Closed form expressions for bayesian sample size

B. Clarke, A. Yuan

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the data. Thus, when a sample size criterion is formalized in terms of a functional of the posterior, its value is a random variable. Generally, such functional have means under the true distribution. We give asymptotic expressions for the expected value, under a fixed parameter, for certain types of functionals of the posterior density in a Bayesian analysis. The generality of our treatment permits us to choose functionals that encapsulate a variety of inference criteria and large ranges of error bounds. Consequently, we get simple inequalities which can be solved to give minimal sample sizes needed for various estimation goals. In several parametric examples, we verify that our asymptotic bounds give good approximations to the expected values of the functionals they approximate. Also, our numerical computations suggest our treatment gives reasonable results.

Original languageEnglish (US)
Pages (from-to)1293-1330
Number of pages38
JournalAnnals of Statistics
Volume34
Issue number3
DOIs
Publication statusPublished - Jun 1 2006

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Keywords

  • Asymptotic
  • Bayesian inference
  • Edgeworth expansion
  • Posterior distribution
  • Sample size

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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