{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T17:15:52Z","timestamp":1792862152405,"version":"4.5.0"},"reference-count":51,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2012,10,12]],"date-time":"2012-10-12T00:00:00Z","timestamp":1350000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-008-BLAN-0218"],"award-info":[{"award-number":["ANR-008-BLAN-0218"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"name":"French Ministry of Research"},{"name":"Ramon y Cajal","award":["MTM2009-09063"],"award-info":[{"award-number":["MTM2009-09063"]}]},{"DOI":"10.13039\/501100000769","name":"University of Oxford","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000769","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008562","name":"University of Texas at Austin","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008562","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000765","name":"University College London","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000765","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,6,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We consider the generic problem of performing sequential Bayesian inference in a state space model with observation process y, state process x and fixed parameter \u03b8. An idealized approach would be to apply the iterated batch importance sampling algorithm of Chopin. This is a sequential Monte Carlo algorithm in the \u03b8-dimension, that samples values of \u03b8, reweights iteratively these values by using the likelihood increments pyt\u2223y1:t\u22121,\u03b8 and rejuvenates the \u03b8-particles through a resampling step and a Markov chain Monte Carlo update step. In state space models these likelihood increments are intractable in most cases, but they may be unbiasedly estimated by a particle filter in the x-dimension, for any fixed \u03b8. This motivates the SMC2 algorithm that is proposed in the paper: a sequential Monte Carlo algorithm, defined in the \u03b8-dimension, which propagates and resamples many particle filters in the x-dimension. The filters in the x-dimension are an example of the random weight particle filter. In contrast, the particle Markov chain Monte Carlo framework that has been developed by Andrieu and colleagues allows us to design appropriate Markov chain Monte Carlo rejuvenation steps. Thus, the \u03b8-particles target the correct posterior distribution at each iteration t, despite the intractability of the likelihood increments. We explore the applicability of our algorithm in both sequential and non-sequential applications and consider various degrees of freedom, as for example increasing dynamically the number of x-particles. We contrast our approach with various competing methods, both conceptually and empirically through a detailed simulation study, and based on particularly challenging examples.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2012.01046.x","type":"journal-article","created":{"date-parts":[[2012,10,12]],"date-time":"2012-10-12T10:30:30Z","timestamp":1350037830000},"page":"397-426","source":"Crossref","is-referenced-by-count":281,"title":["SMC2: An Efficient Algorithm for Sequential Analysis of State Space Models"],"prefix":"10.1093","volume":"75","author":[{"given":"N.","family":"Chopin","sequence":"first","affiliation":[{"name":"Centre de Recherche en Economie et Statistique and Ecole Nationale de la Statistique et de l\u2019Administration , Malakoff , France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P. E.","family":"Jacob","sequence":"additional","affiliation":[{"name":"Centre de Recherche en Economie et Statistique , Malakoff , and , France"},{"name":"Universit\u00e9 Paris Dauphine , Malakoff , and , France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"O.","family":"Papaspiliopoulos","sequence":"additional","affiliation":[{"name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats and Universitat Pompeu Fabra , Barcelona , Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2012,10,12]]},"reference":[{"key":"2023031303053383400_","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. 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