COMPARISON OF ASYMPTOTIC VARIANCES OF INHOMOGENEOUS MARKOV CHAINS WITH APPLICATION TO MARKOV CHAIN MONTE CARLO METHODS
成果类型：
Article
署名作者：
Maire, Florian; Douc, Randal; Olsson, Jimmy
署名单位：
IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Royal Institute of Technology
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/14-AOS1209
发表日期：
2014
页码：
1483-1510
关键词：
摘要：
In this paper, we study the asymptotic variance of sample path averages for inhomogeneous Markov chains that evolve alternatingly according to two different 7-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 Pi and Q(i), i is an element of {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.