{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T06:32:51Z","timestamp":1789194771209,"version":"build-2803163510"},"reference-count":17,"publisher":"Oxford University Press (OUP)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We consider a pseudo-marginal Metropolis\u2013Hastings kernel ${\\mathbb{P}}_m$ that is constructed using an average of $m$ exchangeable random variables, and an analogous kernel ${\\mathbb{P}}_s$ that averages $s&lt;m$ of these same random variables. Using an embedding technique to facilitate comparisons, we provide a lower bound for the asymptotic variance of any ergodic average associated with ${\\mathbb{P}}_m$ in terms of the asymptotic variance of the corresponding ergodic average associated with ${\\mathbb{P}}_s$. We show that the bound is tight and disprove a conjecture that when the random variables to be averaged are independent, the asymptotic variance under ${\\mathbb{P}}_m$ is never less than $s\/m$ times the variance under ${\\mathbb{P}}_s$. The conjecture does, however, hold for 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 pseudo-marginal 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 the second there is a considerable start-up cost at each iteration.<\/jats:p>","DOI":"10.1093\/biomet\/asx031","type":"journal-article","created":{"date-parts":[[2017,5,5]],"date-time":"2017-05-05T19:10:52Z","timestamp":1494011452000},"page":"727-734","source":"Crossref","is-referenced-by-count":18,"title":["Pseudo-marginal Metropolis\u2013Hastings sampling using averages of unbiased estimators"],"prefix":"10.1093","volume":"104","author":[{"given":"Chris","family":"Sherlock","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, U.K. c.sherlock@lancaster.ac.uk"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexandre H.","family":"Thiery","sequence":"additional","affiliation":[{"name":"Department of Statistics and Applied Probability, National University of Singapore, Singapore 117543 a.h.thiery@nus.edu.sg"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Warwick, Coventry CV4 7AL, U.K. anthony.lee@warwick.ac.uk"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,6,21]]},"reference":[{"key":"2019071815501379200_B1","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1111\/j.1467-9868.2009.00736.x","article-title":"Particle Markov chain Monte Carlo methods.","volume":"72","author":"Andrieu","year":"2010","journal-title":"J. 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