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Journal articles on the topic 'Multivariate Markov chains'

Author: Grafiati

Published: 10 September 2021

Last updated: 29 July 2025

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1

Flournoy, Nancy. "Dependency in multivariate markov chains." Linear Algebra and its Applications 127 (1990): 85–106. http://dx.doi.org/10.1016/0024-3795(90)90337-c.

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2

Janssen, A., and J. Segers. "Markov Tail Chains." Journal of Applied Probability 51, no. 4 (2014): 1133–53. http://dx.doi.org/10.1239/jap/1421763332.

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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 inRd. 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 a broader setting, we will show that even for non-Markovian underlying processes a Markovian forward tail chain always imp

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3

Janssen, A., and J. Segers. "Markov Tail Chains." Journal of Applied Probability 51, no. 04 (2014): 1133–53. http://dx.doi.org/10.1017/s0001867800012027.

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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 R d . 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 a broader setting, we will show that even for non-Markovian underlying processes a Markovian forward tail chain always

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4

Janssen, A., and J. Segers. "Markov Tail Chains." Journal of Applied Probability 51, no. 04 (2014): 1133–53. http://dx.doi.org/10.1017/s002190020001202x.

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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 R d . 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 a broader setting, we will show that even for non-Markovian underlying processes a Markovian forward tail chain always

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5

Colombi, R., and S. Giordano. "Graphical models for multivariate Markov chains." Journal of Multivariate Analysis 107 (May 2012): 90–103. http://dx.doi.org/10.1016/j.jmva.2012.01.010.

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6

Lee, Shiowjen, and J. Lynch. "Total Positivity of Markov Chains and the Failure Rate Character of Some First Passage Times." Advances in Applied Probability 29, no. 3 (1997): 713–32. http://dx.doi.org/10.2307/1428083.

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It is shown that totally positive order 2 (TP2) properties of the infinitesimal generator of a continuous-time Markov chain with totally ordered state space carry over to the chain's transition distribution function. For chains with such properties, failure rate characteristics of the first passage times are established. For Markov chains with partially ordered state space, it is shown that the first passage times have an IFR distribution under a multivariate total positivity condition on the transition function.

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7

Lee, Shiowjen, and J. Lynch. "Total Positivity of Markov Chains and the Failure Rate Character of Some First Passage Times." Advances in Applied Probability 29, no. 03 (1997): 713–32. http://dx.doi.org/10.1017/s0001867800028317.

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It is shown that totally positive order 2 (TP2) properties of the infinitesimal generator of a continuous-time Markov chain with totally ordered state space carry over to the chain's transition distribution function. For chains with such properties, failure rate characteristics of the first passage times are established. For Markov chains with partially ordered state space, it is shown that the first passage times have an IFR distribution under a multivariate total positivity condition on the transition function.

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8

Nicolau, João. "A New Model for Multivariate Markov Chains." Scandinavian Journal of Statistics 41, no. 4 (2014): 1124–35. http://dx.doi.org/10.1111/sjos.12087.

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9

Nicolau, João, and Flavio Ivo Riedlinger. "Estimation and inference in multivariate Markov chains." Statistical Papers 56, no. 4 (2014): 1163–73. http://dx.doi.org/10.1007/s00362-014-0630-6.

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10

Perfekt, Roland. "Extreme Value Theory for a Class of Markov Chains with Values in ℝd". Advances in Applied Probability 29, № 1 (1997): 138–64. http://dx.doi.org/10.2307/1427864.

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We consider extreme value theory for a class of stationary Markov chains with values in ℝd. The asymptotic distribution of Mn, the vector of componentwise maxima, is determined under mild dependence restrictions and suitable assumptions on the marginal distribution and the transition probabilities of the chain. This is achieved through computation of a multivariate extremal index of the sequence, extending results of Smith [26] and Perfekt [21] to a multivariate setting. As a by-product, we obtain results on extremes of higher-order, real-valued Markov chains. The results are applied to a freq

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11

Perfekt, Roland. "Extreme Value Theory for a Class of Markov Chains with Values in ℝd". Advances in Applied Probability 29, № 01 (1997): 138–64. http://dx.doi.org/10.1017/s0001867800027828.

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We consider extreme value theory for a class of stationary Markov chains with values in ℝd. The asymptotic distribution of M n , the vector of componentwise maxima, is determined under mild dependence restrictions and suitable assumptions on the marginal distribution and the transition probabilities of the chain. This is achieved through computation of a multivariate extremal index of the sequence, extending results of Smith [26] and Perfekt [21] to a multivariate setting. As a by-product, we obtain results on extremes of higher-order, real-valued Markov chains. The results are applied to a fr

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12

Beare, Brendan K., and Juwon Seo. "Vine Copula Specifications for Stationary Multivariate Markov Chains." Journal of Time Series Analysis 36, no. 2 (2014): 228–46. http://dx.doi.org/10.1111/jtsa.12103.

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13

Vasconcelos, Carolina, and Bruno Damásio. "GenMarkov: Modeling Generalized Multivariate Markov Chains in R." R Journal 16, no. 1 (2025): 96–113. https://doi.org/10.32614/rj-2024-006.

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14

Ching, Wai-Ki, Michael K. Ng, and Eric S. Fung. "Higher-order multivariate Markov chains and their applications." Linear Algebra and its Applications 428, no. 2-3 (2008): 492–507. http://dx.doi.org/10.1016/j.laa.2007.05.021.

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15

Kosorok, Michael R. "Monte Carlo error estimation for multivariate Markov chains." Statistics & Probability Letters 46, no. 1 (2000): 85–93. http://dx.doi.org/10.1016/s0167-7152(99)00090-5.

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16

Zhou, Hua, and Kenneth Lange. "Composition Markov chains of multinomial type." Advances in Applied Probability 41, no. 1 (2009): 270–91. http://dx.doi.org/10.1239/aap/1240319585.

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Suppose that n identical particles evolve according to the same marginal Markov chain. In this setting we study chains such as the Ehrenfest chain that move a prescribed number of randomly chosen particles at each epoch. The product chain constructed by this device inherits its eigenstructure from the marginal chain. There is a further chain derived from the product chain called the composition chain that ignores particle labels and tracks the numbers of particles in the various states. The composition chain in turn inherits its eigenstructure and various properties such as reversibility from

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17

Zhou, Hua, and Kenneth Lange. "Composition Markov chains of multinomial type." Advances in Applied Probability 41, no. 01 (2009): 270–91. http://dx.doi.org/10.1017/s0001867800003220.

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Suppose that n identical particles evolve according to the same marginal Markov chain. In this setting we study chains such as the Ehrenfest chain that move a prescribed number of randomly chosen particles at each epoch. The product chain constructed by this device inherits its eigenstructure from the marginal chain. There is a further chain derived from the product chain called the composition chain that ignores particle labels and tracks the numbers of particles in the various states. The composition chain in turn inherits its eigenstructure and various properties such as reversibility from

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18

Cerqueti, Roy, Paolo Falbo, Gianfranco Guastaroba, and Cristian Pelizzari. "Approximating multivariate Markov chains for bootstrapping through contiguous partitions." OR Spectrum 37, no. 3 (2015): 803–41. http://dx.doi.org/10.1007/s00291-015-0397-8.

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19

Colombi, Roberto, and Sabrina Giordano. "Monotone dependence in graphical models for multivariate Markov chains." Metrika 76, no. 7 (2012): 873–85. http://dx.doi.org/10.1007/s00184-012-0421-9.

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20

Zamparo, Marco, and Massimiliano Semeraro. "Large deviations for quadratic functionals of stable Gauss–Markov chains and entropy production." Journal of Mathematical Physics 64, no. 2 (2023): 023302. http://dx.doi.org/10.1063/5.0096315.

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In this paper, we establish a large deviation principle for the entropy production rate of possible non-stationary, centered stable Gauss–Markov chains, verifying the Gallavotti–Cohen symmetry. We reach this goal by developing a large deviation theory for quasi-Toeplitz quadratic functionals of multivariate centered stable Gauss–Markov chains, which differ from a perfect Toeplitz form by the addition of quadratic boundary terms.

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21

Khare, Kshitij, and Nabanita Mukherjee. "Convergence analysis of some multivariate Markov chains using stochastic monotonicity." Annals of Applied Probability 23, no. 2 (2013): 811–33. http://dx.doi.org/10.1214/12-aap856.

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22

Resnick, Sidney I., and David Zeber. "Asymptotics of Markov Kernels and the Tail Chain." Advances in Applied Probability 45, no. 1 (2013): 186–213. http://dx.doi.org/10.1239/aap/1363354108.

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An asymptotic model for the extreme behavior of certain Markov chains is the ‘tail chain’. Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics, such as point process limits. We place this model in a more general context, formulated in terms of extreme value theory for transition kernels, and extend it by formalizing the distinction between extreme and nonextreme states. We make the link between the update function and transition kernel forms considered in previous work, and we show that the tail chain model leads to a multivariate regula

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23

Resnick, Sidney I., and David Zeber. "Asymptotics of Markov Kernels and the Tail Chain." Advances in Applied Probability 45, no. 01 (2013): 186–213. http://dx.doi.org/10.1017/s0001867800006248.

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An asymptotic model for the extreme behavior of certain Markov chains is the ‘tail chain’. Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics, such as point process limits. We place this model in a more general context, formulated in terms of extreme value theory for transition kernels, and extend it by formalizing the distinction between extreme and nonextreme states. We make the link between the update function and transition kernel forms considered in previous work, and we show that the tail chain model leads to a multivariate regula

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24

Bing-Hwang Juang, S. Levinson, and M. Sondhi. "Maximum likelihood estimation for multivariate mixture observations of markov chains (Corresp.)." IEEE Transactions on Information Theory 32, no. 2 (1986): 307–9. http://dx.doi.org/10.1109/tit.1986.1057145.

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25

Brunel, N. J. B., J. Lapuyade-Lahorgue, and W. Pieczynski. "Modeling and Unsupervised Classification of Multivariate Hidden Markov Chains With Copulas." IEEE Transactions on Automatic Control 55, no. 2 (2010): 338–49. http://dx.doi.org/10.1109/tac.2009.2034929.

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26

Khare, Kshitij, and Hua Zhou. "Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions." Annals of Applied Probability 19, no. 2 (2009): 737–77. http://dx.doi.org/10.1214/08-aap562.

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27

Juang, B. H. "Maximum-Likelihood Estimation for Mixture Multivariate Stochastic Observations of Markov Chains." AT&T Technical Journal 64, no. 6 (1985): 1235–49. http://dx.doi.org/10.1002/j.1538-7305.1985.tb00273.x.

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28

Gauvain, J. L., and Chin-Hui Lee. "Maximum a posteriori estimation for multivariate Gaussian mixture observations of Markov chains." IEEE Transactions on Speech and Audio Processing 2, no. 2 (1994): 291–98. http://dx.doi.org/10.1109/89.279278.

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29

Li, Xutao. "On Multivariate Markov Chains for Common and Non-Common Objects in Multiple Networks." Numerical Mathematics: Theory, Methods and Applications 5, no. 3 (2012): 384–402. http://dx.doi.org/10.4208/nmtma.2012.m1108.

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30

Nascimento, Diego, Cleber Xavier, Israel Felipe, and Francisco Louzada Neto. "Dynamic Conditional Correlation GARCH: A Multivariate Time Series Novel using a Bayesian Approach." Journal of Modern Applied Statistical Methods 18, no. 1 (2020): 2–17. http://dx.doi.org/10.22237/jmasm/1556669220.

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The Dynamic Conditional Correlation GARCH (DCC-GARCH) mutation model is considered using a Monte Carlo approach via Markov chains in the estimation of parameters, time-dependence variation is visually demonstrated. Fifteen indices were analyzed from the main financial markets of developed and developing countries from different continents. The performances of indices are similar, with a joint evolution. Most index returns, especially SPX and NDX, evolve over time with a higher positive correlation.

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31

Li, Wen, Rihuan Ke, Wai-Ki Ching, and Michael K. Ng. "A C-eigenvalue problem for tensors with applications to higher-order multivariate Markov chains." Computers & Mathematics with Applications 78, no. 3 (2019): 1008–25. http://dx.doi.org/10.1016/j.camwa.2019.03.016.

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32

Damásio, Bruno, and Sandro Mendonça. "Modelling insurgent-incumbent dynamics: Vector autoregressions, multivariate Markov chains, and the nature of technological competition." Applied Economics Letters 26, no. 10 (2018): 843–49. http://dx.doi.org/10.1080/13504851.2018.1502863.

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33

Qin, Qian, and James P. Hobert. "Trace-class Monte Carlo Markov chains for Bayesian multivariate linear regression with non-Gaussian errors." Journal of Multivariate Analysis 166 (July 2018): 335–45. http://dx.doi.org/10.1016/j.jmva.2018.03.012.

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34

Griffiths, Robert. "Lancaster distributions and Markov chains with multivariate Poisson–Charlier, Meixner and Hermite–Chebycheff polynomial eigenfunctions." Journal of Approximation Theory 207 (July 2016): 139–64. http://dx.doi.org/10.1016/j.jat.2016.02.013.

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35

Damásio, Bruno, and João Nicolau. "Time inhomogeneous multivariate Markov chains: Detecting and testing multiple structural breaks occurring at unknown dates." Chaos, Solitons & Fractals 180 (March 2024): 114478. http://dx.doi.org/10.1016/j.chaos.2024.114478.

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36

Colangelo, A., A. Müller, and M. Scarsini. "Positive Dependence and Weak Convergence." Journal of Applied Probability 43, no. 1 (2006): 48–59. http://dx.doi.org/10.1239/jap/1143936242.

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A more general definition of MTP2 (multivariate total positivity of order 2) probability measure is given, without assuming the existence of a density. Under this definition the class of MTP2 measures is proved to be closed under weak convergence. Characterizations of the MTP2 property are proved under this more general definition. Then a precise definition of conditionally increasing measure is provided, and closure under weak convergence of the class of conditionally increasing measures is proved. As an application we investigate MTP2 properties of stationary distributions of Markov chains,

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37

Colangelo, A., A. Müller, and M. Scarsini. "Positive Dependence and Weak Convergence." Journal of Applied Probability 43, no. 01 (2006): 48–59. http://dx.doi.org/10.1017/s0021900200001352.

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A more general definition of MTP2 (multivariate total positivity of order 2) probability measure is given, without assuming the existence of a density. Under this definition the class of MTP2 measures is proved to be closed under weak convergence. Characterizations of the MTP2 property are proved under this more general definition. Then a precise definition of conditionally increasing measure is provided, and closure under weak convergence of the class of conditionally increasing measures is proved. As an application we investigate MTP2 properties of stationary distributions of Markov chains,

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38

King, Martin D., Martin J. Crowder, David J. Hand, et al. "Temporal Relation between the ADC and DC Potential Responses to Transient Focal Ischemia in the Rat: A Markov Chain Monte Carlo Simulation Analysis." Journal of Cerebral Blood Flow & Metabolism 23, no. 6 (2003): 677–88. http://dx.doi.org/10.1097/01.wcb.0000066919.40164.c0.

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Markov chain Monte Carlo simulation was used in a reanalysis of the longitudinal data obtained by Harris et al. ( J Cereb Blood Flow Metab 20:28–36) in a study of the direct current (DC) potential and apparent diffusion coefficient (ADC) responses to focal ischemia. The main purpose was to provide a formal analysis of the temporal relationship between the ADC and DC responses, to explore the possible involvement of a common latent (driving) process. A Bayesian nonlinear hierarchical random coefficients model was adopted. DC and ADC transition parameter posterior probability distributions were

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39

Dimitriou, Vasileios A., Andreas C. Georgiou, and Nikolas Tsantas. "On the equilibrium personnel structure in the presence of vertical and horizontal mobility via multivariate Markov chains." Journal of the Operational Research Society 66, no. 6 (2015): 993–1006. http://dx.doi.org/10.1057/jors.2014.66.

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40

Ciampi, Antonio, Alina Dyachenko, Martin Cole, and Jane McCusker. "Delirium superimposed on dementia: defining disease states and course from longitudinal measurements of a multivariate index using latent class analysis and hidden Markov chains." International Psychogeriatrics 23, no. 10 (2011): 1659–70. http://dx.doi.org/10.1017/s1041610211000871.

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ABSTRACTBackground: 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.Methods: 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 disorde

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41

Segers, Johan. "Functionals of clusters of extremes." Advances in Applied Probability 35, no. 4 (2003): 1028–45. http://dx.doi.org/10.1239/aap/1067436333.

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For arbitrary stationary sequences of random variables satisfying a mild mixing condition, distributional approximations are established for functionals of clusters of exceedances over a high threshold. The approximations are in terms of the distribution of the process conditionally on the event that the first variable exceeds the threshold. This conditional distribution is shown to converge to a nontrivial limit if the finite-dimensional distributions of the process are in the domain of attraction of a multivariate extreme-value distribution. In this case, therefore, limit distributions are o

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42

Segers, Johan. "Functionals of clusters of extremes." Advances in Applied Probability 35, no. 04 (2003): 1028–45. http://dx.doi.org/10.1017/s0001867800012726.

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For arbitrary stationary sequences of random variables satisfying a mild mixing condition, distributional approximations are established for functionals of clusters of exceedances over a high threshold. The approximations are in terms of the distribution of the process conditionally on the event that the first variable exceeds the threshold. This conditional distribution is shown to converge to a nontrivial limit if the finite-dimensional distributions of the process are in the domain of attraction of a multivariate extreme-value distribution. In this case, therefore, limit distributions are o

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43

Mikosch, Thomas, and Olivier Wintenberger. "The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains." Probability Theory and Related Fields 159, no. 1-2 (2013): 157–96. http://dx.doi.org/10.1007/s00440-013-0504-1.

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44

Xiong, Zikang, Yao Xiao, Jianhui Ning, and Hong Qin. "Representative Points Based on Power Exponential Kernel Discrepancy." Axioms 11, no. 12 (2022): 711. http://dx.doi.org/10.3390/axioms11120711.

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Representative points (rep-points) are a set of points that are optimally chosen for representing a big original data set or a target distribution in terms of a statistical criterion, such as mean square error and discrepancy. Most of the existing criteria can only assure the representing properties in the whole variable space. In this paper, a new kernel discrepancy, named power exponential kernel discrepancy (PEKD), is proposed to measure the representativeness of the point set with respect to the general multivariate distribution. Different from the commonly used criteria, PEKD can improve

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45

Sedlmeier, Katrin, Sebastian Mieruch, Gerd Schädler, and Christoph Kottmeier. "Compound extremes in a changing climate – a Markov chain approach." Nonlinear Processes in Geophysics 23, no. 6 (2016): 375–90. http://dx.doi.org/10.5194/npg-23-375-2016.

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Abstract. Studies using climate models and observed trends indicate that extreme weather has changed and may continue to change in the future. The potential impact of extreme events such as heat waves or droughts depends not only on their number of occurrences but also on "how these extremes occur", i.e., the interplay and succession of the events. These quantities are quite unexplored, for past changes as well as for future changes and call for sophisticated methods of analysis. To address this issue, we use Markov chains for the analysis of the dynamics and succession of multivariate or comp

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46

Wang, Lei, Yu Sun, and Jining Wang. "Price Volatility Spillovers in Energy Supply Chains: Empirical Evidence from China." Energies 18, no. 12 (2025): 3204. https://doi.org/10.3390/en18123204.

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Based on the theoretical framework of Multivariate Stochastic Volatility (MSV), this paper combines the Dynamic Generalized Correlation (DGC) model with the t-distribution, establishes the DGC-t-MSV model, and employs the Markov Chain Monte Carlo (MCMC) algorithm based on the Bayesian principle for efficient estimation to investigate the price volatility spillover effects in China’s energy supply chains. The results of this study indicate the following: (1) The upstream crude oil spot price has a positive spillover effect on the midstream freight price. The downstream diesel market price, 92 g

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47

Guseva, Maria, and Andrey Silaev. "Applying Bayesian methods for macroeconomic modeling of business cycle phases." St Petersburg University Journal of Economic Studies 37, no. 2 (2021): 298–317. http://dx.doi.org/10.21638/spbu05.2021.205.

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In the present research, the features of applying two models for estimating macroeconomic dynamic in the USA are investigated: Bayesian vector autoregression and Bayesian vector autoregression with Markov switching. The research goal is to identify periods, structure of fluctuations and the main directions of interaction of the variables (real US GDP and employment) using Bayesian vector autoregression models. Models with Markov chains include many equations (structures). The switching mechanisms between these structures are controlled by an unobservable variable that follows a first-order Mar

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48

Grundler, Michael, and Daniel L. Rabosky. "Complex Ecological Phenotypes on Phylogenetic Trees: A Markov Process Model for Comparative Analysis of Multivariate Count Data." Systematic Biology 69, no. 6 (2020): 1200–1211. http://dx.doi.org/10.1093/sysbio/syaa031.

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Abstract The evolutionary dynamics of complex ecological traits—including multistate representations of diet, habitat, and behavior—remain poorly understood. Reconstructing the tempo, mode, and historical sequence of transitions involving such traits poses many challenges for comparative biologists, owing to their multidimensional nature. Continuous-time Markov chains are commonly used to model ecological niche evolution on phylogenetic trees but are limited by the assumption that taxa are monomorphic and that states are univariate categorical variables. A necessary first step in the analysis

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49

Mages, Tobias, Elli Anastasiadi, and Christian Rohner. "Non-Negative Decomposition of Multivariate Information: From Minimum to Blackwell-Specific Information." Entropy 26, no. 5 (2024): 424. http://dx.doi.org/10.3390/e26050424.

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Partial information decompositions (PIDs) aim to categorize how a set of source variables provides information about a target variable redundantly, uniquely, or synergetically. The original proposal for such an analysis used a lattice-based approach and gained significant attention. However, finding a suitable underlying decomposition measure is still an open research question at an arbitrary number of discrete random variables. This work proposes a solution with a non-negative PID that satisfies an inclusion–exclusion relation for any f-information measure. The decomposition is constructed fr

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50

Neumann, Jacob, Yen Ting Lin, Abhishek Mallela, et al. "Implementation of a practical Markov chain Monte Carlo sampling algorithm in PyBioNetFit." Bioinformatics 38, no. 6 (2022): 1770–72. http://dx.doi.org/10.1093/bioinformatics/btac004.

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Abstract Summary Bayesian inference in biological modeling commonly relies on Markov chain Monte Carlo (MCMC) sampling of a multidimensional and non-Gaussian posterior distribution that is not analytically tractable. Here, we present the implementation of a practical MCMC method in the open-source software package PyBioNetFit (PyBNF), which is designed to support parameterization of mathematical models for biological systems. The new MCMC method, am, incorporates an adaptive move proposal distribution. For warm starts, sampling can be initiated at a specified location in parameter space and wi

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