Bayesian Analysis

Bayesian Nonparametric Weighted Sampling Inference

Yajuan Si, Natesh S. Pillai, and Andrew Gelman

Full-text: Open access

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.

Article information

Source
Bayesian Anal. Volume 10, Number 3 (2015), 605-625.

Dates
First available in Project Euclid: 2 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.ba/1422884984

Digital Object Identifier
doi:10.1214/14-BA924

Mathematical Reviews number (MathSciNet)
MR3420817

Zentralblatt MATH identifier
1334.62024

Keywords
survey weighting poststratification model-based survey inference Gaussian process prior Stan

Citation

Si, Yajuan; Pillai, Natesh S.; Gelman, Andrew. Bayesian Nonparametric Weighted Sampling Inference. Bayesian Anal. 10 (2015), no. 3, 605--625. doi:10.1214/14-BA924. https://projecteuclid.org/euclid.ba/1422884984


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