CLTs and asymptotic variance of time-sampled Markov chains

Abstract

For a Markov transition kernel $P$ and a probability distribution $\mu$ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel $P_{\mu }={\sum }_k\mu (k)P^k.$ In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance.

A small simulation illustrating theoretical results added

References in corpus (1)

• Renewal theory and computable convergence rates for geometrically ergodic Markov chains