Regularized Posteriors in Linear Ill‐Posed Inverse Problems
Identifieur interne : 000012 ( Main/Exploration ); précédent : 000011; suivant : 000013Regularized Posteriors in Linear Ill‐Posed Inverse Problems
Auteurs : Jean-Pierre Florens ; Anna SimoniSource :
- Scandinavian Journal of Statistics [ 0303-6898 ] ; 2012-06.
English descriptors
- KwdEn :
Abstract
Abstract. We study the Bayesian solution of a linear inverse problem in a separable Hilbert space setting with Gaussian prior and noise distribution. Our contribution is to propose a new Bayes estimator which is a linear and continuous estimator on the whole space and is stronger than the mean of the exact Gaussian posterior distribution which is only defined as a measurable linear transformation. Our estimator is the mean of a slightly modified posterior distribution called regularized posterior distribution. Frequentist consistency of our estimator and of the regularized posterior distribution is proved. A Monte Carlo study and an application to real data confirm good small‐sample properties of our procedure.
Url:
DOI: 10.1111/j.1467-9469.2011.00784.x
Affiliations:
Links toward previous steps (curation, corpus...)
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Regularized Posteriors in Linear Ill‐Posed Inverse Problems</title><author><name sortKey="Florens, Jean Ierre" sort="Florens, Jean Ierre" uniqKey="Florens J" first="Jean-Pierre" last="Florens">Jean-Pierre Florens</name></author><author><name sortKey="Simoni, Anna" sort="Simoni, Anna" uniqKey="Simoni A" first="Anna" last="Simoni">Anna Simoni</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:D5C34B2985C80181772F07C0F2354A51F839C013</idno><date when="2012" year="2012">2012</date><idno type="doi">10.1111/j.1467-9469.2011.00784.x</idno><idno type="url">https://api.istex.fr/document/D5C34B2985C80181772F07C0F2354A51F839C013/fulltext/pdf</idno><idno type="wicri:Area/Main/Corpus">000F55</idno><idno type="wicri:explorRef" wicri:stream="Main" wicri:step="Corpus" wicri:corpus="ISTEX">000F55</idno><idno type="wicri:Area/Main/Curation">000F55</idno><idno type="wicri:Area/Main/Exploration">000012</idno><idno type="wicri:explorRef" wicri:stream="Main" wicri:step="Exploration">000012</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Regularized Posteriors in Linear Ill‐Posed Inverse Problems</title><author><name sortKey="Florens, Jean Ierre" sort="Florens, Jean Ierre" uniqKey="Florens J" first="Jean-Pierre" last="Florens">Jean-Pierre Florens</name><affiliation><wicri:noCountry code="subField">Capitole</wicri:noCountry></affiliation></author><author><name sortKey="Simoni, Anna" sort="Simoni, Anna" uniqKey="Simoni A" first="Anna" last="Simoni">Anna Simoni</name><affiliation><wicri:noCountry code="subField">Bocconi</wicri:noCountry></affiliation></author></analytic><monogr></monogr><series><title level="j">Scandinavian Journal of Statistics</title><idno type="ISSN">0303-6898</idno><idno type="eISSN">1467-9469</idno><imprint><publisher>Blackwell Publishing Ltd</publisher><pubPlace>Oxford, UK</pubPlace><date type="published" when="2012-06">2012-06</date><biblScope unit="volume">39</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="214">214</biblScope><biblScope unit="page" to="235">235</biblScope></imprint><idno type="ISSN">0303-6898</idno></series><idno type="istex">D5C34B2985C80181772F07C0F2354A51F839C013</idno><idno type="DOI">10.1111/j.1467-9469.2011.00784.x</idno><idno type="ArticleID">SJOS784</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0303-6898</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Gaussian process priors</term><term>Tikhonov regularization</term><term>functional data</term><term>inverse problems</term><term>measurable linear transformation</term><term>posterior consistency</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract. We study the Bayesian solution of a linear inverse problem in a separable Hilbert space setting with Gaussian prior and noise distribution. Our contribution is to propose a new Bayes estimator which is a linear and continuous estimator on the whole space and is stronger than the mean of the exact Gaussian posterior distribution which is only defined as a measurable linear transformation. Our estimator is the mean of a slightly modified posterior distribution called regularized posterior distribution. Frequentist consistency of our estimator and of the regularized posterior distribution is proved. A Monte Carlo study and an application to real data confirm good small‐sample properties of our procedure.</div></front></TEI><affiliations><list></list><tree><noCountry><name sortKey="Florens, Jean Ierre" sort="Florens, Jean Ierre" uniqKey="Florens J" first="Jean-Pierre" last="Florens">Jean-Pierre Florens</name><name sortKey="Simoni, Anna" sort="Simoni, Anna" uniqKey="Simoni A" first="Anna" last="Simoni">Anna Simoni</name></noCountry></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/France/explor/AussoisV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000012 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000012 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/France
|area= AussoisV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:D5C34B2985C80181772F07C0F2354A51F839C013
|texte= Regularized Posteriors in Linear Ill‐Posed Inverse Problems
}}
| This area was generated with Dilib version V0.6.29. |  |