Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors

Consider a standard conjugate family of prior distributions for a vector-parameter indexing an exponential family. Two distinct model parameterizations may well lead to standard conjugate families which are not consistent, i.e. one family cannot be derived from the other by the usual change-of-varia...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Scandinavian journal of statistics 2001-06, Vol.28 (2), p.377-406
Hauptverfasser: Consonni, Guido, Veronese, Piero
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 406
container_issue 2
container_start_page 377
container_title Scandinavian journal of statistics
container_volume 28
creator Consonni, Guido
Veronese, Piero
description Consider a standard conjugate family of prior distributions for a vector-parameter indexing an exponential family. Two distinct model parameterizations may well lead to standard conjugate families which are not consistent, i.e. one family cannot be derived from the other by the usual change-of-variable technique. This raises the problem of finding suitable parameterizations that may lead to enriched conjugate families which are more flexible than the traditional ones. The previous remark motivates the definition of a new property for an exponential family, named conditional reducibility. Features of conditionally-reducible natural exponential families are investigated thoroughly. In particular, we relate this new property to the notion of cut, and show that conditionally-reducible families admit a reparameterization in terms of a vector having likelihood-independent components. A general methodology to obtain enriched conjugate distributions for conditionally-reducible families is described in detail, generalizing previous works and more recent contributions in the area. The theory is illustrated with reference to natural exponential families having simple quadratic variance function.
doi_str_mv 10.1111/1467-9469.00243
format Article
fullrecord <record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1111_1467_9469_00243</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>4616665</jstor_id><sourcerecordid>4616665</sourcerecordid><originalsourceid>FETCH-LOGICAL-c5053-a180afd1977b486408e0695e9d3125a1bc8e83eb1a262589ce21b420fd0031b93</originalsourceid><addsrcrecordid>eNqFUE1P3DAQtRCVWChnLhxy4BqwY8cfxypaoAhBBRQkLtbEcYoXbxLZ2Zb993WaatVbLY1n5Jn35vkhdELwOUnngjAucsW4Ose4YHQPLXYv-2iBKaY5l0oeoMMYVxgTzohcoIeq7xo3ur4D77fZg202xtXeZncwbgL4bPkx9J3tRpfqS1g772zMoGuyZRecebNNlhhWmx8w2uxbcH2In9GnFny0x3_zEfp-uXyqrvPb-6uv1Zfb3JS4pDkQiaFtiBKiZpIzLC3mqrSqoaQogdRGWkltTaDgRSmVsQWpWYHbBmNKakWP0MXMa0IfY7CtHoJbQ9hqgvVkiZ4M0JMB-o8lCXEzI4IdrNmN1x6iWcUR9E9NoZDp2k5FMiklN5UphhRUCM0w12_jOpGdzWRDQoNvA3TGxX80CCHUtJPNY7-ct9v_SdSPN_ePs9TTGZZ09WEHY5xwzsvUzue2i6P92LUhvGsuqCj1y92Vrp7ocyXSf17pbz_KoRE</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors</title><source>RePEc</source><source>JSTOR Mathematics &amp; Statistics</source><source>EBSCOhost Business Source Complete</source><source>Access via Wiley Online Library</source><source>Jstor Complete Legacy</source><creator>Consonni, Guido ; Veronese, Piero</creator><creatorcontrib>Consonni, Guido ; Veronese, Piero</creatorcontrib><description>Consider a standard conjugate family of prior distributions for a vector-parameter indexing an exponential family. Two distinct model parameterizations may well lead to standard conjugate families which are not consistent, i.e. one family cannot be derived from the other by the usual change-of-variable technique. This raises the problem of finding suitable parameterizations that may lead to enriched conjugate families which are more flexible than the traditional ones. The previous remark motivates the definition of a new property for an exponential family, named conditional reducibility. Features of conditionally-reducible natural exponential families are investigated thoroughly. In particular, we relate this new property to the notion of cut, and show that conditionally-reducible families admit a reparameterization in terms of a vector having likelihood-independent components. A general methodology to obtain enriched conjugate distributions for conditionally-reducible families is described in detail, generalizing previous works and more recent contributions in the area. The theory is illustrated with reference to natural exponential families having simple quadratic variance function.</description><identifier>ISSN: 0303-6898</identifier><identifier>EISSN: 1467-9469</identifier><identifier>DOI: 10.1111/1467-9469.00243</identifier><language>eng</language><publisher>Oxford, UK and Boston, USA: Blackwell Publishers Ltd</publisher><subject>Bayesian inference ; conditional reducibility ; cut ; Density ; enriched prior ; Exact sciences and technology ; exponential family ; Linear inference, regression ; Linear transformations ; Mathematical independent variables ; Mathematical vectors ; Mathematics ; Matrices ; Parameterization ; Parametric inference ; Probabilities ; Probability and statistics ; Respect ; Sciences and techniques of general use ; simple quadratic variance function ; Statistical theories ; Statistical variance ; Statistics</subject><ispartof>Scandinavian journal of statistics, 2001-06, Vol.28 (2), p.377-406</ispartof><rights>Copyright 2001 Board of the Foundation of the Scandinavian Journal of Statistics</rights><rights>Board of the Foundation of the Scandinavian Journal of Statistics 2001</rights><rights>2001 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c5053-a180afd1977b486408e0695e9d3125a1bc8e83eb1a262589ce21b420fd0031b93</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/4616665$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/4616665$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,1417,4008,27924,27925,45574,45575,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=1077793$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/blascjsta/v_3a28_3ay_3a2001_3ai_3a2_3ap_3a377-406.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Consonni, Guido</creatorcontrib><creatorcontrib>Veronese, Piero</creatorcontrib><title>Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors</title><title>Scandinavian journal of statistics</title><description>Consider a standard conjugate family of prior distributions for a vector-parameter indexing an exponential family. Two distinct model parameterizations may well lead to standard conjugate families which are not consistent, i.e. one family cannot be derived from the other by the usual change-of-variable technique. This raises the problem of finding suitable parameterizations that may lead to enriched conjugate families which are more flexible than the traditional ones. The previous remark motivates the definition of a new property for an exponential family, named conditional reducibility. Features of conditionally-reducible natural exponential families are investigated thoroughly. In particular, we relate this new property to the notion of cut, and show that conditionally-reducible families admit a reparameterization in terms of a vector having likelihood-independent components. A general methodology to obtain enriched conjugate distributions for conditionally-reducible families is described in detail, generalizing previous works and more recent contributions in the area. The theory is illustrated with reference to natural exponential families having simple quadratic variance function.</description><subject>Bayesian inference</subject><subject>conditional reducibility</subject><subject>cut</subject><subject>Density</subject><subject>enriched prior</subject><subject>Exact sciences and technology</subject><subject>exponential family</subject><subject>Linear inference, regression</subject><subject>Linear transformations</subject><subject>Mathematical independent variables</subject><subject>Mathematical vectors</subject><subject>Mathematics</subject><subject>Matrices</subject><subject>Parameterization</subject><subject>Parametric inference</subject><subject>Probabilities</subject><subject>Probability and statistics</subject><subject>Respect</subject><subject>Sciences and techniques of general use</subject><subject>simple quadratic variance function</subject><subject>Statistical theories</subject><subject>Statistical variance</subject><subject>Statistics</subject><issn>0303-6898</issn><issn>1467-9469</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqFUE1P3DAQtRCVWChnLhxy4BqwY8cfxypaoAhBBRQkLtbEcYoXbxLZ2Zb993WaatVbLY1n5Jn35vkhdELwOUnngjAucsW4Ose4YHQPLXYv-2iBKaY5l0oeoMMYVxgTzohcoIeq7xo3ur4D77fZg202xtXeZncwbgL4bPkx9J3tRpfqS1g772zMoGuyZRecebNNlhhWmx8w2uxbcH2In9GnFny0x3_zEfp-uXyqrvPb-6uv1Zfb3JS4pDkQiaFtiBKiZpIzLC3mqrSqoaQogdRGWkltTaDgRSmVsQWpWYHbBmNKakWP0MXMa0IfY7CtHoJbQ9hqgvVkiZ4M0JMB-o8lCXEzI4IdrNmN1x6iWcUR9E9NoZDp2k5FMiklN5UphhRUCM0w12_jOpGdzWRDQoNvA3TGxX80CCHUtJPNY7-ct9v_SdSPN_ePs9TTGZZ09WEHY5xwzsvUzue2i6P92LUhvGsuqCj1y92Vrp7ocyXSf17pbz_KoRE</recordid><startdate>200106</startdate><enddate>200106</enddate><creator>Consonni, Guido</creator><creator>Veronese, Piero</creator><general>Blackwell Publishers Ltd</general><general>Blackwell Publishers</general><general>Blackwell</general><general>Danish Society for Theoretical Statistics</general><scope>BSCLL</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>200106</creationdate><title>Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors</title><author>Consonni, Guido ; Veronese, Piero</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c5053-a180afd1977b486408e0695e9d3125a1bc8e83eb1a262589ce21b420fd0031b93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Bayesian inference</topic><topic>conditional reducibility</topic><topic>cut</topic><topic>Density</topic><topic>enriched prior</topic><topic>Exact sciences and technology</topic><topic>exponential family</topic><topic>Linear inference, regression</topic><topic>Linear transformations</topic><topic>Mathematical independent variables</topic><topic>Mathematical vectors</topic><topic>Mathematics</topic><topic>Matrices</topic><topic>Parameterization</topic><topic>Parametric inference</topic><topic>Probabilities</topic><topic>Probability and statistics</topic><topic>Respect</topic><topic>Sciences and techniques of general use</topic><topic>simple quadratic variance function</topic><topic>Statistical theories</topic><topic>Statistical variance</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Consonni, Guido</creatorcontrib><creatorcontrib>Veronese, Piero</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><jtitle>Scandinavian journal of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Consonni, Guido</au><au>Veronese, Piero</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors</atitle><jtitle>Scandinavian journal of statistics</jtitle><date>2001-06</date><risdate>2001</risdate><volume>28</volume><issue>2</issue><spage>377</spage><epage>406</epage><pages>377-406</pages><issn>0303-6898</issn><eissn>1467-9469</eissn><abstract>Consider a standard conjugate family of prior distributions for a vector-parameter indexing an exponential family. Two distinct model parameterizations may well lead to standard conjugate families which are not consistent, i.e. one family cannot be derived from the other by the usual change-of-variable technique. This raises the problem of finding suitable parameterizations that may lead to enriched conjugate families which are more flexible than the traditional ones. The previous remark motivates the definition of a new property for an exponential family, named conditional reducibility. Features of conditionally-reducible natural exponential families are investigated thoroughly. In particular, we relate this new property to the notion of cut, and show that conditionally-reducible families admit a reparameterization in terms of a vector having likelihood-independent components. A general methodology to obtain enriched conjugate distributions for conditionally-reducible families is described in detail, generalizing previous works and more recent contributions in the area. The theory is illustrated with reference to natural exponential families having simple quadratic variance function.</abstract><cop>Oxford, UK and Boston, USA</cop><pub>Blackwell Publishers Ltd</pub><doi>10.1111/1467-9469.00243</doi><tpages>30</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0303-6898
ispartof Scandinavian journal of statistics, 2001-06, Vol.28 (2), p.377-406
issn 0303-6898
1467-9469
language eng
recordid cdi_crossref_primary_10_1111_1467_9469_00243
source RePEc; JSTOR Mathematics & Statistics; EBSCOhost Business Source Complete; Access via Wiley Online Library; Jstor Complete Legacy
subjects Bayesian inference
conditional reducibility
cut
Density
enriched prior
Exact sciences and technology
exponential family
Linear inference, regression
Linear transformations
Mathematical independent variables
Mathematical vectors
Mathematics
Matrices
Parameterization
Parametric inference
Probabilities
Probability and statistics
Respect
Sciences and techniques of general use
simple quadratic variance function
Statistical theories
Statistical variance
Statistics
title Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-24T19%3A57%3A37IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Conditionally%20Reducible%20Natural%20Exponential%20Families%20and%20Enriched%20Conjugate%20Priors&rft.jtitle=Scandinavian%20journal%20of%20statistics&rft.au=Consonni,%20Guido&rft.date=2001-06&rft.volume=28&rft.issue=2&rft.spage=377&rft.epage=406&rft.pages=377-406&rft.issn=0303-6898&rft.eissn=1467-9469&rft_id=info:doi/10.1111/1467-9469.00243&rft_dat=%3Cjstor_cross%3E4616665%3C/jstor_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=4616665&rfr_iscdi=true