Si, YajuanPillai, NateshGelman, Andrew2021-02-242015-09Yajuan Si. Natesh S. Pillai. Andrew Gelman. 2015. "Bayesian Nonparametric Weighted Sampling Inference." Bayesian Anal. 10 (3) 605 - 625. https://doi.org/10.1214/14-BA9241936-0975https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37366951It 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.en-USJournal Article2018-01-2620152021-02-2410.1214/14-ba924