Bayesian Methods for Hidden Markov Models Recursive Computing in the 21st Century

Markov chain Monte Carlo (MCMC) sampling strategies can be used to simulate hidden Markov model (HMM) parameters from their posterior distribution given observed data. Some MCMC methods used in practice (for computing likelihood, conditional probabilities of hidden states, and the most likely sequen...

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Vydané v:	Journal of the American Statistical Association Ročník 97; číslo 457; s. 337 - 351
Hlavný autor:	Scott, Steven L
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Alexandria, VA Taylor & Francis 01.03.2002 American Statistical Association Taylor & Francis Ltd
Predmet:	21st century Algorithms Bayes estimators Bayesian analysis Bayesian method Computers Data sampling Distribution theory Exact sciences and technology Forward-backward recursion Fraud Gibbs sampler Gross national product Inference from stochastic processes; time series analysis Kalman filter Local computation Markov analysis Markov chain Monte Carlo Markov chains Markov models Markov processes Markovian processes Mathematics Methods Metropolitan areas Modeling Monte Carlo simulation Parametric models Polytopes Probability Probability and statistics Probability theory and stochastic processes Recursion Review Paper Sciences and techniques of general use Statistical analysis Statistical methods Statistics Mixed distribution Conditional distribution Statistical analysis Kalman filter Mixture model Statistical estimation Gibbs sampling Poisson distribution Asymptotic convergence MCMC algorithm Marginal distribution Log likelihood Hidden Markov model Recursive method Predictive value Forward backward recursion Bayes methods Computing method Posterior distribution
ISSN:	0162-1459, 1537-274X
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Popis
Shrnutí:	Markov chain Monte Carlo (MCMC) sampling strategies can be used to simulate hidden Markov model (HMM) parameters from their posterior distribution given observed data. Some MCMC methods used in practice (for computing likelihood, conditional probabilities of hidden states, and the most likely sequence of states) can be improved by incorporating established recursive algorithms. The most important of these is a set of forward-backward recursions calculating conditional distributions of the hidden states given observed data and model parameters. I show how to use the recursive algorithms in an MCMC context and demonstrate mathematical and empirical results showing a Gibbs sampler using the forward-backward recursions mixes more rapidly than another sampler often used for HMMs. Iintroduce an augmented variables technique for obtaining unique state labels in HMMs and finite mixture models. I show how recursive computing allows the statistically efficient use of MCMC output when estimating the hidden states. I directly calculate the posterior distribution of the hidden chain's state-space size by MCMC, circumventing asymptotic arguments underlying the Bayesian information criterion, which is shown to be inappropriate for a frequently analyzed dataset in the HMM literature. The use of log-likelihood for assessing MCMC convergence is illustrated, and posterior predictive checks are used to investigate application specific questions of model adequacy.
Bibliografia:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0162-1459 1537-274X
DOI:	10.1198/016214502753479464