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A coarse-grained Markov chain is a hidden Markov model

Physica A: Statistical Mechanics and its Applications, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Finite dimensional predictors for hidden Markov chains

Systems & Control Letters, 1992
Using a general filtering equation for processes (obtained recently by R. J. Elliott) related to a continuous time Markov chain observed in Gaussian noise, finite-dimensional normalized and unnormalized predictors for the state, for the number of jumps from a state to another and for the occupation time in any state, are obtained.
Aggoun, Lakhdar, Elliott, Robert J.
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Hidden Markov chains in generalized linear models

Canadian Journal of Statistics, 1998
AbstractWe show how the concept of hidden Markov model may be accommodated in a setting involving multiple sequences of observations. The resulting class of models allows for both interrelationships between different sequences and serial dependence within sequences. Missing values in the observation sequences may be handled in a straightforward manner.
Turner, T. Rolf   +2 more
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Inference and minimization of hidden Markov chains

Proceedings of the seventh annual conference on Computational learning theory - COLT '94, 1994
A hidden Markov chain (hmc) is a finite ergodic Markov chain in which each of the states is labelled 0 or 1. As the Markov chain moves through a random trajectory, the hmc emits a 0 or a 1 at each times step according to the label of the state just entered.The inference problem is to construct a mechanism which will emit 0's and 1's and which is ...
David Gillman, Michael Sipser
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FUZZY HIDDEN MARKOV CHAIN FOR WEB APPLICATIONS

International Journal of Information Technology & Decision Making, 2013
Hidden Markov model (HMM) has become increasingly popular in the last several years. Real-world problems such as prediction of web navigation are uncertain in nature; in this case, HMM is less appropriate i.e., we cannot assign certain probability values while in fuzzy set theory everything has elasticity.
R. SUJATHA, T. M. RAJALAXMI, B. PRABA
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Reliability modeling with hidden Markov and semi-Markov chains

2013 IEEE Integration of Stochastic Energy in Power Systems Workshop (ISEPS), 2013
Abstract form only given. Semi-Markov processes and Markov renewal processes represent a class of stochastic processes that generalize Markov and renewal processes. As it is well known, for a discrete-time (respectively continuous-time) Markov process, the sojourn time in each state is geometrically (respectively exponentially) distributed. In the semi-
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Markov chain Monte Carlo simulation for Bayesian Hidden Markov Models

AIP Conference Proceedings, 2016
A hidden Markov model (HMM) is a mixture model which has a Markov chain with finite states as its mixing distribution. HMMs have been applied to a variety of fields, such as speech and face recognitions. The main purpose of this study is to investigate the Bayesian approach to HMMs.
Lay Guat Chan   +1 more
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Finite-dimensional models for hidden Markov chains

Advances in Applied Probability, 1995
A continuous-time, non-linear filtering problem is considered in which both signal and observation processes are Markov chains. New finite-dimensional filters and smoothers are obtained for the state of the signal, for the number of jumps from one state to another, for the occupation time in any state of the signal, and for joint occupation times of ...
Aggoun, Lakhdar, Elliott, Robert J.
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Bayesian estimation of hidden Markov chains: a stochastic implementation

Statistics & Probability Letters, 1993
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Robert, Christian P.   +2 more
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On the Markov property of a finite hidden Markov chain

Statistics & Probability Letters, 2001
The question of the conditions under which a hidden Markov chain itself exhibits Markovian behaviour is studied. The provided answer is based on two different approaches: 1) the authors use known results by Rubino and Sericola for deterministic functions of a Markov chain by considering a bivariate chain; 2) a method based on a recursive filtering ...
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