Bayesian Spatial Process Models for High-Dimensional Finite Population Sampling

• Activity Number: 391 - Statistical Advancements in Forestry, Ecology and Climate Modeling
• Type: Invited
• Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Sudipto Banerjee* and Alec Goldstein-Chan
• Companies: UCLA School of Public Health and University of California Los Angeles
• Keywords: Bayesian inference; Finite population surveys; Gaussian processes; High-dimensional inference; Scalable Gaussian processes

Abstract

This talk will outline a Bayesian framework for analyzing geographically-referenced survey data from finite population contexts. The focus will be on tackling high-dimensional inference when the data are conceived as partial realizations of a spatial process. The proposed approach builds Bayesian hierarchical models for stratified, multi-stage and cluster sampling designs assuming that the observed units come from a finite population which is assumed apriori to be a stochastic process. Two sources of correlation need to to accounted for: the first comes from an underlying stochastic process inducing spatial correlations and the second comes from the specific sampling designs. Inference is sought at the finite population level as well as for the underlying spatial process. The Bayesian framework is rich, but it is computationally prohibitive for high-dimensional data. The talk will offer some effective and massively scalable model-based solutions based upon nearest-neighbor Gaussian processes that can be implemented on modest computing environments, perhaps even on single processor laptops. Applications from the environmental sciences and public health surveys will be discussed.