Resolution Adaptive Fixed Rank Kriging
Professor Sheng-Li Tzeng
(Department of Applied Mathematics, National Sun Yat-sen University)
The spatial random effects model (SREM) is a popular choice for kriging (spatial prediction) of large spatial data. SREM is flexible in modeling spatial covariance functions and is computationally efficient for prediction via fixed rank kriging (FRK). However, the model relies on a class of basis functions, which if not selected properly, may result in unstable or undesirable results. Additionally, the maximum likelihood (ML) estimates of the model parameters are commonly computed using an expectation-maximization (EM) algorithm, which further limits its applicability when a large number of basis functions are required. In this talk, I will introduce a novel class of basis functions which avoids the difficult knot-allocation or scale-selection problem. The functions are extracted from thin-plate splines, and ordered in terms of their degrees of smoothness, with higher-order functions corresponding to larger-scale features and lower-order ones corresponding to smaller-scale details. These ordered functions lead to a parsimonious representation of a (nonstationary) spatial covariance function, in a systematic way that the number of basis functions playing the role of spatial resolution. Furthermore, I will show that the ML estimates of the random effects covariance matrix can be expressed in simple closed forms, and hence the resulting FRK can accommodate a much larger number of basis functions without numerical difficulties. Then Akaike information criterion, which also possesses a simple closed-form expression, can be used to select the number of basis functions. The whole procedure, involving no additional tuning parameter, is efficient to compute, easy to program, automatic to implement, and applicable to massive amounts of spatial data even when they are sparsely and irregularly located. Some extensions and potential applications will also be discussed.
日 期：108年10月16日(星期三) 16:10~17:00