{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T10:16:57Z","timestamp":1682504217220},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p>In this paper we study the mixing time of certain adaptive Markov chain Monte Carlo (MCMC) algorithms. Under some regularity conditions, we show that the convergence rate of importance resampling MCMC algorithms, measured in terms of the total variation distance, is<jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>-1<\/jats:sup>). By means of an example, we establish that, in general, this algorithm does not converge at a faster rate. We also study the interacting tempering algorithm, a simplified version of the equi-energy sampler, and establish that its mixing time is of order<jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>-1\/2<\/jats:sup>).<\/jats:p>","DOI":"10.1017\/s0021900200113452","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T20:26:34Z","timestamp":1459369594000},"page":"811-825","source":"Crossref","is-referenced-by-count":0,"title":["On the convergence rates of some adaptive Markov chain Monte Carlo algorithms"],"prefix":"10.1017","volume":"52","author":[{"given":"Yves","family":"Atchad\u00e9","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yizao","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,3,30]]},"reference":[{"key":"S0021900200113452_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/11-AOS938"},{"key":"S0021900200113452_ref10","doi-asserted-by":"publisher","DOI":"10.3150\/12-BEJ493"},{"key":"S0021900200113452_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2012.01.001"},{"key":"S0021900200113452_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511984679.003"},{"key":"S0021900200113452_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/09-AAP636"},{"key":"S0021900200113452_ref4","first-page":"81","volume":"27","year":"2009","journal-title":"Far East J. Theoret. Statist"},{"key":"S0021900200113452_ref16","doi-asserted-by":"publisher","DOI":"10.1214\/08-AAP555"},{"key":"S0021900200113452_ref3","doi-asserted-by":"publisher","DOI":"10.3150\/10-BEJ307"},{"key":"S0021900200113452_ref15","volume-title":"Weak Convergence and Empirical Processes: With Applications to Statistics","year":"1996"},{"key":"S0021900200113452_ref2","doi-asserted-by":"publisher","DOI":"10.1080\/07362990701857178"},{"key":"S0021900200113452_ref14","volume-title":"Lower bounds on the convergence rates of adaptive MCMC methods","year":"2011"},{"key":"S0021900200113452_ref1","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1214\/ECP.v12-1320","volume":"12","year":"2007","journal-title":"Electron. Commun. Prob"},{"key":"S0021900200113452_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1033066201"},{"key":"S0021900200113452_ref12","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000000515"},{"key":"S0021900200113452_ref11","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1214\/ECP.v12-1336","volume":"12","year":"2007","journal-title":"Electron. Commun. Prob"},{"key":"S0021900200113452_ref8","doi-asserted-by":"publisher","DOI":"10.1051\/ps:2007032"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200113452","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:35:03Z","timestamp":1682501703000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200113452\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9]]},"references-count":16,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2015,9]]}},"alternative-id":["S0021900200113452"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200113452","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9]]}}}