Annals of Operations Research

, Volume 56, Issue 1, pp 1–13

Approximations of Bayes decision problems: the epigraphical approach

  • J. O. Berger
  • G. Salinetti
Article

Abstract

Solving Bayesian decision problems usually requires approximation procedures, all leading to study the convergence of the approximating infima. This aspect is analysed in the context of epigraphical convergence of integral functionals, as minimal context for convergence of infima. The results, applied to the Monte Carlo importance sampling, give a necessary and sufficient condition for convergence of the approximations of Bayes decision problems and sufficient conditions for a large class of Bayesian statistical decision problems.

Keywords

Bayesian decisions epi-convergence integral functionals Monte Carlo importance sampling 

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Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • J. O. Berger
    • 1
  • G. Salinetti
    • 2
  1. 1.Department of StatisticsPurdue UniversityWest LafayetteUSA
  2. 2.Universitá di Roma “La Sapienza”RomeItaly

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