Sequential quasi Monte Carlo
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)}, whe...
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| Veröffentlicht in: | Journal of the Royal Statistical Society. Series B, Methodological Methodological, 2015-06, Vol.77 (3), p.509-579 |
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| container_end_page | 579 |
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| container_title | Journal of the Royal Statistical Society. Series B, Methodological |
| container_volume | 77 |
| creator | Gerber, Mathieu Chopin, Nicolas |
| description | 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−1/2). The only requirement to implement SQMC algorithms is the ability to write the simulation of particle xtn given xt−1n as a deterministic function of xt−1n 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. |
| doi_str_mv | 10.1111/rssb.12104 |
| format | Article |
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Series B, Methodological, 2015-06, Vol.77 (3), p.509-579</ispartof><rights>2015 Royal Statistical Society</rights><rights>Copyright © 2015 The Royal Statistical Society and Blackwell Publishing Ltd</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c5324-3ce9437d96202c464572848560a40e3c6d869f3a08a91c9d25113a725b0518363</citedby><cites>FETCH-LOGICAL-c5324-3ce9437d96202c464572848560a40e3c6d869f3a08a91c9d25113a725b0518363</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1111%2Frssb.12104$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1111%2Frssb.12104$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>230,314,777,781,882,1412,27905,27906,45555,45556</link.rule.ids><backlink>$$Uhttps://hal.science/hal-01409255$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Gerber, Mathieu</creatorcontrib><creatorcontrib>Chopin, Nicolas</creatorcontrib><title>Sequential quasi Monte Carlo</title><title>Journal of the Royal Statistical Society. Series B, Methodological</title><addtitle>J. R. Stat. Soc. B</addtitle><description>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−1/2). The only requirement to implement SQMC algorithms is the ability to write the simulation of particle xtn given xt−1n as a deterministic function of xt−1n 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.</description><subject>Algorithms</subject><subject>Array-randomized quasi Monte Carlo</subject><subject>Economic analysis</subject><subject>Low discrepancy</subject><subject>Markov chain</subject><subject>Markovian processes</subject><subject>Mathematics</subject><subject>Monte Carlo method</subject><subject>Monte Carlo simulation</subject><subject>Particle filtering</subject><subject>Probability theory</subject><subject>Quasi Monte Carlo</subject><subject>Quasi Monte Carlo; Randomized quasi Monte Carlo; Sequential Monte Carlo</subject><subject>Randomized quasi Monte Carlo</subject><subject>Sequential Monte Carlo</subject><subject>Simulation</subject><subject>Statistical analysis</subject><subject>Statistical methods</subject><subject>Statistics</subject><subject>Studies</subject><issn>1369-7412</issn><issn>0035-9246</issn><issn>1467-9868</issn><issn>0035-9246</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp90TtPwzAQAOAIgUQpLMxIVGIBpMCdX7HHtkCLKA9REKNlUhcCoQE7AfrvcQh0YOAG27K-O53PUbSJcIAhDp339wdIENhS1EImklhJIZfDmQoVJwzJarTm_ROEEAltRVtj-1bZWZmZvPNWGZ91zotZaTt94_JiPVqZmtzbjZ-9Hd2eHN_0h_HocnDa747ilFPCYppaxWgyUYIASZlgPCGSSS7AMLA0FRMp1JQakEZhqiaEI1KTEH4PHCUVtB3tNXUfTa5fXfZi3FwXJtPD7kjXd4AMFOH8HYPdbeyrK0LnvtQvmU9tnpuZLSqvUUjBwiJZoDt_6FNRuVl4Sa0ACVGkVvuNSl3hvbPTRQcIuh6qroeqv4caMDb4I8vt_B-pr8fj3m9O3ORkvrSfixzjnnX4goTru4uBBnqlzo5ET9d-u_FTU2jz4DKvb8cEUEDdMgGgX-X-i80</recordid><startdate>201506</startdate><enddate>201506</enddate><creator>Gerber, Mathieu</creator><creator>Chopin, Nicolas</creator><general>Royal Statistical Society</general><general>Blackwell Publishing Ltd</general><general>Oxford University Press</general><scope>FBQ</scope><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8BJ</scope><scope>8FD</scope><scope>FQK</scope><scope>JBE</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>201506</creationdate><title>Sequential quasi Monte Carlo</title><author>Gerber, Mathieu ; Chopin, Nicolas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c5324-3ce9437d96202c464572848560a40e3c6d869f3a08a91c9d25113a725b0518363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algorithms</topic><topic>Array-randomized quasi Monte Carlo</topic><topic>Economic analysis</topic><topic>Low discrepancy</topic><topic>Markov chain</topic><topic>Markovian processes</topic><topic>Mathematics</topic><topic>Monte Carlo method</topic><topic>Monte Carlo simulation</topic><topic>Particle filtering</topic><topic>Probability theory</topic><topic>Quasi Monte Carlo</topic><topic>Quasi Monte Carlo; Randomized quasi Monte Carlo; Sequential Monte Carlo</topic><topic>Randomized quasi Monte Carlo</topic><topic>Sequential Monte Carlo</topic><topic>Simulation</topic><topic>Statistical analysis</topic><topic>Statistical methods</topic><topic>Statistics</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gerber, Mathieu</creatorcontrib><creatorcontrib>Chopin, Nicolas</creatorcontrib><collection>AGRIS</collection><collection>Istex</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>Technology Research Database</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Journal of the Royal Statistical Society. Series B, Methodological</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gerber, Mathieu</au><au>Chopin, Nicolas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sequential quasi Monte Carlo</atitle><jtitle>Journal of the Royal Statistical Society. Series B, Methodological</jtitle><addtitle>J. R. Stat. Soc. B</addtitle><date>2015-06</date><risdate>2015</risdate><volume>77</volume><issue>3</issue><spage>509</spage><epage>579</epage><pages>509-579</pages><issn>1369-7412</issn><issn>0035-9246</issn><eissn>1467-9868</eissn><eissn>0035-9246</eissn><abstract>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−1/2). The only requirement to implement SQMC algorithms is the ability to write the simulation of particle xtn given xt−1n as a deterministic function of xt−1n 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.</abstract><cop>Oxford</cop><pub>Royal Statistical Society</pub><doi>10.1111/rssb.12104</doi><tpages>71</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 1369-7412 |
| ispartof | Journal of the Royal Statistical Society. Series B, Methodological, 2015-06, Vol.77 (3), p.509-579 |
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| source | Wiley Online Library Journals Frontfile Complete; Business Source Complete; JSTOR Mathematics & Statistics; Jstor Complete Legacy; Oxford University Press Journals All Titles (1996-Current) |
| subjects | Algorithms Array-randomized quasi Monte Carlo Economic analysis Low discrepancy Markov chain Markovian processes Mathematics Monte Carlo method Monte Carlo simulation Particle filtering Probability theory Quasi Monte Carlo Quasi Monte Carlo Randomized quasi Monte Carlo Sequential Monte Carlo Randomized quasi Monte Carlo Sequential Monte Carlo Simulation Statistical analysis Statistical methods Statistics Studies |
| title | Sequential quasi Monte Carlo |
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