Partition-Based Nonstationary Covariance Estimation Using the Stochastic Score Approximation
针对大尺度空间数据，提出一种基于分区的非平稳协方差估计方法，通过随机得分近似降低计算复杂度，适用于网格子集数据，并用日均温度预测验证效果。
We introduce computational methods that allow for effective estimation of a flexible nonstationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field is defined as a weighted spatially varying linear combination of a globally stationary process and locally stationary processes. Often in such a model, the difficulty in its practical use is in the definition of the boundaries for the local processes, and therefore, we describe one such selection procedure that generally captures complex nonstationary relationships. We generalize the use of a stochastic approximation to the score equations in this nonstationary case and provide tools for evaluating the approximate score in O(n log n) operations and O(n) storage for data on a subset of a grid. We perform various simulations to explore the effectiveness and speed of the proposed methods and conclude by predicting average daily temperature. Supplementary materials for this article are available online.