A0538
Title: Nonstationary spatial modeling, estimation, and prediction using a divide-and-conquer approach
Authors: Hsin-Cheng Huang - Academia Sinica (Taiwan) [presenting]
Chun-Shu Chen - National Central University (Taiwan)
Yung-Huei Chiou - National Central University (Taiwan)
Abstract: Spatial data over a large domain generally shows nonstationary spatial covariance characteristics. However, estimating a nonstationary covariance function from a single realization of data is challenging, and the computation of the optimal spatial prediction is intractable when the dataset is massive. Initially, a method is proposed for visualizing nonstationary covariance structures, and a statistical test is introduced for spatial stationarity. Upon detection of nonstationarity, a segmentation technique is proposed that decomposes the spatial domain into $K$ subregions wherein the process is approximately stationary. A stationary process is also considered for each of these $K$ subregions. Subsequently, a novel nonstationary model that employs a linear combination of these processes with spatially varying weights is developed. Contrary to independent stationary models, our approach treats the $K$ stationary processes as interdependent and represents them using a multivariate Matern covariance model. The proposed nonstationary model showcases flexibility, morphing into a globally stationary process when all stationary components exhibit a shared spatial covariance structure. Finally, a divide-and-conquer strategy for fast spatial prediction is proposed. The effectiveness of our approach is demonstrated through numerical experiments.
