On consistency of Bayesian parameter estimations for a class of ergodic Markov models

TL;DR

This paper proves the consistency of Bayesian parameter estimation for a class of ergodic Markov chains, extending classical methods to dependent data and highlighting potential applications in reliability and financial risk management.

Contribution

It extends Doob's method to establish Bayesian consistency for ergodic Markov models, a novel application of classical theory to dependent processes.

Findings

Bayesian estimators are consistent for ergodic Markov chains.

The method adapts Doob's approach from i.i.d. to Markov dependence.

Potential applications in reliability and financial risk analysis.

Abstract

The consistency of the Bayesian estimation of a parameter is shown for a class of ergodic discrete Markov chains. J.L. Doob's method was used, offered earlier for the i.i.d. situation. The result may be useful in the reliability theory for models with unknown parameters, in the risk management in financial mathematics, and in other applications.