Asymptotic Normality of the Posterior Distributions in a Class of Hidden Markov Models

TL;DR

This paper proves that the posterior distribution in a class of hidden Markov models becomes normally distributed as data size grows, using a novel approach based on testing conditions and transportation inequalities.

Contribution

It introduces a new proof technique for asymptotic normality of posterior distributions in hidden Markov models, leveraging optimal transportation inequalities.

Findings

Posterior distributions are asymptotically normal in the specified HMM class.

The proof employs a testing condition and optimal transportation inequality.

The approach offers a new perspective on asymptotic analysis in HMMs.

Abstract

We show that the posterior distribution of parameters in a hidden Markov model with parametric emission distributions and discrete and known state space is asymptotically normal. The main novelty of our proof is that it is based on a testing condition and the sequence of test functions is obtained using an optimal transportation inequality.