Bayesian Nonparametric Weighted Sampling Inference

Abstract

It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierar- chical approach in which we model the distribution of the weights of the nonsam- pled units in the population and simultaneously include them as predictors in a nonparametric Gaussian process regression. We use simulation studies to evaluate the performance of our procedure and compare it to the classical design-based es- timator. We apply our method to the Fragile Family and Child Wellbeing Study. Our studies find the Bayesian nonparametric finite population estimator to be more robust than the classical design-based estimator without loss in efficiency, which works because we induce regularization for small cells and thus this is a way of automatically smoothing the highly variable weights.