Elodie Vernet (Université Paris Sud): Posterior consistency for nonparametric hidden Markov models with fi nite state space

Hidden Markov models (HMMs) have been widely used in diverse fields such as speech recognition, genomics, econometrics. Because parametric modeling of emission distributions may lead to poor results in practice, in particular for clustering purposes, recent interest in using non parametric HMMs appeared in applications, see Yau, Papaspiliopoulos, Roberts and Holmes (2011). Here we study posterior consistency for different topologies on the parameters for nonparametric hidden Markov models with finite state space. We first obtain weak and strong posterior consistency for the marginal density function of finitely many consecutive observations and deduce posterior consistency for the different components of the parameter. We finally apply our results to independent emission probabilities, translated emission probabilities and discrete HMMs, some priors for which the posterior is consistent are given.

Keywords: Bayesian nonparametrics, consistency, hidden Markov models

link to article: arxiv.org/pdf/1311.3092