UC Santa Cruz

Spatial modeling with stationary Gaussian processes (GPs) has been widely used, but the assumption that the correlation structure is independent of 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, a more computationally efficient GP model is developed by convolving a smoothing kernel with a latent process. Nonstationarity in the GP is obtained by partitioning the spatial domain and allowing a separate latent process and kernel for each partition. Partitioning is achieved using a binary tree generating process. A Bayesian approach is used to simultaneously guide partitioning and estimate the parameters of the treed model. Results based on a large real dataset show that this model is fairly computational efficient and has better prediction performance than other competitive models in the literature. In addition to the treed model, a sequential design for the standard process convolution GP model is also developed based on a method called Particle Learning, which makes on-line inference more efficient than running a batch inference procedure.