Large spatial datasets become more common as a result of automatic sensors, remote sensing and the increase in data storage capacity. But large spatial datasets are hard to analyse. Even in the simplest Gaussian situation, parameter estimation and prediction are troublesome because one requires matrix factorization of a large covariance matrix. We consider a composite likelihood construction built on the joint densities of subsets of variables. This composite model thus splits a datasets in many smaller datasets, each of which can be evaluated separately. These subsets of data are combined through a summation giving the final composite likelihood. Massive datasets can be handled with this approach.
In particular, we consider a block composite likelihood model, constructed over pairs of spatial blocks. The blocks can be disjoint, overlapping or at various resolution. The main idea is that the spatial blocking should capture the important correlation effects in the data.
Estimates for unknown parameters as well as optimal spatial predictions under the block composite model are obtained. Asymptotic variances for both parameter estimates and predictions are computed using Godambe sandwich matrices. The procedure is demonstrated on 2D and 3D datasets with regular and irregular sampling of data. For smaller data size we compare with optimal predictors, for larger data size we discuss and compare various blocking schemes. |
