Bayesian Finite Population Estimates from a Two-Stage Sample with Spatial Correlation

• Activity Number: 238 - SPEED: Environment and Health, Governmental Policies and Population Surveys, Part 1
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Alec M Chan-Golston* and Sudipto Banerjee and Mark Handcock
• Companies: University of California, Los Angeles and UCLA and University of California, Los Angles
• Keywords: Finite Population; Bayesian Inference; Gaussian Processes; Spatial Data

Abstract

This talk will present a Bayesian model-based approach to estimate finite population parameters given spatially correlated data collected from a two-stage sampling scheme. Specifically, we examine a two-stage cluster sampling design in which the primary stage is a geographic region and the data is assumed to be a partial realization of a spatial process. Therefore, there is a concern that simple spatial models will fail to account for correlations induced by design and design-based estimates will ignore the spatial association among sampled and non-sampled units. Two simulation studies are presented, comparing various Bayesian hierarchical models. We find that models not accounting for spatial dependency have poorer model fit and spuriously low variability in finite population estimates. However, spatial models which account for study-design performed well in both regards. A data analysis examining Nitrate levels in California wells yields similar conclusions. The talk will conclude with a discussion of extending this framework to more sophisticated sampling strategies, such as preferential sampling, and its implications on finite population estimates.