In population studies, it is standard to sample data via designs in which thepopulation is divided into strata, with the different strata assigned differentprobabilities of inclusion. Although there have been some proposals forincluding sample survey weights into Bayesian analyses, existing methodsrequire complex models or ignore the stratified design underlying the surveyweights. We propose a simple approach based on modeling the distribution of theselected sample as a mixture, with the mixture weights appropriately adjusted,while accounting for uncertainty in the adjustment. We focus for simplicity onDirichlet process mixtures but the proposed approach can be applied morebroadly. We sketch a simple Markov chain Monte Carlo algorithm for computation,and assess the approach via simulations and an application.
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