Electronic Journal of Statistics

Posterior consistency for nonparametric hidden Markov models with finite state space

Elodie Vernet

Full-text: Open access

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 distributions, translated emission distributions and discrete HMMs, under various types of priors.

Article information

Source
Electron. J. Statist., Volume 9, Number 1 (2015), 717-752.

Dates
First available in Project Euclid: 2 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1427990070

Digital Object Identifier
doi:10.1214/15-EJS1017

Mathematical Reviews number (MathSciNet)
MR3331855

Zentralblatt MATH identifier
1309.62143

Subjects
Primary: 62G20: Asymptotic properties

Keywords
Bayesian nonparametrics consistency hidden Markov models

Citation

Vernet, Elodie. Posterior consistency for nonparametric hidden Markov models with finite state space. Electron. J. Statist. 9 (2015), no. 1, 717--752. doi:10.1214/15-EJS1017. https://projecteuclid.org/euclid.ejs/1427990070


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