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- W4386090136 abstract "AbstractThere 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.KEYWORDS: Bayesian posterior concentrationLocally stationary modelsNonstationary Gaussian processRandom spanning trees AcknowledgementsThe authors thank the referees and the editor for their valuable comments. The authors also thank Dr. Mark Risser for providing the CONUS precipitation data.Additional informationFundingThe research of Zhao Tang Luo and Huiyan Sang was partially supported by NSF grant no. NSF DMS-2210456 and 2220231. The research of Bani Mallick was partially supported by NSF grant no. NSF CCF-1934904 and National Cancer Institute of the National Institutes of Health grant under award number R01CA194391." @default.
- W4386090136 created "2023-08-24" @default.
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- W4386090136 date "2023-08-23" @default.
- W4386090136 modified "2023-10-16" @default.
- W4386090136 title "A Nonstationary Soft Partitioned Gaussian Process Model via Random Spanning Trees" @default.
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- W4386090136 doi "https://doi.org/10.1080/01621459.2023.2249642" @default.
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