A randomized multi-index sequential Monte Carlo method
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption, this work builds upon a recently introduced multi-index seque...
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| Veröffentlicht in: | Statistics and computing 2023-10, Vol.33 (5), Article 97 |
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| creator | Liang, Xinzhu Yang, Shangda Cotter, Simon L. Law, Kody J. H. |
| description | We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption, this work builds upon a recently introduced multi-index sequential Monte Carlo (SMC) ratio estimator, which provably enjoys the complexity improvements of multi-index Monte Carlo (MIMC) and the efficiency of SMC for inference. The present work leverages a randomization strategy to remove bias entirely, which simplifies estimation substantially, particularly in the MIMC context, where the choice of index set is otherwise important. Under reasonable assumptions, the proposed method provably achieves the same canonical complexity of MSE
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as the original method (where MSE is mean squared error), but without discretization bias. It is illustrated on examples of Bayesian inverse and spatial statistics problems. |
| doi_str_mv | 10.1007/s11222-023-10249-9 |
| format | Article |
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as the original method (where MSE is mean squared error), but without discretization bias. It is illustrated on examples of Bayesian inverse and spatial statistics problems.</description><identifier>ISSN: 0960-3174</identifier><identifier>EISSN: 1573-1375</identifier><identifier>DOI: 10.1007/s11222-023-10249-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Artificial Intelligence ; Bias ; Complexity ; Computer Science ; Estimation ; Monte Carlo simulation ; Original Paper ; Probability and Statistics in Computer Science ; Randomization ; Statistical Theory and Methods ; Statistics and Computing/Statistics Programs</subject><ispartof>Statistics and computing, 2023-10, Vol.33 (5), Article 97</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c314t-a5af6e4ef2acbbb3275f1d74fbcd893356f438c38bbe3d7c82cf46133c30ab893</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11222-023-10249-9$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11222-023-10249-9$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Liang, Xinzhu</creatorcontrib><creatorcontrib>Yang, Shangda</creatorcontrib><creatorcontrib>Cotter, Simon L.</creatorcontrib><creatorcontrib>Law, Kody J. H.</creatorcontrib><title>A randomized multi-index sequential Monte Carlo method</title><title>Statistics and computing</title><addtitle>Stat Comput</addtitle><description>We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption, this work builds upon a recently introduced multi-index sequential Monte Carlo (SMC) ratio estimator, which provably enjoys the complexity improvements of multi-index Monte Carlo (MIMC) and the efficiency of SMC for inference. The present work leverages a randomization strategy to remove bias entirely, which simplifies estimation substantially, particularly in the MIMC context, where the choice of index set is otherwise important. Under reasonable assumptions, the proposed method provably achieves the same canonical complexity of MSE
-
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as the original method (where MSE is mean squared error), but without discretization bias. It is illustrated on examples of Bayesian inverse and spatial statistics problems.</description><subject>Artificial Intelligence</subject><subject>Bias</subject><subject>Complexity</subject><subject>Computer Science</subject><subject>Estimation</subject><subject>Monte Carlo simulation</subject><subject>Original Paper</subject><subject>Probability and Statistics in Computer Science</subject><subject>Randomization</subject><subject>Statistical Theory and Methods</subject><subject>Statistics and Computing/Statistics Programs</subject><issn>0960-3174</issn><issn>1573-1375</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kE1LxDAQhoMouK7-AU8Fz9EkkzbpcVn8AsWLnkM-tUvbrEkX1F9v1grePA0Dz_vO8CB0TsklJURcZUoZY5gwwJQw3uL2AC1oLcoKoj5EC9I2BAMV_Bid5LwhhNIG-AI1qyrp0cWh-_KuGnb91OFudP6jyv5958ep0331GMfJV2ud-lgNfnqL7hQdBd1nf_Y7l-jl5vp5fYcfnm7v16sHbIHyCetah8ZzH5i2xhhgog7UCR6MdbIFqJvAQVqQxnhwwkpmA28ogAWiTSGW6GLu3aZY3smT2sRdGstJxSQArbmUpFBspmyKOScf1DZ1g06fihK196NmP6r4UT9-1L4a5lAu8Pjq01_1P6lvXe9n9Q</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Liang, Xinzhu</creator><creator>Yang, Shangda</creator><creator>Cotter, Simon L.</creator><creator>Law, Kody J. H.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20231001</creationdate><title>A randomized multi-index sequential Monte Carlo method</title><author>Liang, Xinzhu ; Yang, Shangda ; Cotter, Simon L. ; Law, Kody J. H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c314t-a5af6e4ef2acbbb3275f1d74fbcd893356f438c38bbe3d7c82cf46133c30ab893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Artificial Intelligence</topic><topic>Bias</topic><topic>Complexity</topic><topic>Computer Science</topic><topic>Estimation</topic><topic>Monte Carlo simulation</topic><topic>Original Paper</topic><topic>Probability and Statistics in Computer Science</topic><topic>Randomization</topic><topic>Statistical Theory and Methods</topic><topic>Statistics and Computing/Statistics Programs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liang, Xinzhu</creatorcontrib><creatorcontrib>Yang, Shangda</creatorcontrib><creatorcontrib>Cotter, Simon L.</creatorcontrib><creatorcontrib>Law, Kody J. H.</creatorcontrib><collection>SpringerOpen (Open Access)</collection><collection>CrossRef</collection><jtitle>Statistics and computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liang, Xinzhu</au><au>Yang, Shangda</au><au>Cotter, Simon L.</au><au>Law, Kody J. H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A randomized multi-index sequential Monte Carlo method</atitle><jtitle>Statistics and computing</jtitle><stitle>Stat Comput</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>33</volume><issue>5</issue><artnum>97</artnum><issn>0960-3174</issn><eissn>1573-1375</eissn><abstract>We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption, this work builds upon a recently introduced multi-index sequential Monte Carlo (SMC) ratio estimator, which provably enjoys the complexity improvements of multi-index Monte Carlo (MIMC) and the efficiency of SMC for inference. The present work leverages a randomization strategy to remove bias entirely, which simplifies estimation substantially, particularly in the MIMC context, where the choice of index set is otherwise important. Under reasonable assumptions, the proposed method provably achieves the same canonical complexity of MSE
-
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as the original method (where MSE is mean squared error), but without discretization bias. It is illustrated on examples of Bayesian inverse and spatial statistics problems.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11222-023-10249-9</doi><oa>free_for_read</oa></addata></record> |
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| source | Springer Online Journals - JUSTICE |
| subjects | Artificial Intelligence Bias Complexity Computer Science Estimation Monte Carlo simulation Original Paper Probability and Statistics in Computer Science Randomization Statistical Theory and Methods Statistics and Computing/Statistics Programs |
| title | A randomized multi-index sequential Monte Carlo method |
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