Multivariate Spatial Factor Analysis Using Gaussian Predictive Processes

• Activity Number: 179
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Qian Ren*+ and Sudipto Banerjee
• Companies: University of Minnesota and University of Minnesota
• Keywords: Bayesian factor analysis ; Gaussian predictive process ; Latent variables ; Markov Chain Monte Carlo ; Multivariate spatial analysis

Abstract

Multivariate spatial data often arise in the natural and environmental sciences, where inferential needs require joint modeling of several correlated outcome variables. Hierarchical factor analysis models posit that a smaller set of latent variables can capture multivariate dependencies, thereby reducing the model dimension. In the spatial context, dimension reduction is also required with respect to the number of observed locations. Here, we demonstrate how a dimension-reducing low-rank spatial process (called a predictive process) leads to a class of computationally feasible spatial factor analysis model, thereby reducing the computational burden. Various additional modeling and implementation issues will be discussed and we will illustrate our methodology with simulated data as well as an environmental data set.