Estimating basis functions in massive fields under the spatial mixed effects model

Spatial prediction is commonly achieved under the assumption of a Gaussian random field (GRF) by obtaining maximum likelihood estimates parameters, and then using kriging equations to arrive at predicted values. For massive datasets, fixed rank Expectation-Maximization (EM) algorithm for estimation has been proposed as an alternative usual but computationally prohibitive method. The method reduces computation cost redefining spatial process linear combination basis functions effects. A disadvantage this that it imposes constraints on relationship between observed locations knots. We develop utilizes Mixed Effects (SME) model, allows additional flexibility estimating range dependence observations knots via Alternating Expectation Conditional Maximization (AECM) algorithm. Experiments show our methodology improves without sacrificing accuracy while also minimizing computational burden extra parameter estimation. applied temperature data set archived United States National Climate Data Center, with improved results over previous methodology.