• DOI:10.1214/14-AOS1209
• Corpus ID: 88519838

Comparison of asymptotic variances of inhomogeneous Markov chains with application to Markov chain Monte Carlo methods

@article{Maire2013ComparisonOA,
  title={Comparison of asymptotic variances of inhomogeneous Markov chains with application to Markov chain Monte Carlo methods},
  author={Florian Maire and Randal Douc and Jimmy Olsson},
  journal={arXiv: Methodology},
  year={2013}
}

• Florian Maire, R. Douc, J. Olsson
• Published 14 July 2013
• Mathematics, Computer Science
• arXiv: Methodology

In this paper, we study the asymptotic variance of sample path averages for inhomogeneous Markov chains that evolve alternatingly according to two different $\pi$-reversible Markov transition kernels $P$ and $Q$. More specifically, our main result allows us to compare directly the asymptotic variances of two inhomogeneous Markov chains associated with different kernels $P_i$ and $Q_i$, $i\in\{0,1\}$, as soon as the kernels of each pair $(P_0,P_1)$ and $(Q_0,Q_1)$ can be ordered in the sense of lag-one autocovariance. As an important application, we use this result for comparing different data-augmentation-type Metropolis-Hastings algorithms. In particular, we compare some pseudo-marginal algorithms and propose a novel exact algorithm, referred to as the random refreshment algorithm, which is more efficient, in terms of asymptotic variance, than the Grouped Independence Metropolis-Hastings algorithm and has a computational complexity that does not exceed that of the Monte Carlo Within Metropolis algorithm.