CLTs and asymptotic variance of time-sampled Markov chains

Details CLTs and asymptotic variance of time-sampled Markov chains CLTs and asymptotic variance of time-sampled Markov chains

2011-02-10

arxiv.org/abs/1102.2171v2

Mathematics

Probability

A small simulation illustrating theoretical results added

Scientific paper

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.

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