Asymptotic normality of the posterior given a statistic

Ao Yuan, Bertrand Clarke

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

The authors establish the asymptotic normality and determine the limiting variance of the posterior density for a multivariate parameter, given the value of a consistent and asymptotically Gaussian statistic satisfying a uniform local central limit theorem. Their proof is given in the continuous case but generalizes to lattice-valued random variables. It hinges on a uniform Edgeworth expansion used to control the behaviour of the conditioning statistic. They provide examples and show how their result can help in identifying reference priors.

Original languageEnglish (US)
Pages (from-to)119-137
Number of pages19
JournalCanadian Journal of Statistics
Volume32
Issue number2
DOIs
Publication statusPublished - Jun 2004

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Keywords

  • Local limit theorem
  • Partial information
  • Posterior normality

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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