Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the part...
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Veröffentlicht in: | Probability theory and related fields 2013-04, Vol.155 (3-4), p.665-701 |
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description | We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the particle system approximation. In a few simple examples, including high dimensional product measures, bounds with explicit constants of feasible size are obtained. Our main motivation are applications to sequential MCMC methods for Monte Carlo integral estimation. |
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Our main motivation are applications to sequential MCMC methods for Monte Carlo integral estimation.</description><subject>Approximation</subject><subject>Chain mobility</subject><subject>Constants</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Economics</subject><subject>Evolution</subject><subject>Finance</subject><subject>Importance sampling</subject><subject>Insurance</subject><subject>Management</subject><subject>Markov analysis</subject><subject>Markov chains</subject><subject>Mathematical and Computational Biology</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Monte Carlo methods</subject><subject>Monte Carlo simulation</subject><subject>Operations Research/Decision Theory</subject><subject>Probability</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Quantitative Finance</subject><subject>Regularity</subject><subject>Resampling</subject><subject>Statistics for Business</subject><subject>System dynamics</subject><subject>Theoretical</subject><issn>0178-8051</issn><issn>1432-2064</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kEtLAzEUhYMoWKs_wF3AjZvRm8e8llJ8QYsIug53ZpJ26jSpyUxx_r0pFQTBVbjkO4fDR8glgxsGkN8GACkhAcYTkAyS8YhMmBQ84ZDJYzIBlhdJASk7JWchrAGAC8knpHsd0PZtj3270xS3W---2k28nA3UGap3rtu1dknjR4VV27X9SDcaw-B1oGgbGvTnoGMFdnSB_sPtaL3C1tKFs72mM_Sdi4F-5ZpwTk4MdkFf_LxT8v5w_zZ7SuYvj8-zu3lSi5L3SV43UPFMGsyLpkwLYaDSdZrKskRkzGAJLJVgRM3yDIoKoDRNWqZSojG1yMWUXB964-g4LvRq04Zadx1a7YagmJClFHkhZUSv_qBrN3gb1ymeZSyu4HxfyA5U7V0IXhu19dGSHxUDtfevDv5V9K_2_tUYM_yQCZG1S-1_m_8PfQNoXYoG</recordid><startdate>20130401</startdate><enddate>20130401</enddate><creator>Eberle, Andreas</creator><creator>Marinelli, Carlo</creator><general>Springer-Verlag</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20130401</creationdate><title>Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods</title><author>Eberle, Andreas ; Marinelli, Carlo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c392t-7cd0b264fa78d9583f0bec55499aa11fa901540f3c17608b009fd59544affc373</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Approximation</topic><topic>Chain mobility</topic><topic>Constants</topic><topic>Dynamical systems</topic><topic>Dynamics</topic><topic>Economics</topic><topic>Evolution</topic><topic>Finance</topic><topic>Importance sampling</topic><topic>Insurance</topic><topic>Management</topic><topic>Markov analysis</topic><topic>Markov chains</topic><topic>Mathematical and Computational Biology</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Monte Carlo methods</topic><topic>Monte Carlo simulation</topic><topic>Operations Research/Decision Theory</topic><topic>Probability</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Quantitative Finance</topic><topic>Regularity</topic><topic>Resampling</topic><topic>Statistics for Business</topic><topic>System dynamics</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Eberle, Andreas</creatorcontrib><creatorcontrib>Marinelli, Carlo</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>ProQuest Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer science database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering 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>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>ProQuest research library</collection><collection>ProQuest Science Journals</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>One Business (ProQuest)</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering collection</collection><collection>ProQuest Central Basic</collection><jtitle>Probability theory and related fields</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Eberle, Andreas</au><au>Marinelli, Carlo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods</atitle><jtitle>Probability theory and related fields</jtitle><stitle>Probab. 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subjects | Approximation Chain mobility Constants Dynamical systems Dynamics Economics Evolution Finance Importance sampling Insurance Management Markov analysis Markov chains Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Monte Carlo methods Monte Carlo simulation Operations Research/Decision Theory Probability Probability Theory and Stochastic Processes Quantitative Finance Regularity Resampling Statistics for Business System dynamics Theoretical |
title | Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods |
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