Bayesian Uncertainty Estimation Under Complex Sampling

• Activity Number: 89 - SPEED: Survey Methods, Transportation Studies, SocioEconomics, and General Statistical Methods Part 2
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 5:05 PM to 5:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Matthew Williams* and Terrance Savitsky
• Companies: National Science Foundation and Bureau of Labor Statistics
• Keywords: pseudo-posterior; credible set; Stan; survey sampling; variance estimation

Abstract

Complex survey sampling designs typically produce a correlation between the response variables of interest and the survey sampling inclusion probabilities such that the balance of information in the observed sample is different from the underlying population targeted for inference. A data analyst may use a sampling-weighted pseudo-posterior distribution to estimate the population model on the observed sample. While the pseudo-posterior distribution contracts on the true population model parameters, we demonstrate that the scale and shape of the asymptotic distributions are different between each of the MLE, the pseudo-posterior and the MLE under simple random sampling. Motivated by the different forms of the asymptotic covariance matrices and the within cluster dependence, we devise a correction applied as a simple and fast post-processing step to our MCMC draws from the pseudo-posterior distribution such that the nominal coverage is approximately achieved for posterior intervals. We implement in R by weaving together functionality from the rstan and survey packages.