"Robust Bayesian Predictive Inference for Finite Population Quantities in Survey Sampling"
This research is motivated by the statistical issues connected with the University of Michigan Dioxin Exposure Study (UMDES), a population-based environmental health study. It is often of interest to estimate the finite-population prevalence of rare events and to estimate the contaminant level in the upper-percentile of the population from a complex survey sample. However, the traditional sample-weighted estimator for finite population quantities can sometimes be inefficient, especially in these two scenarios, which motivates the search for alternative estimators. We develop robust Bayesian model-based estimators of finite population proportions, distribution functions, and percentiles based on a penalized spline regression model relating the outcome to the probabilities of inclusion in unequal probability sampling. Inferences are based on the posterior predictive distributions of the nonsampled values. We show by simulation studies and real examples that this model-based approach yields gains in efficiency over standard design-based approaches, with confidence coverages close to nominal levels. Some extension of current research will also be discussed in this talk.
