Multivariate Spatial Factor Analysis with Missingness Using Gaussian Predictive Processes

• Activity Number: 503
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Qian Ren*+
• Companies: University of Minnesota
• Keywords: Bayesian inference ; Factor analysis ; Gaussian predictive process ; Latent factor models ; Multivariate spatial process

Abstract

Multivariate spatial data often arise in the natural and environmental sciences, where inferential requirements entail joint modeling of several correlated outcome variables. Hierarchical factor analysis (FA) 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. A Markov chain Monte Carlo (MCMC) algorithm was developed for estimation with an emphasis toward missing data. We present sampling-based methods that condition on the observed data and recover the full posterior distribution of the missing values (along with model parameters) in a Bayesian predictive framework. Various additional modeling and implementation issues are discussed as well and we illustrate our methodology with simulated data as well as an environmental data set.