Asymptotics of maximum likelihood estimators based on Markov chain Monte Carlo methods

TL;DR

This paper proves the asymptotic normality of maximum likelihood estimators approximated via Markov chain Monte Carlo methods in complex models with intractable likelihoods, when both data and Monte Carlo sample sizes grow large.

Contribution

It establishes the asymptotic properties of MCMC-based MLEs in complex models, extending theoretical understanding to intractable likelihood scenarios.

Findings

MLE based on MCMC is asymptotically normal

Results apply to models with intractable norming constants

Applicable to missing data models

Abstract

In many complex statistical models maximum likelihood estimators cannot be calculated. In the paper we solve this problem using Markov chain Monte Carlo approximation of the true likelihood. In the main result we prove asymptotic normality of the estimator, when both sample sizes (the initial and Monte Carlo one) tend to infinity. Our result can be applied to models with intractable norming constants and missing data models.