A Nonstationary Soft Partitioned Gaussian Process Model via Random Spanning Trees
提出一种新的非平稳高斯过程模型，通过随机生成树实现软分区，灵活捕捉空间场的局部平滑与突变，适用于降水等空间数据分析。
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.