UCSC-SOE-11-25: Bayesian Nonstationary Gaussian Process Models for Large Datasets via Treed Process Convolutions

Waley W. J. Liang and Herbert K. H. Lee
12/05/2011 09:10 PM
Applied Mathematics & Statistics
Spatial modeling often relies upon stationary Gaussian processes (GPs), but the assumption that the correlation structure is independent of the spatial location is invalid in many applications. Various nonstationary GP models have been developed to solve this problem, however, many of them become impractical when the sample size is large. To tackle this problem, we develop a process convolutions-based GP model by convolving a smoothing kernel with a partitioned latent process. Nonstationarity in the GP is obtained by allowing the variability of the latent process and the kernel size to change across partitions. Partitioning is achieved using a method similar to that of Classification and Regression Trees, which results in a binary tree structure. A Bayesian approach is used to simultaneously guide the partitioning process and estimate the parameters of the treed model.