A note on one of the Markov chain Monte Carlo novice's questions

TL;DR

This paper introduces a new Markov embedding for certain inhomogeneous Markov chains used in Monte Carlo methods, providing insights into their implementation and connecting to recent theoretical results.

Contribution

It presents a novel time-homogeneous embedding for inhomogeneous Markov chains, aiding practical implementation and theoretical understanding of Monte Carlo algorithms.

Findings

Provides a new embedding technique for Markov chains

Clarifies implementation challenges in Monte Carlo sampling

Links to recent theoretical results on Markov chains

Abstract

We introduce a novel time-homogeneous Markov embedding of a class of time inhomogeneous Markov chains widely used in the context of Monte Carlo sampling algorithms which allows us to answer one of the most basic, yet hard, question about the practical implementation of these techniques. We also show that this embedding sheds some light on the recent result of [#maire-douc-olsson2013]. We discuss further applications of the technique.