Estimation and Prediction in Spatial Models with Block Composite Likelihoods

• Activity Number: 6
• Type: Invited
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Ryan J. Parker*+ and Jo Eidsvik and Ben Shaby and Brian J. Reich and Matthew Wheeler and Jarad Niemi
• Companies: North Carolina State University and Norwegian University of Science and Technology and UC - Berkeley and North Carolina State University and University of California, Santa Barbara and Iowa State University
• Keywords: composite likelihood ; massive data ; spatial statistics

Abstract

A block composite likelihood is constructed from the joint densities of pairs of adjacent spatial blocks. This allows large datasets to be split into many smaller datasets, each of which can be evaluated separately, and combined through a summation. Estimates for unknown parameters are obtained by maximizing the block composite likelihood function. In addition, we propose a method for optimal spatial prediction from the composite likelihood model. Asymptotic variances for both parameter estimates and predictions are computed using Godambe sandwich matrices. The approach gives considerable improvements in computational efficiency, and obviates memory problems. Synthetic and real-data examples are presented. These methods are implemented in an R package, spacious, that will allow the user to quickly estimate spatial model parameters for large data sets using this block composite structure.