Partition-Based Non-Stationary Covariance Estimation using the Stochastic Score Approximation

We introduce computational methods that allow for effective estimation of a flexible non-stationary 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 non-stationary relationships. We generalize the use of a stochastic approximation to the score equations in this non-stationary case and provide tools for evaluating the approximate score in O(n log n) operations and <i>O</i>(<i>n</i>) 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.