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.

arXiv commentA small simulation illustrating theoretical results added

References in corpus (2)

• General state space Markov chains and MCMC algorithms
• Renewal theory and computable convergence rates for geometrically ergodic Markov chains