{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T03:54:53Z","timestamp":1789012493401,"version":"build-2803163510"},"reference-count":21,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,7,11]],"date-time":"2020-07-11T00:00:00Z","timestamp":1594425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,2]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The pseudo-marginal algorithm is a variant of the Metropolis\u2013Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density. Practically, one has to trade off the computational resources used to obtain this estimator against the asymptotic variances of the ergodic averages obtained by the pseudo-marginal algorithm. Recent works on optimizing this trade-off rely on some strong assumptions, which can cast doubts over their practical relevance. In particular, they all assume that the distribution of the difference between the log-density, and its estimate is independent of the parameter value at which it is evaluated. Under regularity conditions we show that as the number of data points tends to infinity, a space-rescaled version of the pseudo-marginal chain converges weakly to another pseudo-marginal chain for which this assumption indeed holds. A study of this limiting chain allows us to provide parameter dimension-dependent guidelines on how to optimally scale a normal random walk proposal, and the number of Monte Carlo samples for the pseudo-marginal method in the large-sample regime. These findings complement and validate currently available results.<\/jats:p>","DOI":"10.1093\/biomet\/asaa044","type":"journal-article","created":{"date-parts":[[2020,5,21]],"date-time":"2020-05-21T11:08:06Z","timestamp":1590059286000},"page":"37-51","source":"Crossref","is-referenced-by-count":18,"title":["Large-sample asymptotics of the pseudo-marginal method"],"prefix":"10.1093","volume":"108","author":[{"given":"S M","family":"Schmon","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Oxford, 24\u201329 St Giles\u2019, Oxford OX1 3LB, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G","family":"Deligiannidis","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Oxford, 24\u201329 St Giles\u2019, Oxford OX1 3LB, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A","family":"Doucet","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Oxford, 24\u201329 St Giles\u2019, Oxford OX1 3LB, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M K","family":"Pitt","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King\u2019s College London, Strand, London WC2R 2LS, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,7,11]]},"reference":[{"key":"2021031914232255900_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 (with Discussion)","volume":"72","author":"Andrieu,","year":"2010","journal-title":"J. R. Statist. Soc. B"},{"key":"2021031914232255900_B2","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1214\/07-AOS574","article-title":"The pseudo-marginal approach for efficient Monte Carlo computations","volume":"37","author":"Andrieu,","year":"2009","journal-title":"Ann. Statist."},{"key":"2021031914232255900_B3","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.1214\/14-AAP1022","article-title":"Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms","volume":"25","author":"Andrieu,","year":"2015","journal-title":"Ann. Appl. Prob."},{"key":"2021031914232255900_B4","doi-asserted-by":"crossref","first-page":"2661","DOI":"10.1214\/15-AAP1158","article-title":"Establishing some order amongst exact approximations of MCMCs","volume":"26","author":"Andrieu,","year":"2016","journal-title":"Ann. Appl. Prob."},{"key":"2021031914232255900_B5","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1093\/genetics\/164.3.1139","article-title":"Estimation of population growth or decline in genetically monitored populations","volume":"164","author":"Beaumont,","year":"2003","journal-title":"Genetics"},{"key":"2021031914232255900_B6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/EJP.v19-3428","article-title":"A lognormal central limit theorem for particle approximations of normalizing constants","volume":"19","author":"B\u00e9rard,","year":"2014","journal-title":"Electron. J. Prob."},{"key":"2021031914232255900_B7","author":"Crauel,","year":"2003","journal-title":"Random Probability Measures on Polish Spaces"},{"key":"2021031914232255900_B8","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1111\/rssb.12280","article-title":"The correlated pseudomarginal method","volume":"80","author":"Deligiannidis,","year":"2018","journal-title":"J. R. Statist. Soc. B"},{"key":"2021031914232255900_B9","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1093\/biomet\/asu075","article-title":"Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator","volume":"102","author":"Doucet,","year":"2015","journal-title":"Biometrika"},{"key":"2021031914232255900_B10","author":"Kallenberg,","journal-title":"Foundations of Modern Probability"},{"key":"2021031914232255900_B11","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1214\/12-EJS675","article-title":"The Bernstein-von-Mises theorem under misspecification","volume":"6","author":"Kleijn,","year":"2012","journal-title":"Electron. J. Statist."},{"key":"2021031914232255900_B12","doi-asserted-by":"crossref","first-page":"074505","DOI":"10.1103\/PhysRevD.61.074505","article-title":"A noisy Monte Carlo algorithm","volume":"61","author":"Lin,","year":"2000","journal-title":"Phys. Rev. D"},{"key":"2021031914232255900_B13","doi-asserted-by":"crossref","DOI":"10.1002\/0470011815.b2a10021","article-title":"Generalized linear mixed models","volume":"4","author":"McCulloch,","year":"2005","journal-title":"Encyclopedia of Biostatistics"},{"key":"2021031914232255900_B14","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1093\/biomet\/asw020","article-title":"Particle Metropolis-adjusted Langevin algorithms","volume":"103","author":"Nemeth,","year":"2016","journal-title":"Biometrika"},{"key":"2021031914232255900_B15","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.jeconom.2012.06.004","article-title":"On some properties of Markov chain Monte Carlo simulation methods based on the particle filter","volume":"171","author":"Pitt,","year":"2012","journal-title":"J. Economet."},{"key":"2021031914232255900_B16","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1214\/aoap\/1034625254","article-title":"Weak convergence and optimal scaling of random walk Metropolis algorithms","volume":"7","author":"Roberts,","year":"1997","journal-title":"Ann. Appl. Prob."},{"key":"2021031914232255900_B17","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1214\/12-AAP918","article-title":"Minimising MCMC variance via diffusion limits, with an application to simulated tempering","volume":"24","author":"Roberts,","year":"2014","journal-title":"Ann. Appl. Prob."},{"key":"2021031914232255900_B18","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1093\/biomet\/asx031","article-title":"Pseudo-marginal Metropolis\u2013Hastings sampling using averages of unbiased estimators","volume":"104","author":"Sherlock,","year":"2017","journal-title":"Biometrika"},{"key":"2021031914232255900_B19","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1214\/14-AOS1278","article-title":"On the efficiency of pseudo-marginal random walk Metropolis algorithms","volume":"43","author":"Sherlock,","year":"2015","journal-title":"Ann. Statist."},{"key":"2021031914232255900_B20","author":"van der Vaart,","journal-title":"Asymptotic Statistics"},{"key":"2021031914232255900_B21","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1080\/01621459.1991.10475006","article-title":"Generalized linear models with random effects; a Gibbs sampling approach","volume":"86","author":"Zeger,","year":"1991","journal-title":"J. Am. Statist. Assoc."}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/108\/1\/37\/36645753\/asaa044.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asaa044\/33487358\/asaa044.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/108\/1\/37\/36645753\/asaa044.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T13:13:14Z","timestamp":1666617194000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/108\/1\/37\/5869975"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,11]]},"references-count":21,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,7,11]]},"published-print":{"date-parts":[[2021,3,2]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asaa044","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,3,1]]},"published":{"date-parts":[[2020,7,11]]}}}