Annals of Statistics

A Bayesian Method for Weighted Sampling

Albert Y. Lo

Full-text: Open access


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.

Article information

Ann. Statist., Volume 21, Number 4 (1993), 2138-2148.

First available in Project Euclid: 12 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62G09: Resampling methods
Secondary: 62G20: Asymptotic properties 62G99: None of the above, but in this section

Weighted distribution models weighted gamma process priors bootstrap approximations Bayesian bootstrap clone approximations asymptotic accuracy


Lo, Albert Y. A Bayesian Method for Weighted Sampling. Ann. Statist. 21 (1993), no. 4, 2138--2148. doi:10.1214/aos/1176349414.

Export citation