Bayesian Nonparametric Weighted Sampling Inference

TL;DR

This paper introduces a Bayesian nonparametric approach for survey sampling inference that models weight distributions and improves robustness over classical methods, demonstrated through simulations and real data application.

Contribution

It develops a hierarchical Bayesian model using Gaussian processes to handle inverse-probability weights in survey data, enhancing robustness and smoothing small cell variability.

Findings

Bayesian estimator outperforms classical in robustness.

Method effectively smooths highly variable weights.

Approach validated through simulations and real data.

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 hierarchical approach in which we model the distribution of the weights of the nonsampled 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 estimator. 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.