A Nonstationary Soft Partitioned Gaussian Process Model by Huiyan Sang
Date: April 5, 2023
Speaker: Huiyan Sang
Title: A Nonstationary Soft Partitioned Gaussian Process Model
Abstract: In this work, we develop a new class of locally stationary Gaussian processes for modeling nonstationary spatial data. To address the challenging issues regarding acquiring flexible partitions and making predictions near boundaries, we propose a novel soft space partition process constructed from a predictive random partition model on graphs, which allows for highly flexible space partitions while accounting for uncertainties around cluster boundaries and enabling reduced graph computations. We will present a variety of options and new constructions for the latent graph partition model. We prove the validity of the proposed nonstationary process model and show that both parameter estimation and prediction can be performed under a unified and coherent framework. We propose a theoretical framework to study the Bayesian posterior concentration concerning the behavior of this Bayesian nonstationary process model. The performance of the proposed model is illustrated with simulation studies and real data analysis of precipitation rates over the contiguous United States.