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A Universal Prior Distribution for Bayesian Consistency of Non parametric Procedures

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Author

Summary, in English

The introduction of the Hausdorff alpha-entropy in Xing (2008a), Xing (2008b), Xing (2010), Xing (2011), and Xing and Ranneby (2009) has lead a series of improvements of well-known results on posterior consistency. In this paper we discuss an application of the Hausdorff a-entropy. We construct a universal prior distribution such that the corresponding posterior distribution is almost surely consistent. The approach of the construction of this type of prior distribution is natural, but it works very well for all separable models. We illustrate such prior distributions by examples. In particular, we obtain that if the true density function is known to be some normal probability density function with unknown mean and unknown variance then without any additional assumption one can construct a prior distribution which leads to posterior consistency.

Publishing year

2015

Language

English

Pages

972-982

Publication/Series

Communications in Statistics: Theory and Methods

Volume

44

Issue

5

Document type

Journal article

Publisher

Marcel Dekker

Topic

  • Mathematics

Keywords

  • Density function
  • Hausdorff entropy
  • Infinite-dimensional model
  • Posterior consistency

Status

Published

ISBN/ISSN/Other

  • ISSN: 0361-0926