Bayesian Predictive Inference For Finite Population Quantities Under Informative Sampling

TL;DR

This paper develops a Bayesian predictive framework for finite population inference under informative sampling, effectively handling limited design information and improving accuracy over traditional models.

Contribution

It introduces a novel Bayesian method using MCMC that accounts for informative sampling with limited design info, providing measures of precision and interval estimates.

Findings

Improved precision over ignorable models

Corrects for selection bias in finite population estimates

Uses MCMC to avoid asymptotic approximations

Abstract

We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection probabilities corresponding to the sample units are known. Our methodology, unlike that of Chambers, Dorfman and Wang (1998), can be used to make inference for finite population quantities and provides measures of precision and intervals. Moreover, our methodology, using Markov chain Monte Carlo methods, avoids the necessity of using asymptotic closed form approximations, necessary for the other approaches that have been proposed. A set of simulated examples shows that the informative model provides improved precision over a standard ignorable model, and corrects for the selection bias.