Bayesian posterior mean estimates for Poisson hidden Markov models

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.