Reparameterisation Issues in Mixture Modelling and their bearing on MCMC algorithms
Identifieur interne : 00D632 ( Main/Merge ); précédent : 00D631; suivant : 00D633Reparameterisation Issues in Mixture Modelling and their bearing on MCMC algorithms
Auteurs : C. P. Robert [France] ; K. L. Mengersen [Australie]Source :
- Computational statistics & data analysis [ 0167-9473 ] ; 1999.
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- Pascal (Inist)
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Abstract
There is increasing need for efficient estimation of mixture distributions, especially following the explosion in the use of these as modelling tools in many applied fields. We propose in this paper a Bayesian noninformative approach for the estimation of normal mixtures which relies on a reparameterisation of the secondary components of the mixture in terms of divergence from the main component. As well as providing an intuitively appealing representation at the modelling stage, this reparameterisation has important bearing on both the prior distribution and the performance of MCMC algorithms. We compare two possible reparameterisations extending Mengersen and Robert (1996) and show that the reparameterisation which does not link the secondary components together is associated with poor convergence properties of MCMC algorithms.
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Mengersen</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>School of Mathematics, Queensland University of Technology Brisbane</s1><s3>AUS</s3><sZ>2 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>School of Mathematics, Queensland University of Technology Brisbane</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">00-0206357</idno><date when="1999">1999</date><idno type="stanalyst">PASCAL 00-0206357 INIST</idno><idno type="RBID">Pascal:00-0206357</idno><idno type="wicri:Area/PascalFrancis/Corpus">006005</idno><idno type="wicri:Area/PascalFrancis/Curation">000165</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">005F19</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">005F19</idno><idno type="wicri:doubleKey">0167-9473:1999:Robert C:reparameterisation:issues:in</idno><idno type="wicri:Area/Main/Merge">00D632</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Reparameterisation Issues in Mixture Modelling and their bearing on MCMC algorithms</title><author><name sortKey="Robert, C P" sort="Robert, C P" uniqKey="Robert C" first="C. P." last="Robert">C. P. Robert</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>CREST, INSEE</s1><s2>75675 Paris</s2><s3>FRA</s3><sZ>1 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Paris</settlement></placeName></affiliation></author><author><name sortKey="Mengersen, K L" sort="Mengersen, K L" uniqKey="Mengersen K" first="K. L." last="Mengersen">K. L. Mengersen</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>School of Mathematics, Queensland University of Technology Brisbane</s1><s3>AUS</s3><sZ>2 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>School of Mathematics, Queensland University of Technology Brisbane</wicri:noRegion></affiliation></author></analytic><series><title level="j" type="main">Computational statistics & data analysis</title><title level="j" type="abbreviated">Comput. stat. data anal.</title><idno type="ISSN">0167-9473</idno><imprint><date when="1999">1999</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Computational statistics & data analysis</title><title level="j" type="abbreviated">Comput. stat. data anal.</title><idno type="ISSN">0167-9473</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algorithm</term><term>Bayes estimation</term><term>Convergence</term><term>Estimator efficiency</term><term>Gaussian distribution</term><term>Gibbs sampling</term><term>Identifiability</term><term>Markov chain</term><term>Mixed distribution</term><term>Monte Carlo method</term><term>Prior distribution</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Estimation Bayes</term><term>Efficacité estimateur</term><term>Mélange loi probabilité</term><term>Loi a priori</term><term>Convergence</term><term>Algorithme</term><term>Chaîne Markov</term><term>Méthode Monte Carlo</term><term>Echantillonnage Gibbs</term><term>Loi normale</term><term>Identifiabilité</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">There is increasing need for efficient estimation of mixture distributions, especially following the explosion in the use of these as modelling tools in many applied fields. We propose in this paper a Bayesian noninformative approach for the estimation of normal mixtures which relies on a reparameterisation of the secondary components of the mixture in terms of divergence from the main component. As well as providing an intuitively appealing representation at the modelling stage, this reparameterisation has important bearing on both the prior distribution and the performance of MCMC algorithms. We compare two possible reparameterisations extending Mengersen and Robert (1996) and show that the reparameterisation which does not link the secondary components together is associated with poor convergence properties of MCMC algorithms.</div></front></TEI><affiliations><list><country><li>Australie</li><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Paris</li></settlement></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Robert, C P" sort="Robert, C P" uniqKey="Robert C" first="C. P." last="Robert">C. P. Robert</name></region></country><country name="Australie"><noRegion><name sortKey="Mengersen, K L" sort="Mengersen, K L" uniqKey="Mengersen K" first="K. L." last="Mengersen">K. L. Mengersen</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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