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Article: A noniterative sampling method for computing posteriors in the structure of EM-type algorithms

TitleA noniterative sampling method for computing posteriors in the structure of EM-type algorithms
Authors
KeywordsBayesian computation
Data augmentation
EM algorithm
Gibbs sampler
Inverse Bayes formulae
MCMC
Sampling/importance resampling
Issue Date2003
PublisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/
Citation
Statistica Sinica, 2003, v. 13 n. 3, p. 625-639 How to Cite?
AbstractWe propose a noniterative sampling approach by combining the inverse Bayes formulae (IBF), sampling/importance resampling and posterior mode estimates from the Expectation/Maximization (EM) algorithm to obtain an i.i.d. sample approximately from the posterior distribution for problems where the EM-type algorithms apply. The IBF shows that the posterior is proportional to the ratio of two conditional distributions and its numerator provides a natural class of built-in importance sampling functions (ISFs) directly from the model specification. Given that the posterior mode by an EM-type algorithm is relatively easy to obtain, a best ISF can be identified by using that posterior mode, which results in a large overlap area under the target density and the ISF. We show why this procedure works theoretically. Therefore, the proposed method provides a novel alternative to perfect sampling and eliminates the convergence problems of Markov chain Monte Carlo methods. We first illustrate the method with a proof-of-principle example and then apply the method to hierarchical (or mixed-effects) models for longitudinal data. We conclude with a discussion.
Persistent Identifierhttp://hdl.handle.net/10722/45365
ISSN
2015 Impact Factor: 0.838
2015 SCImago Journal Rankings: 2.292
References

 

DC FieldValueLanguage
dc.contributor.authorTan, Men_HK
dc.contributor.authorTian, GLen_HK
dc.contributor.authorNg, KWen_HK
dc.date.accessioned2007-10-30T06:23:49Z-
dc.date.available2007-10-30T06:23:49Z-
dc.date.issued2003en_HK
dc.identifier.citationStatistica Sinica, 2003, v. 13 n. 3, p. 625-639en_HK
dc.identifier.issn1017-0405en_HK
dc.identifier.urihttp://hdl.handle.net/10722/45365-
dc.description.abstractWe propose a noniterative sampling approach by combining the inverse Bayes formulae (IBF), sampling/importance resampling and posterior mode estimates from the Expectation/Maximization (EM) algorithm to obtain an i.i.d. sample approximately from the posterior distribution for problems where the EM-type algorithms apply. The IBF shows that the posterior is proportional to the ratio of two conditional distributions and its numerator provides a natural class of built-in importance sampling functions (ISFs) directly from the model specification. Given that the posterior mode by an EM-type algorithm is relatively easy to obtain, a best ISF can be identified by using that posterior mode, which results in a large overlap area under the target density and the ISF. We show why this procedure works theoretically. Therefore, the proposed method provides a novel alternative to perfect sampling and eliminates the convergence problems of Markov chain Monte Carlo methods. We first illustrate the method with a proof-of-principle example and then apply the method to hierarchical (or mixed-effects) models for longitudinal data. We conclude with a discussion.en_HK
dc.format.extent225168 bytes-
dc.format.extent2525 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/en_HK
dc.relation.ispartofStatistica Sinicaen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBayesian computationen_HK
dc.subjectData augmentationen_HK
dc.subjectEM algorithmen_HK
dc.subjectGibbs sampleren_HK
dc.subjectInverse Bayes formulaeen_HK
dc.subjectMCMCen_HK
dc.subjectSampling/importance resamplingen_HK
dc.titleA noniterative sampling method for computing posteriors in the structure of EM-type algorithmsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1017-0405&volume=13&issue=3&spage=625&epage=639&date=2003&atitle=A+noniterative+sampling+method+for+computing+posteriors+in+the+structure+of+EM-type+algorithmsen_HK
dc.identifier.emailTian, GL: gltian@hku.hken_HK
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_HK
dc.identifier.authorityTian, GL=rp00789en_HK
dc.identifier.authorityNg, KW=rp00765en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.scopuseid_2-s2.0-0012546232en_HK
dc.identifier.hkuros95254-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0012546232&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume13en_HK
dc.identifier.issue3en_HK
dc.identifier.spage625en_HK
dc.identifier.epage639en_HK
dc.publisher.placeTaiwan, Republic of Chinaen_HK
dc.identifier.scopusauthoridTan, M=7401464681en_HK
dc.identifier.scopusauthoridTian, GL=25621549400en_HK
dc.identifier.scopusauthoridNg, KW=7403178774en_HK

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