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Bayesian posterior mean estimates for Poisson hidden Markov models

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  • Murakami, Junko

Abstract

This paper focuses on the Bayesian posterior mean estimates (or Bayes' estimate) of the parameter set of Poisson hidden Markov models in which the observation sequence is generated by a Poisson distribution whose parameter depends on the underlining discrete-time time-homogeneous Markov chain. Although the most commonly used procedures for obtaining parameter estimates for hidden Markov models are versions of the expectation maximization and Markov chain Monte Carlo approaches, this paper exhibits an algorithm for calculating the exact posterior mean estimates which, although still cumbersome, has polynomial rather than exponential complexity, and is a feasible alternative for use with small scale models and data sets. This paper also shows simulation results, comparing the posterior mean estimates obtained by this algorithm and the maximum likelihood estimates obtained by expectation maximization approach.

Suggested Citation

  • Murakami, Junko, 2009. "Bayesian posterior mean estimates for Poisson hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 941-955, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:941-955
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    References listed on IDEAS

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    1. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    2. Ching, Wai Ki, 1997. "Markov-modulated Poisson processes for multi-location inventory problems," International Journal of Production Economics, Elsevier, vol. 53(2), pages 217-223, November.
    3. Scott S. L., 2002. "Bayesian Methods for Hidden Markov Models: Recursive Computing in the 21st Century," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 337-351, March.
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    1. Spezia, L. & Cooksley, S.L. & Brewer, M.J. & Donnelly, D. & Tree, A., 2014. "Modelling species abundance in a river by Negative Binomial hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 599-614.

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