Bayesian Predictive Inference from a Probability Proportional to Size (PPS) Sample

• Activity Number: 263
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Donald Malec*
• Companies: National Center for Health Statistics
• Keywords: Nonparametric Bayes ; Informative Sample Selection

Abstract

PPS sampling is a widely used method to collect data in large, national surveys. Randomization-based methods for inference regarding the underlying finite populations are available but nonparametric Bayesian methods regarding the unknown finite population are less developed, especially when the selection probabilities are informative but not relevant to the inference. Although methods to remove the possible effects of selection probability through the use of Bayesian nonparametric methods have been previously proposed, they have focused solely on incorporating the marginal selection probabilities of each unit into the analysis and ignore the joint sample selection. Since Bayesian inference relies on inference from a likelihood and since a specific PPS sample design and resulting joint selection may contribute to the likelihood in a specific way, the effect of the PPS sample design on the posterior inference is investigated. Focusing on the Bayesian bootstrap approach, which consists of placing full support on only the observed sample outcomes via an unknown multinomial distribution, the additional effects of two different PPS sample designs to the likelihood and resulting posterior inference are investigated. Specifically, an exact likelihood Bayesian nonparametric method is developed for both Poisson sampling and for a continuous approximation to multinomial sampling. Comparisons using a small example will be made with the Bayesian approaches that are based on only the marginal probability of selection and with a naïve approach that ignores the sample design completely.