Annals of Statistics

A Bayesian Method for Weighted Sampling

Albert Y. Lo

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349414

Digital Object Identifier
doi:10.1214/aos/1176349414

Mathematical Reviews number (MathSciNet)
MR1245785

Zentralblatt MATH identifier
0793.62024

JSTOR
links.jstor.org

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

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

Citation

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


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