Simulating the Invariant Measures of Markov Chains Using Backward Coupling at Regeneration Times

Abstract

We develop an algorithm for simulating approximate random samples from the invariant measure of a Markov chain using backward coupling of embedded regeneration times. Related methods have been used effectively for finite chains and for stochastically monotone chains: here we propose a method of implementation which avoids these restrictions by using a “cycle-length” truncation. We show that the coupling times have good theoretical properties and describe benefits and difficulties of implementing the methods in practice.