{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T17:25:53Z","timestamp":1791393953254,"version":"4.3.3"},"reference-count":157,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2015,5,12]],"date-time":"2015-05-12T00:00:00Z","timestamp":1431388800000},"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-11-LABEX-0047"],"award-info":[{"award-number":["ANR-11-LABEX-0047"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,6,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We derive and study sequential quasi Monte Carlo (SQMC), a class of algorithms obtained by introducing QMC point sets in particle filtering. SQMC is related to, and may be seen as an extension of, the array-RQMC algorithm of L'Ecuyer and his colleagues. The complexity of SQMC is O{Nlog(N)}, where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate OP(N\u22121\/2). The only requirement to implement SQMC algorithms is the ability to write the simulation of particle xtn given xt\u22121n as a deterministic function of xt\u22121n and a fixed number of uniform variates. We show that SQMC is amenable to the same extensions as standard SMC, such as forward smoothing, backward smoothing and unbiased likelihood evaluation. In particular, SQMC may replace SMC within a particle Markov chain Monte Carlo algorithm. We establish several convergence results. We provide numerical evidence that SQMC may significantly outperform SMC in practical scenarios.<\/jats:p>","DOI":"10.1111\/rssb.12104","type":"journal-article","created":{"date-parts":[[2015,5,12]],"date-time":"2015-05-12T10:53:05Z","timestamp":1431427985000},"page":"509-579","source":"Crossref","is-referenced-by-count":92,"title":["Sequential Quasi Monte Carlo"],"prefix":"10.1093","volume":"77","author":[{"given":"Mathieu","family":"Gerber","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Lausanne, Switzerland, and Centre de Recherche en Economie et Statistique , Paris , France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolas","family":"Chopin","sequence":"additional","affiliation":[{"name":"Centre de Recherche en Economie et Statistique and Ecole Nationale de la Statistique et de l\u2019Administration Economique , Paris , France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2015,5,12]]},"reference":[{"key":"2023021709294086100_rssb12104-cit-0001","doi-asserted-by":"crossref","first-page":"143","DOI":"10.4064\/aa167-2-4","article-title":"Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality","volume":"167","author":"Aistleitner","year":"2015","journal-title":"Acta Arithm."},{"key":"2023021709294086100_rssb12104-cit-0002","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. 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