Bayesian statistical inference for sampling a finite population is studied by using the Dirichlet-multinomial process as prior. It is shown that if the finite population variables have a Dirichlet-multinomial prior, then the posterior distribution of the inobserved variables given a sample is also Dirichlet-multinomial. If the population size tends to infinity (the sample size is fixed), sampling without replacement from a Dirichlet multinomial process is equivalent to the iid sampling from a Dirichlet process. If both the population size and sample size tend to infinity, then given a sample, the posterior distribution of the population empirical distribution function converges in distribution to a Brownian bridge. The large-sample Bayes confidence band interval are given and shown to be equivalent to the usual ones obtained from simple random sampling.
Publié le : 1986-09-14
Classification:
Finite population,
Dirichlet-multinomial process,
prior and posterior distributions,
limiting posterior distribution,
Brownian bridge,
62G30,
62G05
@article{1176350061,
author = {Lo, Albert Y.},
title = {Bayesian Statistical Inference for Sampling a Finite Population},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 1226-1233},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350061}
}
Lo, Albert Y. Bayesian Statistical Inference for Sampling a Finite Population. Ann. Statist., Tome 14 (1986) no. 2, pp. 1226-1233. http://gdmltest.u-ga.fr/item/1176350061/