Approximating Likelihoods Through Precision Matrix for Large Spatial Data Sets

• Activity Number: 687
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Huang Huang* and Ying Sun
• Companies: KAUST and King Abdullah University of Science and Technology
• Keywords: precision matrix ; Gaussian process ; composite likelihood ; large datasets ; parallel computing

Abstract

Environmental datasets are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statistics face tremendous computational challenges due to the calculation required by the large precision matrix. Various methods based on covariance function approximations have been introduced to reduce the computational cost. However, most of them rely on unrealistic assumptions of the underlying process and retaining statistical efficiency remains an issue. In this work, we develop a new approximation scheme through precision matrix approximation. We show how the composite likelihood method can be adapted to provide different types of precision matrix approximations that allow for efficient computation of the maximum likelihood estimation. The statistical efficiency of the proposed method is evaluated by numerical and simulation studies. To be able to handle very large datasets, we also explore parallel computing techniques and demonstrate our method on real datasets for environmental applications.