Inference and model choice for sequentially ordered hidden Markov models

Author: Chopin, Nicolas

Source: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 69, Number 2, April 2007 , pp. 269-284(16)

Publisher: Wiley-Blackwell

Buy & download fulltext article:

Price: $48.00 plus tax (Refund Policy)

Abstract:

Summary.

The system equation of a hidden Markov model is rewritten to label the components by order of appearance, and to make explicit the random behaviour of the number of components, m_t. We argue that this reformulation is often a good way to achieve identifiability, as it facilitates the interpretation of the posterior density, and the estimation of the number of components that have appeared in a given sample. We develop a sequential Monte Carlo algorithm for estimating the reformulated model, which relies on particle filtering and Gibbs sampling. Our algorithm has a computational cost that is similar to that of a Markov chain Monte Carlo sampler and is much less likely to be affected by label switching, i.e. the possibility of becoming trapped in a local mode of the posterior density. The extension to transdimensional priors is also considered. The approach is illustrated by two real data examples.

Keywords: Hidden Markov models; Label switching; Particle filtering; Sequential Monte Carlo sampling; Time ordering

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2007.00588.x

Affiliations: 1: University of Bristol, UK

Publication date: 2007-04-01