A Nonstationary Soft Partitioned Gaussian Process Model via Random Spanning Trees

• 成果类型: Article
• 署名作者: Luo, Zhao Tang; Sang, Huiyan; Mallick, Bani
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2249642
• 发表日期: 2024
• 页码: 2105-2116
• 关键词: prediction; rates

摘要

There has been a long-standing challenge in developing locally stationary Gaussian process models concerning how to obtain flexible partitions and make 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 that leads to highly flexible spatially contiguous subregion shapes. This valid nonstationary process model knits together local models such that both parameter estimation and prediction can be performed under a unified and coherent framework, and it captures both discontinuities/abrupt changes and local 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 real data analysis of precipitation rates over the contiguous United States. Supplementary materials for this article are available online.