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Sufficient conditions for Bayesian consistency

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Author

Summary, in English

We introduce the Hausdorff α-entropy to study the strong Hellinger consistency of posterior distributions. We obtain general Bayesian consistency theorems which extend the well-known results of Barron et al. [1999. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536–561] and Ghosal et al. [1999. Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27, 143–158] and Walker [2004. New approaches to Bayesian consistency. Ann. Statist. 32, 2028–2043]. As an application we strengthen previous results on Bayesian consistency of the (normal) mixture models.

Publishing year

2009

Language

English

Pages

2479-2489

Publication/Series

Journal of Statistical Planning and Inference

Volume

139

Issue

7

Document type

Journal article

Publisher

North-Holland

Topic

  • Mathematics

Keywords

  • Infinite-dimensional model
  • Sieve
  • Posterior distribution
  • Hellinger consistency

Status

Published

ISBN/ISSN/Other

  • ISSN: 1873-1171