Waley Liang, Graduate Student, Statistics and Applied Mathematics
Friday, February 17, 2012, 8:30 AM to 10:30 AM
Location: Baskin Engineering, Room 330
Hosted By Herbert Lee

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.  In addition to this work, we also present an on-line inference method for the basic process convolutions GP model.  This approach is targeted for sequential applications where data arrives on-line and model update is required for each new data arrival.  In the Bayesian setting, Markov chain Monte Carlo is the standard tool of inference, but is computationally inefficient for sequential applications because it must be repeated on the full dataset after each data arrival.  Our approach is based on a Sequential Monte Carlo method called Particle Learning which makes sequential inference more efficient for the process convolutions GP model.