A comparison between marginal likelihood and data augmented MCMC algorithms for Gaussian hidden Markov models

Abstract

We provide a comparison between marginal likelihood and data augmented Markov chain Monte Carlo (MCMC) algorithms for Bayesian estimation of hidden Markov models. In particular, we focus on a specification of these models based on a multivariate Gaussian distribution for the response variables. We evaluate the performance of both methods on the basis of simulated samples and an empirical application, where we compare these approaches in terms of standard measures of estimation and time efficiency. The results show that the augmented algorithm is preferable, obtaining optimal convergence properties and producing larger values of the effective sample size. Instead of using variable dimensional techniques for model selection, we suggest a method based on the so-called parallel sampling for this aim.