Hierarchical Models for Spatial Data with Errors That Are Correlated with the Latent Process

• Activity Number: 454 - Advances in Spatial and Spatio-Temporal Methodology with Applications to Official Statistics
• Type: Topic Contributed
• Date/Time: Wednesday, August 2, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Government Statistics Section
• Author(s): Jonathan R Bradley* and Christopher Wikle and Scott H. Holan
• Companies: Florida State University and University of Missouri and University of Missouri
• Keywords: Big Data ; Spatial ; Bayesian ; Hierarchical Model

Abstract

Prediction of a spatial Gaussian process using a "big dataset" has become a topical area of research over the last decade. The available solutions often involve placing strong assumptions on the error process associated with the data. Specifically, it has typically been assumed that the data is equal to the spatial process of principal interest plus a mutually independent error process. Further, to obtain computationally efficient predictions, additional assumptions on the latent random processes and/or parameter models have become a practical necessity (e.g., low rank models, sparse precision matrices, etc.). In this article, we consider an alternative latent process modeling schematic where it is assumed that the error process is spatially correlated and correlated with the spatial random process of principal interest. We show the counterintuitive result that error process dependencies allow one to remove assumptions on the spatial process of principal interest, and obtain computationally efficient predictions. At the core of this proposed methodology is the definition of a corrupted version of the latent process of interest, which we call the data specific latent process (DSLP).