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COMPARISON OF ASYMPTOTIC VARIANCES OF INHOMOGENEOUS MARKOV CHAINS WITH APPLICATION TO MARKOV CHAIN MONTE CARLO METHODS
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-0772-846X
2014 (English)In: Annals of Statistics, ISSN 0090-5364, E-ISSN 2168-8966, Vol. 42, no 4, 1483-1510 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2014. Vol. 42, no 4, 1483-1510 p.
Keyword [en]
Markov chain Monte Carlo, asymptotic variance, Peskun ordering, inhomogeneous Markov chains, pseudo-marginal algorithms
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-154769DOI: 10.1214/14-AOS1209ISI: 000342481700009Scopus ID: 2-s2.0-84987968040OAI: oai:DiVA.org:kth-154769DiVA: diva2:760094
Funder
Swedish Research Council, 2011-5577
Note

QC 20141103

Available from: 2014-11-03 Created: 2014-10-27 Last updated: 2017-12-05Bibliographically approved

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Olsson, Jimmy

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