A Nonstationary Soft Partitioned Gaussian Process Model via Random Spanning Trees

• Activity Number: 327 - On Surrogate Modeling of Emerging Issues in Physical and Engineering Simulators
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Zhao Tang Luo and Huiyan Sang* and Bani Mallick
• Companies: Texas A&M University and Texas A&M University and Texas A&M University
• Keywords: Bayesian posterior concentration; Gaussian process; Locally stationary models; Random spanning trees

Abstract

There has been a long-standing challenge in developing locally stationary Gaussian process (GP) models concerning how to obtain flexible partitions and how to do predictions near boundaries. In this work, we develop a new class of locally stationary stochastic processes, where local partitions are modeled by a soft partition process via predictive random spanning trees for highly flexible spatially contiguous cluster shapes. This valid nonstationary process model allows to knit together local models such that both parameter estimation and prediction can be performed under a unified and coherent framework, and to capture both discontinuities/abrupt changes and smoothness in a spatial random field. 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 a real data analysis.