Inference and model choice for sequentially ordered hidden Markov models


Journal of the Royal Statistical Society: Series B - Statistical Methodology

mars 2007, vol. 69, n°2, pp.269-284

Départements : Economie et Sciences de la décision

Mots clés : Hidden Markov models, Label switching, Particle filtering, Sequential Monte Carlo sampling, Time ordering

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<sub> t</sub>. 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.