Rates of convergence of posterior distributions

Xiaotong Shen, Larry Wasserman

Research output: Contribution to journalArticlepeer-review

141 Scopus citations

Abstract

We compute the rate at which the posterior distribution concentrates around the true parameter value. The spaces we work in are quite general and include infinite dimensional cases. The rates are driven by two quantities: the size of the space, as measured by bracketing entropy, and the degree to which the prior concentrates in a small ball around the true parameter. We consider two examples.

Original languageEnglish (US)
Pages (from-to)687-714
Number of pages28
JournalAnnals of Statistics
Volume29
Issue number3
DOIs
StatePublished - Jun 2001

Keywords

  • Asymptotic inference
  • Bayesian inference
  • Non-parametric models
  • Sieves

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