Posterior consistency for nonparametric hidden Markov models with finite state space

2013/11/13 by Elodie Vernet, Vernet, Elodie
Computer Science · Mathematics · #62G20 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G20 #stat.TH

paper · pdf · doi:10.48550/arxiv.1311.3092

32 pages, 1 figure

openalex publication_date 2013/11/13 · arxiv created 2014/07/08 · arxiv updated 2014/07/09 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

In this paper we study posterior consistency for different topologies on the parameters for 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. We deduce posterior consistency for the different components of the parameter. We also obtain posterior consistency for marginal smoothing distributions in the discrete case. We finally apply our results to independent emission probabilities, translated emission probabilities and discrete HMMs, under various types of priors.

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