Bayesian Nonparametric Weighted Sampling Inference

Survey weighting adjusts for known or expected dierences between sample and population. Weights are constructed on design or benchmarking variables that are predictors of inclusion probability. In this paper, we assume that the only information we have about the weighting procedure is the values of the weights in the sample. We propose a hierarchical Bayesian approach in which we model the weights of the nonsampled units in the population and simultaneously include them as predictors in a nonparametric Gaussian process regression to yield valid inference for the underlying nite population and capture the uncertainty induced by sampling and the unobserved outcomes. 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 Child Wellbeing Study. Our studies nd the Bayesian nonparametric nite population estimator to be more robust than the classical design-based estimator without loss in eciency.

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