method and apply them for investigating memory and structure of human navigation on the Web. Our experiments reveal that the complexity of higher order models grows faster than their utility, and thus we confirm that the memoryless model represents a quite practical model for human navigation on a page level. However, when we expand our analysis to a topical level, where we abstract away from specific page transitions to transitions between topics, we find that the memoryless assumption is violated and specific regularities can be observed. We report results from experiments with two types of navigational datasets (goal-oriented vs. free form and observe interesting structural differences that make a strong argument for more contextual studies of human navigation in future work.
Uncovering and testing the fuzzy clusters based on lumped Markov chain in complex network.
Jing, Fan; Jianbin, Xie; Jinlong, Wang; Jinshuai, Qu
2013-01-01
Identifying clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. By means of a lumped Markov chain model of a random walker, we propose two novel ways of inferring the lumped markov transition matrix. Furthermore, some useful results are proposed based on the analysis of the properties of the lumped Markov process. To find the best partition of complex networks, a novel framework including two algorithms for network partition based on the optimal lumped Markovian dynamics is derived to solve this problem. The algorithms are constructed to minimize the objective function under this framework. It is demonstrated by the simulation experiments that our algorithms can efficiently determine the probabilities with which a node belongs to different clusters during the learning process and naturally supports the fuzzy partition. Moreover, they are successfully applied to real-world network, including the social interactions between members of a karate club.
Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media
Delgoshaie, A. H.; Jenny, P.; Tchelepi, H.
2017-12-01
The transport of fluids in porous media is dominated by flow-field heterogeneity resulting from the underlying permeability field. Due to the high uncertainty in the permeability field, many realizations of the reference geological model are used to describe the statistics of the transport phenomena in a Monte Carlo (MC) framework. There has been strong interest in working with stochastic formulations of the transport that are different from the standard MC approach. Several stochastic models based on a velocity process for tracer particle trajectories have been proposed. Previous studies have shown that for high variances of the log-conductivity, the stochastic models need to account for correlations between consecutive velocity transitions to predict dispersion accurately. The correlated velocity models proposed in the literature can be divided into two general classes of temporal and spatial Markov models. Temporal Markov models have been applied successfully to tracer transport in both the longitudinal and transverse directions. These temporal models are Stochastic Differential Equations (SDEs) with very specific drift and diffusion terms tailored for a specific permeability correlation structure. The drift and diffusion functions devised for a certain setup would not necessarily be suitable for a different scenario, (e.g., a different permeability correlation structure). The spatial Markov models are simple discrete Markov chains that do not require case specific assumptions. However, transverse spreading of contaminant plumes has not been successfully modeled with the available correlated spatial models. Here, we propose a temporal discrete Markov chain to model both the longitudinal and transverse dispersion in a two-dimensional domain. We demonstrate that these temporal Markov models are valid for different correlation structures without modification. Similar to the temporal SDEs, the proposed model respects the limited asymptotic transverse spreading of
Mohammad Sayemuzzaman; Manoj K. Jha
2014-01-01
State wide variant topographic features in North Carolina attract the hydro-climatologist. There is none modeling study found that predict future Land Cover Land Use (LCLU) change for whole North Carolina. In this study, satellite-derived land cover maps of year 1992, 2001 and 2006 of North Carolina were integrated within the framework of the Markov-Cellular Automata (Markov-CA) model which combines the Markov chain and Cellular Automata (CA) techniques. A Multi-Criteria Evaluation (MCE) was ...
Lithofacies cyclicity determination in the guaduas formation (Colombia using Markov chains
Directory of Open Access Journals (Sweden)
Jorge Eliecer Mariño Martinez
2016-07-01
Full Text Available Statistical embedded Markov Chain processes were used to analyze facies transitions and to determine the stacking pattern of the lithofacies of the Guaduas Formation. Twelve Lithofacies were found and characterized based on lithology and sedimentary structures in four stratigraphic sections. The findings were compared with a previous assemblage of lithofacies, interpretations of sedimentary environments, and depositional systems. As a result, four depositional Systems were established. Through the statistical analyses of facies transitions it was found that tidal facies are prevalent in the Socota section, especially in the upper part, whereas in the Sogamoso, Umbita and Peñas de Sutatausa sections, fluvial facies are prevalent in the upper part of the sections, and follow a regressive sequence with more continental deposits around the upper part of the sections. For each of these sections the Markov Chain transition matrices illustrates a strong interaction between tidal facies and fluvial facies, specially in the Peñas de Sutatausa matrix, where facies 6, made up of tidal deposits, appears several times. From the facies model and Markov Chain analyses, it is evident that the Guaduas Formation is a cyclic sequence in which the Markov facies repetitions are consistent with the lithofacies analyses conducted in previous stratigraphic studies. The results reveal that the Markov Chain statistical process can be used to predict stratigraphy in order to correlate contiguous geologically unexplored areas in the Guaduas Formation, where much work relating to correlation and the continuity of coal beds has yet to be done. Determinacion de la ciclicidad de las facies en la formacion Guaduas (Colombia usando las cadenas de Markov Resumen Se utilizaron los procesos estadísticos de las cadenas de Markov para analizar las transiciones de facies y para determinar el patrón de apilamiento de las litofacies de la formación Guaduas. Se encontraron y
Masuyama, Hiroyuki
2015-01-01
This paper studies the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of discrete-time block-monotone Markov chains under subgeometric drift conditions. The main result of this paper is to present an upper bound for the total variation distance between the stationary probability vectors of a block-monotone Markov chain and its LC-block-augmented truncation. The main result is extended to Markov chains that themselves may not be block monoton...
Process Modeling for Energy Usage in “Smart House” System with a Help of Markov Discrete Chain
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Victor Kravets
2016-05-01
Full Text Available Method for evaluating economic efficiency of technical systems using discrete Markov chains modelling illustrated by the system of “Smart house”, consisting, for example, of the three independently functioning elements. Dynamic model of a random power consumption process in the form of a symmetrical state graph of heterogeneous discrete Markov chain is built. The corresponding mathematical model of a random Markov process of power consumption in the “smart house” system in recurrent matrix form is being developed. Technique of statistical determination of probability of random transition elements of the system and the corresponding to the transition probability matrix of the discrete inhomogeneous Markov chain are developed. Statistically determined random transitions of system elements power consumption and the corresponding distribution laws are introduced. The matrix of transition prices, expectations for the possible states of a system price transition and, eventually, the cost of Markov process of power consumption throughout the day.
Density Control of Multi-Agent Systems with Safety Constraints: A Markov Chain Approach
Demirer, Nazli
The control of systems with autonomous mobile agents has been a point of interest recently, with many applications like surveillance, coverage, searching over an area with probabilistic target locations or exploring an area. In all of these applications, the main goal of the swarm is to distribute itself over an operational space to achieve mission objectives specified by the density of swarm. This research focuses on the problem of controlling the distribution of multi-agent systems considering a hierarchical control structure where the whole swarm coordination is achieved at the high-level and individual vehicle/agent control is managed at the low-level. High-level coordination algorithms uses macroscopic models that describes the collective behavior of the whole swarm and specify the agent motion commands, whose execution will lead to the desired swarm behavior. The low-level control laws execute the motion to follow these commands at the agent level. The main objective of this research is to develop high-level decision control policies and algorithms to achieve physically realizable commanding of the agents by imposing mission constraints on the distribution. We also make some connections with decentralized low-level motion control. This dissertation proposes a Markov chain based method to control the density distribution of the whole system where the implementation can be achieved in a decentralized manner with no communication between agents since establishing communication with large number of agents is highly challenging. The ultimate goal is to guide the overall density distribution of the system to a prescribed steady-state desired distribution while satisfying desired transition and safety constraints. Here, the desired distribution is determined based on the mission requirements, for example in the application of area search, the desired distribution should match closely with the probabilistic target locations. The proposed method is applicable for both
Directory of Open Access Journals (Sweden)
Chudech Losiri
2016-07-01
Full Text Available Urban expansion is considered as one of the most important problems in several developing countries. Bangkok Metropolitan Region (BMR is the urbanized and agglomerated area of Bangkok Metropolis (BM and its vicinity, which confronts the expansion problem from the center of the city. Landsat images of 1988, 1993, 1998, 2003, 2008, and 2011 were used to detect the land use and land cover (LULC changes. The demographic and economic data together with corresponding maps were used to determine the driving factors for land conversions. This study applied Cellular Automata-Markov Chain (CA-MC and Multi-Layer Perceptron-Markov Chain (MLP-MC to model LULC and urban expansions. The performance of the CA-MC and MLP-MC yielded more than 90% overall accuracy to predict the LULC, especially the MLP-MC method. Further, the annual population and economic growth rates were considered to produce the land demand for the LULC in 2014 and 2035 using the statistical extrapolation and system dynamics (SD. It was evident that the simulated map in 2014 resulting from the SD yielded the highest accuracy. Therefore, this study applied the SD method to generate the land demand for simulating LULC in 2035. The outcome showed that urban occupied the land around a half of the BMR.
Summary statistics for end-point conditioned continuous-time Markov chains
DEFF Research Database (Denmark)
Hobolth, Asger; Jensen, Jens Ledet
Continuous-time Markov chains are a widely used modelling tool. Applications include DNA sequence evolution, ion channel gating behavior and mathematical finance. We consider the problem of calculating properties of summary statistics (e.g. mean time spent in a state, mean number of jumps between...... two states and the distribution of the total number of jumps) for discretely observed continuous time Markov chains. Three alternative methods for calculating properties of summary statistics are described and the pros and cons of the methods are discussed. The methods are based on (i) an eigenvalue...... decomposition of the rate matrix, (ii) the uniformization method, and (iii) integrals of matrix exponentials. In particular we develop a framework that allows for analyses of rather general summary statistics using the uniformization method....
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.
Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains
Directory of Open Access Journals (Sweden)
Francesca Biagini
2016-07-01
Full Text Available We study risk-minimization for a large class of insurance contracts. Given that the individual progress in time of visiting an insurance policy’s states follows an F -doubly stochastic Markov chain, we describe different state-dependent types of insurance benefits. These cover single payments at maturity, annuity-type payments and payments at the time of a transition. Based on the intensity of the F -doubly stochastic Markov chain, we provide the Galtchouk-Kunita-Watanabe decomposition for a general insurance contract and specify risk-minimizing strategies in a Brownian financial market setting. The results are further illustrated explicitly within an affine structure for the intensity.
Network Security Risk Assessment System Based on Attack Graph and Markov Chain
Sun, Fuxiong; Pi, Juntao; Lv, Jin; Cao, Tian
2017-10-01
Network security risk assessment technology can be found in advance of the network problems and related vulnerabilities, it has become an important means to solve the problem of network security. Based on attack graph and Markov chain, this paper provides a Network Security Risk Assessment Model (NSRAM). Based on the network infiltration tests, NSRAM generates the attack graph by the breadth traversal algorithm. Combines with the international standard CVSS, the attack probability of atomic nodes are counted, and then the attack transition probabilities of ones are calculated by Markov chain. NSRAM selects the optimal attack path after comprehensive measurement to assessment network security risk. The simulation results show that NSRAM can reflect the actual situation of network security objectively.
Application of Markov chains-entropy to analysis of depositional environments
Energy Technology Data Exchange (ETDEWEB)
Men Guizhen; Shi Xiaohong; Zhao Shuzhi
1989-01-01
The paper systematically and comprehensively discussed application of Markov chains-entropy to analysis of depositional environments of the upper Carboniferous series Taiyuan Formation in Anjialing, Pingshuo open-cast mine, Shanxi. Definite geological meanings were given respectively to calculated values of transition probability matrix, extremity probability matrix, substitution matrix and the entropy. The lithologic successions of coarse-fine-coarse grained layers from bottom upwards in the coal-bearing series made up the general symmetric cyclic patterns. It was suggested that the coal-bearing strata deposited in the coal-forming environment in delta plain-littoral swamps. Quantitative study of cyclic visibility and variation of formation was conducted. The assemblage relation among stratigraphic sequences and the significance of predicting vertical change were emphasized. Results of study showed that overall analysis of Markov chains was an effective method for analysis of depositional environments of coal-bearing strata. 2 refs., 5 figs.
Overshoot in biological systems modelled by Markov chains: a non-equilibrium dynamic phenomenon.
Jia, Chen; Qian, Minping; Jiang, Daquan
2014-08-01
A number of biological systems can be modelled by Markov chains. Recently, there has been an increasing concern about when biological systems modelled by Markov chains will perform a dynamic phenomenon called overshoot. In this study, the authors found that the steady-state behaviour of the system will have a great effect on the occurrence of overshoot. They showed that overshoot in general cannot occur in systems that will finally approach an equilibrium steady state. They further classified overshoot into two types, named as simple overshoot and oscillating overshoot. They showed that except for extreme cases, oscillating overshoot will occur if the system is far from equilibrium. All these results clearly show that overshoot is a non-equilibrium dynamic phenomenon with energy consumption. In addition, the main result in this study is validated with real experimental data.