Loading…
Misspecification in Infinite-Dimensional Bayesian Statistics
We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P₀, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the pri...
Saved in:
| Published in: | The Annals of statistics 2006-04, Vol.34 (2), p.837-877 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-c427t-6018f12d47b960bdbb21e32f5f3d0a25c21fa5f402ccdeb0bb69382247fd63883 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c427t-6018f12d47b960bdbb21e32f5f3d0a25c21fa5f402ccdeb0bb69382247fd63883 |
| container_end_page | 877 |
| container_issue | 2 |
| container_start_page | 837 |
| container_title | The Annals of statistics |
| container_volume | 34 |
| creator | Kleijn, B. J. K. van der Vaart, A. W. |
| description | We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P₀, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback-Leibler divergence with respect to P₀. An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to several examples, with special interest for infinite-dimensional models. These include Gaussian mixtures, nonparametric regression and parametric models. |
| doi_str_mv | 10.1214/009053606000000029 |
| format | article |
| fullrecord | <record><control><sourceid>jstor_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_aos_1151418243</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>25463439</jstor_id><sourcerecordid>25463439</sourcerecordid><originalsourceid>FETCH-LOGICAL-c427t-6018f12d47b960bdbb21e32f5f3d0a25c21fa5f402ccdeb0bb69382247fd63883</originalsourceid><addsrcrecordid>eNpl0M9LwzAUB_AgCs7pPyAIRfBYTV5-NAEP6vw1mHjQnUuaJpDRtTPpDvvvzWiZB3N58PJ535CH0CXBtwQIu8NYYU4FFng4oI7QBIiQuVRCHKPJHuRJsFN0FuMqEa4YnaD7Dx_jxhrvvNG979rMt9m8db71vc2f_dq2MXV1kz3pnY1et9lXn2DsvYnn6MTpJtqLsU7R8vXle_aeLz7f5rPHRW4YFH0uMJGOQM2KSglc1VUFxFJw3NEaa-AGiNPcMQzG1LbCVSUUlQCscLWgUtIpehhyN6FbWdPbrWl8XW6CX-uwKzvty9lyMXbHortYEsIJIxIYTRHXh4ifrY19ueq2If0rKSUUYQXlCcGATOhiDNYdniC43O-5_L_nNHQzJutodOOCbo2Pf5OFAi4FSe5qcKvYd-FwD5wJyqiiv0Wqhjs</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>196914735</pqid></control><display><type>article</type><title>Misspecification in Infinite-Dimensional Bayesian Statistics</title><source>JSTOR Archival Journals and Primary Sources Collection</source><source>Project Euclid Complete</source><creator>Kleijn, B. J. K. ; van der Vaart, A. W.</creator><creatorcontrib>Kleijn, B. J. K. ; van der Vaart, A. W.</creatorcontrib><description>We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P₀, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback-Leibler divergence with respect to P₀. An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to several examples, with special interest for infinite-dimensional models. These include Gaussian mixtures, nonparametric regression and parametric models.</description><identifier>ISSN: 0090-5364</identifier><identifier>EISSN: 2168-8966</identifier><identifier>DOI: 10.1214/009053606000000029</identifier><identifier>CODEN: ASTSC7</identifier><language>eng</language><publisher>Hayward, CA: Institute of Mathematical Statistics</publisher><subject>62F05 ; 62F15 ; 62G07 ; 62G08 ; 62G20 ; Average linear density ; Bayesian Analysis ; Convexity ; Density ; Entropy ; Exact sciences and technology ; infinite-dimensional model ; Logarithms ; Mathematical functions ; Mathematical models ; Mathematics ; Minimax ; Misspecification ; Nonparametric inference ; Parametric inference ; Parametric models ; Perceptron convergence procedure ; posterior distribution ; Probability and statistics ; rate of convergence ; Sciences and techniques of general use ; Statistical methods ; Statistics ; Studies ; Topological theorems</subject><ispartof>The Annals of statistics, 2006-04, Vol.34 (2), p.837-877</ispartof><rights>Copyright 2006 The Institute of Mathematical Statistics</rights><rights>2006 INIST-CNRS</rights><rights>Copyright Institute of Mathematical Statistics Apr 2006</rights><rights>Copyright 2006 Institute of Mathematical Statistics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c427t-6018f12d47b960bdbb21e32f5f3d0a25c21fa5f402ccdeb0bb69382247fd63883</citedby><cites>FETCH-LOGICAL-c427t-6018f12d47b960bdbb21e32f5f3d0a25c21fa5f402ccdeb0bb69382247fd63883</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/25463439$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/25463439$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,780,784,885,926,27922,27923,58236,58469</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17925861$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Kleijn, B. J. K.</creatorcontrib><creatorcontrib>van der Vaart, A. W.</creatorcontrib><title>Misspecification in Infinite-Dimensional Bayesian Statistics</title><title>The Annals of statistics</title><description>We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P₀, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback-Leibler divergence with respect to P₀. An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to several examples, with special interest for infinite-dimensional models. These include Gaussian mixtures, nonparametric regression and parametric models.</description><subject>62F05</subject><subject>62F15</subject><subject>62G07</subject><subject>62G08</subject><subject>62G20</subject><subject>Average linear density</subject><subject>Bayesian Analysis</subject><subject>Convexity</subject><subject>Density</subject><subject>Entropy</subject><subject>Exact sciences and technology</subject><subject>infinite-dimensional model</subject><subject>Logarithms</subject><subject>Mathematical functions</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Minimax</subject><subject>Misspecification</subject><subject>Nonparametric inference</subject><subject>Parametric inference</subject><subject>Parametric models</subject><subject>Perceptron convergence procedure</subject><subject>posterior distribution</subject><subject>Probability and statistics</subject><subject>rate of convergence</subject><subject>Sciences and techniques of general use</subject><subject>Statistical methods</subject><subject>Statistics</subject><subject>Studies</subject><subject>Topological theorems</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNpl0M9LwzAUB_AgCs7pPyAIRfBYTV5-NAEP6vw1mHjQnUuaJpDRtTPpDvvvzWiZB3N58PJ535CH0CXBtwQIu8NYYU4FFng4oI7QBIiQuVRCHKPJHuRJsFN0FuMqEa4YnaD7Dx_jxhrvvNG979rMt9m8db71vc2f_dq2MXV1kz3pnY1et9lXn2DsvYnn6MTpJtqLsU7R8vXle_aeLz7f5rPHRW4YFH0uMJGOQM2KSglc1VUFxFJw3NEaa-AGiNPcMQzG1LbCVSUUlQCscLWgUtIpehhyN6FbWdPbrWl8XW6CX-uwKzvty9lyMXbHortYEsIJIxIYTRHXh4ifrY19ueq2If0rKSUUYQXlCcGATOhiDNYdniC43O-5_L_nNHQzJutodOOCbo2Pf5OFAi4FSe5qcKvYd-FwD5wJyqiiv0Wqhjs</recordid><startdate>20060401</startdate><enddate>20060401</enddate><creator>Kleijn, B. J. K.</creator><creator>van der Vaart, A. W.</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20060401</creationdate><title>Misspecification in Infinite-Dimensional Bayesian Statistics</title><author>Kleijn, B. J. K. ; van der Vaart, A. W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c427t-6018f12d47b960bdbb21e32f5f3d0a25c21fa5f402ccdeb0bb69382247fd63883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>62F05</topic><topic>62F15</topic><topic>62G07</topic><topic>62G08</topic><topic>62G20</topic><topic>Average linear density</topic><topic>Bayesian Analysis</topic><topic>Convexity</topic><topic>Density</topic><topic>Entropy</topic><topic>Exact sciences and technology</topic><topic>infinite-dimensional model</topic><topic>Logarithms</topic><topic>Mathematical functions</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Minimax</topic><topic>Misspecification</topic><topic>Nonparametric inference</topic><topic>Parametric inference</topic><topic>Parametric models</topic><topic>Perceptron convergence procedure</topic><topic>posterior distribution</topic><topic>Probability and statistics</topic><topic>rate of convergence</topic><topic>Sciences and techniques of general use</topic><topic>Statistical methods</topic><topic>Statistics</topic><topic>Studies</topic><topic>Topological theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kleijn, B. J. K.</creatorcontrib><creatorcontrib>van der Vaart, A. W.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kleijn, B. J. K.</au><au>van der Vaart, A. W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Misspecification in Infinite-Dimensional Bayesian Statistics</atitle><jtitle>The Annals of statistics</jtitle><date>2006-04-01</date><risdate>2006</risdate><volume>34</volume><issue>2</issue><spage>837</spage><epage>877</epage><pages>837-877</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><coden>ASTSC7</coden><abstract>We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P₀, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback-Leibler divergence with respect to P₀. An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to several examples, with special interest for infinite-dimensional models. These include Gaussian mixtures, nonparametric regression and parametric models.</abstract><cop>Hayward, CA</cop><pub>Institute of Mathematical Statistics</pub><doi>10.1214/009053606000000029</doi><tpages>41</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0090-5364 |
| ispartof | The Annals of statistics, 2006-04, Vol.34 (2), p.837-877 |
| issn | 0090-5364 2168-8966 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_aos_1151418243 |
| source | JSTOR Archival Journals and Primary Sources Collection; Project Euclid Complete |
| subjects | 62F05 62F15 62G07 62G08 62G20 Average linear density Bayesian Analysis Convexity Density Entropy Exact sciences and technology infinite-dimensional model Logarithms Mathematical functions Mathematical models Mathematics Minimax Misspecification Nonparametric inference Parametric inference Parametric models Perceptron convergence procedure posterior distribution Probability and statistics rate of convergence Sciences and techniques of general use Statistical methods Statistics Studies Topological theorems |
| title | Misspecification in Infinite-Dimensional Bayesian Statistics |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-10T06%3A38%3A26IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Misspecification%20in%20Infinite-Dimensional%20Bayesian%20Statistics&rft.jtitle=The%20Annals%20of%20statistics&rft.au=Kleijn,%20B.%20J.%20K.&rft.date=2006-04-01&rft.volume=34&rft.issue=2&rft.spage=837&rft.epage=877&rft.pages=837-877&rft.issn=0090-5364&rft.eissn=2168-8966&rft.coden=ASTSC7&rft_id=info:doi/10.1214/009053606000000029&rft_dat=%3Cjstor_proje%3E25463439%3C/jstor_proje%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c427t-6018f12d47b960bdbb21e32f5f3d0a25c21fa5f402ccdeb0bb69382247fd63883%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=196914735&rft_id=info:pmid/&rft_jstor_id=25463439&rfr_iscdi=true |