Journal of the Royal Statistical Society Series B (Statistical Methodology) · 2001 · 106 citations · 20 references
Natural SciencesMathematicsBayesian Data AnalysisProbability TheoryStatisticsBayesian ComputationBayesian InferenceBayesian ModelingBayesian StatisticsPosterior DistributionsPrior DistributionsBayesian Finite Mixture ModelsBayesian Polya Tree ModelsConditional DistributionsExponential Family DistributionsFinite Mixture ModelsInfinite Mixture ModelsPolya Tree PriorsPosterior Consistency
Summary We consider a sequence of posterior distributions based on a data-dependent prior (which we shall refer to as a pseudoposterior distribution) and establish simple conditions under which the sequence is Hellinger consistent. It is shown how investigations into these pseudo posteriors assist with the understanding of some true posterior distributions, including Pólya trees, the infinite dimensional exponential family and mixture models.
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On the Consistency of Bayes Estimates
Persi Diaconis, David A. Freedman · The Annals of Statistics · 1986 · 624 citations