Diagnostic tools for approximate Bayesian computation using the coverage property
Identifieur interne : 002544 ( Istex/Corpus ); précédent : 002543; suivant : 002545Diagnostic tools for approximate Bayesian computation using the coverage property
Auteurs : D. Prangle ; M. G. B. Blum ; G. Popovic ; S. A. SissonSource :
- Australian & New Zealand Journal of Statistics [ 1369-1473 ] ; 2014-12.
Abstract
Approximate Bayesian computation (ABC) is an approach to sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model, parameter and dataset triples from the prior, and then accepting as samples from the approximate posterior, those model and parameter pairs for which the corresponding dataset, or a summary of that dataset, is ‘close’ to the observed data. Closeness is typically determined though a distance measure and a kernel scale parameter. Appropriate choice of that parameter is important in producing a good quality approximation. This paper proposes diagnostic tools for the choice of the kernel scale parameter based on assessing the coverage property, which asserts that credible intervals have the correct coverage levels in appropriately designed simulation settings. We provide theoretical results on coverage for both model and parameter inference, and adapt these into diagnostics for the ABC context. We re‐analyse a study on human demographic history to determine whether the adopted posterior approximation was appropriate. Code implementing the proposed methodology is freely available in the R package abctools.
Url:
DOI: 10.1111/anzs.12087
Links to Exploration step
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Diagnostic tools for approximate Bayesian computation using the coverage property</title><author><name sortKey="Prangle, D" sort="Prangle, D" uniqKey="Prangle D" first="D." last="Prangle">D. Prangle</name><affiliation><mods:affiliation>Mathematics and Statistics Department, Lancaster University, Lancaster, UK</mods:affiliation></affiliation></author><author><name sortKey="Blum, M G B" sort="Blum, M G B" uniqKey="Blum M" first="M. G. B." last="Blum">M. G. B. Blum</name><affiliation><mods:affiliation>Centre National de la Recherche Scientifique, Laboratoire TIMC‐IMAG, UMR 5525, Université Joseph Fourier, F‐38041, Grenoble, France</mods:affiliation></affiliation></author><author><name sortKey="Popovic, G" sort="Popovic, G" uniqKey="Popovic G" first="G." last="Popovic">G. 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Sisson</name><affiliation><mods:affiliation>School of Mathematics and Statistics, University of New South Wales, Sydney, Australia</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: Scott.Sisson@unsw.edu.au</mods:affiliation></affiliation><affiliation><mods:affiliation>Correspondence address: Author to whom correspondence should be addressed.</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j" type="main">Australian & New Zealand Journal of Statistics</title><title level="j" type="alt">AUSTRALIAN AND NEW ZEALAND JOURNAL OF STATISTICS</title><idno type="ISSN">1369-1473</idno><idno type="eISSN">1467-842X</idno><imprint><biblScope unit="vol">56</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="309">309</biblScope><biblScope unit="page" to="329">329</biblScope><biblScope unit="page-count">21</biblScope><date type="published" when="2014-12">2014-12</date></imprint><idno type="ISSN">1369-1473</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1369-1473</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract">Approximate Bayesian computation (ABC) is an approach to sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. 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Code implementing the proposed methodology is freely available in the R package abctools.</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>D. Prangle</name><affiliations><json:string>Mathematics and Statistics Department, Lancaster University, Lancaster, UK</json:string></affiliations></json:item><json:item><name>M. G. B. Blum</name><affiliations><json:string>Centre National de la Recherche Scientifique, Laboratoire TIMC‐IMAG, UMR 5525, Université Joseph Fourier, F‐38041, Grenoble, France</json:string></affiliations></json:item><json:item><name>G. Popovic</name><affiliations><json:string>School of Mathematics and Statistics, University of New South Wales, Sydney, Australia</json:string></affiliations></json:item><json:item><name>S. A. 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A.</forename><surname>Sisson</surname></persName><email>Scott.Sisson@unsw.edu.au</email><affiliation><orgName>School of Mathematics and Statistics</orgName><orgName>University of New South Wales</orgName><address><settlement type="city">Sydney</settlement><country key="AU">Australia</country></address></affiliation><affiliation>Author to whom correspondence should be addressed.</affiliation></author><idno type="istex">C939A1CF7BD18ECF3250E937CC7214BB4FD1807F</idno><idno type="ark">ark:/67375/WNG-SWPFLWXV-W</idno><idno type="DOI">10.1111/anzs.12087</idno><idno type="unit">ANZS12087</idno><idno type="toTypesetVersion">file:ANZS.ANZS12087.pdf</idno></analytic><monogr><title level="j" type="main">Australian & New Zealand Journal of Statistics</title><title level="j" type="alt">AUSTRALIAN AND NEW ZEALAND JOURNAL OF STATISTICS</title><idno type="pISSN">1369-1473</idno><idno type="eISSN">1467-842X</idno><idno type="book-DOI">10.1111/(ISSN)1467-842X</idno><idno type="book-part-DOI">10.1111/anzs.2014.56.issue-4</idno><idno type="product">ANZS</idno><imprint><biblScope unit="vol">56</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="309">309</biblScope><biblScope unit="page" to="329">329</biblScope><biblScope unit="page-count">21</biblScope><date type="published" when="2014-12"></date></imprint></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><abstract style="main" xml:id="anzs12087-abs-0001"><head>Summary</head><p>Approximate Bayesian computation (ABC) is an approach to sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. 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Code implementing the proposed methodology is freely available in the <emph><span>R</span></emph> package <emph><span>abctools</span></emph>.</p></abstract><textClass><keywords><term xml:id="anzs12087-kwd-0001">likelihood‐free inference</term><term xml:id="anzs12087-kwd-0002">model inference</term><term xml:id="anzs12087-kwd-0003">parameter inference</term></keywords><keywords rend="articleCategory"><term>Invited Paper</term></keywords><keywords rend="tocHeading1"><term>Invited Papers</term></keywords></textClass><langUsage><language ident="en"></language></langUsage></profileDesc></teiHeader></istex:fulltextTEI></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component type="serialArticle" version="2.0" xml:id="anzs12087" xml:lang="en"><header><publicationMeta level="product"><doi origin="wiley" registered="yes">10.1111/(ISSN)1467-842X</doi><issn type="print">1369-1473</issn><issn type="electronic">1467-842X</issn><idGroup><id type="product" value="ANZS"></id></idGroup><titleGroup><title sort="AUSTRALIAN AND NEW ZEALAND JOURNAL OF STATISTICS" type="main">Australian & New Zealand Journal of Statistics</title><title type="short">Aust. N. Z. J. Stat.</title></titleGroup></publicationMeta><publicationMeta level="part" position="40"><doi origin="wiley">10.1111/anzs.2014.56.issue-4</doi><copyright ownership="thirdParty">Copyright © 2014 Australian Statistical Publishing Association Inc.</copyright><numberingGroup><numbering type="journalVolume" number="56">56</numbering><numbering type="journalIssue">4</numbering></numberingGroup><coverDate startDate="2014-12">December 2014</coverDate></publicationMeta><publicationMeta level="unit" position="10" status="forIssue" type="article"><doi>10.1111/anzs.12087</doi><idGroup><id type="unit" value="ANZS12087"></id></idGroup><countGroup><count number="21" type="pageTotal"></count></countGroup><titleGroup><title type="articleCategory">Invited Paper</title><title type="tocHeading1">Invited Papers</title></titleGroup><copyright ownership="publisher">© 2014 Australian Statistical Publishing Association Inc. 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G. B.</givenNames> <familyName>Blum</familyName></personName></creator><creator affiliationRef="#anzs12087-aff-0003" creatorRole="author" xml:id="anzs12087-cr-0003"><personName><givenNames>G.</givenNames> <familyName>Popovic</familyName></personName></creator><creator affiliationRef="#anzs12087-aff-0003" corresponding="yes" creatorRole="author" xml:id="anzs12087-cr-0004"><personName><givenNames>S. A.</givenNames> <familyName>Sisson</familyName></personName><contactDetails><email>Scott.Sisson@unsw.edu.au</email></contactDetails></creator></creators><affiliationGroup><affiliation countryCode="GB" type="organization" xml:id="anzs12087-aff-0001"><orgDiv>Mathematics and Statistics Department</orgDiv> <orgName>Lancaster University</orgName> <address><city>Lancaster</city> <country>UK</country></address></affiliation><affiliation countryCode="FR" type="organization" xml:id="anzs12087-aff-0002"><orgDiv>Centre National de la Recherche Scientifique, Laboratoire TIMC‐IMAG, UMR 5525</orgDiv> <orgName>Université Joseph Fourier</orgName> <address><city>Grenoble</city> <postCode>F‐38041</postCode><country>France</country></address></affiliation><affiliation countryCode="AU" type="organization" xml:id="anzs12087-aff-0003"><orgDiv>School of Mathematics and Statistics</orgDiv> <orgName>University of New South Wales</orgName> <address><city>Sydney</city> <country>Australia</country></address></affiliation></affiliationGroup><keywordGroup type="author"><keyword xml:id="anzs12087-kwd-0001">likelihood‐free inference</keyword><keyword xml:id="anzs12087-kwd-0002">model inference</keyword><keyword xml:id="anzs12087-kwd-0003">parameter inference</keyword></keywordGroup><fundingInfo><fundingAgency>Australian Research Council</fundingAgency><fundingNumber>DP1092805</fundingNumber></fundingInfo><supportingInformation><supportingInfoItem><mediaResource alt="supporting" mimeType="application/PDF" href="urn-x:wiley:13691473:media:anzs12087:anzs12087-sup-0001-FigureS1-S6"></mediaResource><caption><p>Figure S1. As Figure <link href="#anzs12087-fig-0001"></link> (main text), but with <i>K</i> = 500.</p><p>Figure S2. As Figure <link href="#anzs12087-fig-0001"></link> (main text), but with <i>K</i> = 100</p><p>Figure S3. As for Figure <link href="#anzs12087-fig-0004"></link> (main text), but for the remaining model parameters <i>T</i><sub><i>g</i></sub>, <i>b</i>,<i> N</i><sub><i>B</i></sub>, <i>T</i><sub>dur</sub> and <i>n</i>.</p><p>Figure S4. As for Figure <link href="#anzs12087-fig-0005"></link> (main text), but for the remaining model parameters <i>T</i><sub><i>g</i></sub>, <i>b</i>,<i> N</i><sub><i>B</i></sub>, <i>T</i><sub>dur</sub> and <i>n</i>.</p><p>Figure S5. Histograms of the <i>K</i> = 200 <i>p</i><sub>0</sub> estimates for the parameters <i>d</i>,<i> N</i><sub>0</sub>, <i>N</i><sub><i>A</i></sub> and <i>T</i><sub><i>b</i></sub> in the human demographic history analysis, with <i>ε</i>=1:36. Regression‐adjusted post‐processing is not implemented. Rows correspond to individual parameters; columns correspond to the three models.</p><p>Figure S6. Histograms of the <i>K</i>=200 <i>p</i><sub>0</sub> estimates for the parameters <i>d</i>,<i> N</i><sub>0</sub>, <i>N</i><sub><i>A</i></sub> and <i>T</i><sub><i>b</i></sub> in the human demographic history analysis, with <i>ε</i>=1:36. Regression‐adjusted post‐processing has been implemented. Rows correspond to individual parameters; columns correspond to the three models.</p></caption></supportingInfoItem></supportingInformation><abstractGroup><abstract type="main" xml:id="anzs12087-abs-0001"><title type="main">Summary</title><p>Approximate Bayesian computation (ABC) is an approach to sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model, parameter and dataset triples from the prior, and then accepting as samples from the approximate posterior, those model and parameter pairs for which the corresponding dataset, or a summary of that dataset, is ‘close’ to the observed data. Closeness is typically determined though a distance measure and a kernel scale parameter. Appropriate choice of that parameter is important in producing a good quality approximation. This paper proposes diagnostic tools for the choice of the kernel scale parameter based on assessing the coverage property, which asserts that credible intervals have the correct coverage levels in appropriately designed simulation settings. We provide theoretical results on coverage for both model and parameter inference, and adapt these into diagnostics for the ABC context. We re‐analyse a study on human demographic history to determine whether the adopted posterior approximation was appropriate. Code implementing the proposed methodology is freely available in the <span cssStyle="font-family:sans-serif">R</span> package <span cssStyle="font-family:monospace">abctools</span>.</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Diagnostic tools for approximate Bayesian computation using the coverage property</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Diagnostic tools for approximate Bayesian computation using the coverage property</title></titleInfo><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Prangle</namePart><affiliation>Mathematics and Statistics Department, Lancaster University, Lancaster, UK</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M. G. B.</namePart><namePart type="family">Blum</namePart><affiliation>Centre National de la Recherche Scientifique, Laboratoire TIMC‐IMAG, UMR 5525, Université Joseph Fourier, F‐38041, Grenoble, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">G.</namePart><namePart type="family">Popovic</namePart><affiliation>School of Mathematics and Statistics, University of New South Wales, Sydney, Australia</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S. A.</namePart><namePart type="family">Sisson</namePart><affiliation>School of Mathematics and Statistics, University of New South Wales, Sydney, Australia</affiliation><affiliation>E-mail: Scott.Sisson@unsw.edu.au</affiliation><affiliation>Correspondence address: Author to whom correspondence should be addressed.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</genre><originInfo><publisher>Blackwell Publishing Ltd</publisher><dateIssued encoding="w3cdtf">2014-12</dateIssued><dateCreated encoding="w3cdtf">2014-09-22</dateCreated><copyrightDate encoding="w3cdtf">2014</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract>Approximate Bayesian computation (ABC) is an approach to sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model, parameter and dataset triples from the prior, and then accepting as samples from the approximate posterior, those model and parameter pairs for which the corresponding dataset, or a summary of that dataset, is ‘close’ to the observed data. Closeness is typically determined though a distance measure and a kernel scale parameter. Appropriate choice of that parameter is important in producing a good quality approximation. This paper proposes diagnostic tools for the choice of the kernel scale parameter based on assessing the coverage property, which asserts that credible intervals have the correct coverage levels in appropriately designed simulation settings. We provide theoretical results on coverage for both model and parameter inference, and adapt these into diagnostics for the ABC context. We re‐analyse a study on human demographic history to determine whether the adopted posterior approximation was appropriate. Code implementing the proposed methodology is freely available in the R package abctools.</abstract><note type="additional physical form">Figure S1. As Figure (main text), but with K = 500. Figure S2. As Figure (main text), but with K = 100 Figure S3. As for Figure (main text), but for the remaining model parameters Tg, b, NB, Tdur and n. Figure S4. As for Figure (main text), but for the remaining model parameters Tg, b, NB, Tdur and n. Figure S5. Histograms of the K = 200 p0 estimates for the parameters d, N0, NA and Tb in the human demographic history analysis, with ε=1:36. Regression‐adjusted post‐processing is not implemented. Rows correspond to individual parameters; columns correspond to the three models. Figure S6. Histograms of the K=200 p0 estimates for the parameters d, N0, NA and Tb in the human demographic history analysis, with ε=1:36. Regression‐adjusted post‐processing has been implemented. Rows correspond to individual parameters; columns correspond to the three models.</note><note type="funding">Australian Research Council - No. DP1092805; </note><subject><genre>keywords</genre><topic>likelihood‐free inference</topic><topic>model inference</topic><topic>parameter inference</topic></subject><relatedItem type="host"><titleInfo><title>Australian & New Zealand Journal of Statistics</title></titleInfo><titleInfo type="abbreviated"><title>Aust. N. Z. J. Stat.</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><subject><genre>article-category</genre><topic>Invited Paper</topic></subject><identifier type="ISSN">1369-1473</identifier><identifier type="eISSN">1467-842X</identifier><identifier type="DOI">10.1111/(ISSN)1467-842X</identifier><identifier type="PublisherID">ANZS</identifier><part><date>2014</date><detail type="volume"><caption>vol.</caption><number>56</number></detail><detail type="issue"><caption>no.</caption><number>4</number></detail><extent unit="pages"><start>309</start><end>329</end><total>21</total></extent></part></relatedItem><identifier type="istex">C939A1CF7BD18ECF3250E937CC7214BB4FD1807F</identifier><identifier type="ark">ark:/67375/WNG-SWPFLWXV-W</identifier><identifier type="DOI">10.1111/anzs.12087</identifier><identifier type="ArticleID">ANZS12087</identifier><accessCondition type="use and reproduction" contentType="copyright">Copyright © 2014 Australian Statistical Publishing Association Inc.© 2014 Australian Statistical Publishing Association Inc. 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