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Article: The nested dirichlet distribution and incomplete categorical data analysis

TitleThe nested dirichlet distribution and incomplete categorical data analysis
Authors
KeywordsData augmentation
Dirichlet distribution
EM
Incomplete categorical data
Matrix rate of convergence
Mixing rate of a markov chain
Nested dirichlet distribution
Issue Date2009
PublisherAcademia Sinica, Institute of Statistical Science. The Journal's web site is located at http://www.stat.sinica.edu.tw/statistica/
Citation
Statistica Sinica, 2009, v. 19 n. 1, p. 251-271 How to Cite?
AbstractThe nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dimensional simplex. It includes the classical Dirichlet distribution and is useful in incomplete categorical data (ICD) analysis. In this article, we develop the distributional properties of NDD. New large-sample likelihood and small-sample Bayesian approaches for analyzing ICD are proposed and compared with existing likelihood/Bayesian strategies. We show that the new approaches have at least three advantages over existing approaches based on the traditional Dirichlet distribution in both frequentist and conjugate Bayesian inference for ICD. The new methods possess closed-form expressions for both the maximum likelihood and Bayes estimates when the likelihood function is in NDD form; produce computationally efficient EM and data augmentation algorithms when the likelihood is not in NDD form; and provide exact sampling procedures for some special cases. The methodologies are illustrated with simulated and real data.
Persistent Identifierhttp://hdl.handle.net/10722/82765
ISSN
2015 Impact Factor: 0.838
2015 SCImago Journal Rankings: 2.292
References

 

DC FieldValueLanguage
dc.contributor.authorNg, KWen_HK
dc.contributor.authorTang, MLen_HK
dc.contributor.authorTian, GLen_HK
dc.contributor.authorTan, Men_HK
dc.date.accessioned2010-09-06T08:33:09Z-
dc.date.available2010-09-06T08:33:09Z-
dc.date.issued2009en_HK
dc.identifier.citationStatistica Sinica, 2009, v. 19 n. 1, p. 251-271en_HK
dc.identifier.issn1017-0405en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82765-
dc.description.abstractThe nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dimensional simplex. It includes the classical Dirichlet distribution and is useful in incomplete categorical data (ICD) analysis. In this article, we develop the distributional properties of NDD. New large-sample likelihood and small-sample Bayesian approaches for analyzing ICD are proposed and compared with existing likelihood/Bayesian strategies. We show that the new approaches have at least three advantages over existing approaches based on the traditional Dirichlet distribution in both frequentist and conjugate Bayesian inference for ICD. The new methods possess closed-form expressions for both the maximum likelihood and Bayes estimates when the likelihood function is in NDD form; produce computationally efficient EM and data augmentation algorithms when the likelihood is not in NDD form; and provide exact sampling procedures for some special cases. The methodologies are illustrated with simulated and real data.en_HK
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.subjectData augmentationen_HK
dc.subjectDirichlet distributionen_HK
dc.subjectEMen_HK
dc.subjectIncomplete categorical dataen_HK
dc.subjectMatrix rate of convergenceen_HK
dc.subjectMixing rate of a markov chainen_HK
dc.subjectNested dirichlet distributionen_HK
dc.titleThe nested dirichlet distribution and incomplete categorical data analysisen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1017-0405&volume=19&issue=1&spage=251&epage=271&date=2009&atitle=The+Nested+Dirichlet+Distribution+and+Incomplete+Categorical+Data+Analysisen_HK
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_HK
dc.identifier.emailTian, GL: gltian@hku.hken_HK
dc.identifier.authorityNg, KW=rp00765en_HK
dc.identifier.authorityTian, GL=rp00789en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.scopuseid_2-s2.0-64549085976en_HK
dc.identifier.hkuros163556en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-64549085976&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume19en_HK
dc.identifier.issue1en_HK
dc.identifier.spage251en_HK
dc.identifier.epage271en_HK
dc.publisher.placeTaiwan, Republic of Chinaen_HK
dc.identifier.scopusauthoridNg, KW=7403178774en_HK
dc.identifier.scopusauthoridTang, ML=7401974011en_HK
dc.identifier.scopusauthoridTian, GL=25621549400en_HK
dc.identifier.scopusauthoridTan, M=7401464681en_HK

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