Bayesian Hierarchical Spatio-Temporal Smoothing for Massive Data Sets

• Activity Number: 523
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Matthias Katzfuss*+ and Noel Cressie
• Companies: University of Heidelberg and The Ohio State University
• Keywords: Bayesian Hierarchical Modeling ; Remote Sensing ; Large Dataset ; Dimension Reduction ; Varying Model Dimension ; Global CO2

Abstract

Spatio-temporal statistics is prone to the curse of dimensionality: One manifestation of this is inversion of the data-covariance matrix, which is not in general feasible for very-large-to-massive datasets, such as those observed by satellite instruments. This becomes even more of a problem in fully Bayesian models, where the inversion typically has to be carried out many times in an MCMC sampler. We propose a Bayesian hierarchical spatio-temporal random effects (STRE) model that offers fast computation: Dimension reduction is achieved by projecting the process onto a basis-function space of low, fixed dimension, and the temporal evolution is modeled using a dynamical autoregressive model in time. We develop a multiresolutional prior for the propagator matrix that allows for random sparsity and shrinkage. Sampling from the posterior distribution can be achieved in an efficient way, even if this matrix is very large. Finally, we compare inference based on our fully Bayesian STRE model to inference based on EM estimation of the parameters. The comparison is carried out in a simulation study and on a real-world dataset of global satellite CO2 measurements.