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Pseudo-marginal Metropolis–Hastings using averages of unbiased estimators
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Sherlock, Chris, Thiéry, Alexandre H. and Lee, Anthony (2017) Pseudo-marginal Metropolis–Hastings using averages of unbiased estimators. Biometrika, 104 (3). pp. 727-743. doi:10.1093/biomet/asx031 ISSN 0006-3444.
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Official URL: https://doi.org/10.1093/biomet/asx031
Abstract
We consider a pseudo-marginal Metropolis–Hastings kernel Pm that is constructed using an average of m exchangeable random variables, as well as an analogous kernel Ps that averages 15 s < m of these same random variables. Using an embedding technique to facilitate comparisons, we show that the asymptotic variances of ergodic averages associated with Pm are lower bounded in terms of those associated with Ps. We show that the bound provided is tight and disprove a conjecture that when the random variables to be averaged are independent, the asymptotic variance under Pm is never less than s/m times the variance under Ps. The conjecture does, 20 however, hold when considering continuous-time Markov chains. These results imply that if the computational cost of the algorithm is proportional to m, it is often better to set m = 1. We provide intuition as to why these findings differ so markedly from recent results for pseudomarginal
kernels employing particle filter approximations. Our results are exemplified through two simulation studies; in the first the computational cost is effectively proportional to m and in 25 the second there is a considerable start-up cost at each iteration.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Markov processes , Monte Carlo method, Sampling (Statistics) | ||||||||
Journal or Publication Title: | Biometrika | ||||||||
Publisher: | Biometrika Trust | ||||||||
ISSN: | 0006-3444 | ||||||||
Official Date: | 1 September 2017 | ||||||||
Dates: |
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Volume: | 104 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 727-743 | ||||||||
DOI: | 10.1093/biomet/asx031 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 25 April 2017 | ||||||||
Date of first compliant Open Access: | 1 June 2018 |
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