Bayesian mixture models: Theory and methods

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dc.contributor.author Rousseau, J en
dc.contributor.author Grazian, C en
dc.contributor.author Lee, Jeong en
dc.contributor.editor Fruhwirth-Schnatter, S en
dc.contributor.editor Celeux, G en
dc.contributor.editor Robert, CP en
dc.date.accessioned 2019-02-26T22:00:05Z en
dc.date.issued 2019-01-07 en
dc.identifier.isbn 9781498763813 en
dc.identifier.uri http://hdl.handle.net/2292/45273 en
dc.description.abstract This chapter presents some aspects of Bayesian inference in the context of mixture models. It describes the asymptotic behaviour of the corresponding posterior distributions and explores proposals to construct non-informative or vaguely informative priors in mixture models with a known number of components. The chapter analyses the mixture models can be used for density estimation, for classification or clustering, or for parameter estimation. It also describes the asymptotic behaviour of the posterior distribution in terms of the marginal density of the observations, which is a starting point of most asymptotic analysis. The chapter provides some general results on the concentration of the posterior distribution around the true marginal density of the observations. Then all the usual asymptotic results are valid: namely, the Bernstein–von Mises theorem on the parameters, the Laplace approximation of the marginal density of the observations and 1/n convergence rates of Bayesian estimators such as posterior means. en
dc.description.uri https://www.taylorfrancis.com/books/e/9780429055911/chapters/10.1201/9780429055911-4 en
dc.publisher Chapman and Hall/CRC en
dc.relation.ispartof Handbook of mixture analysis en
dc.relation.ispartofseries Chapman & Hall/CRC Handbooks of Modern Statistical Methods en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Bayesian mixture models: Theory and methods en
dc.type Book Item en
pubs.begin-page 55 en
dc.rights.holder Copyright: The author en
pubs.author-url https://books.google.co.nz/books?id=N3yCDwAAQBAJ en
pubs.end-page 75 en
pubs.place-of-publication Boca Raton, Florida, USA en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.elements-id 759095 en
pubs.org-id Science en
pubs.org-id Statistics en
pubs.number 4 en
pubs.record-created-at-source-date 2019-01-07 en
pubs.online-publication-date 2019-01-04 en


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