A Bayesian Method for Weighted Sampling

The Annals of Statistics · 1993 · Volume 21 · Issue 4

Abstract

Bayesian statistical inference for sampling from weighted distribution models is studied. Small-sample Bayesian bootstrap clone (BBC) approximations to the posterior distribution are discussed. A second-order property for the BBC in unweighted i.i.d. sampling is given. A consequence is that BBC approximations to a posterior distribution of the mean and to the sampling distribution of the sample average, can be made asymptotically accurate by a proper choice of the random variables that generate the clones. It also follows from this result that in weighted sampling models, BBC approximations to a posterior distribution of the reciprocal of the weighted mean are asymptotically accurate; BBC approximations to a sampling distribution of the reciprocal of the empirical weighted mean are also asymptotically accurate.

Keywords

62G09; 62G20; 62G99; asymptotic accuracy; Bayesian bootstrap clone approximations; bootstrap approximations; Weighted distribution models; weighted gamma process priors;

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