Scalable Statistical Analysis of Gaussian Models for Petascale Spatiotemporal Data (Final Technical Report)
Gaussian process models for spatial and spatiotemporal data are ubiquitous in scientific and engineering applications. Likelihood-based methods for fitting such models, which includes all Bayesian methods, have desirable statistical properties and are thus the methods of choice when feasible. However, calculating the likelihood function even once can be a challenge for N irregularly sited observations from such a process, requiring O(N 2 ) memory and O(N 3 ) complexity. Thus, there is a need for fast and accurate likelihood approximation even for N on the order of 10 5 , not to mention the 10 15 implied by petascale data. The main objective of this research was to develop computational tools for the statistical analysis of massive spatiotemporal datasets based on Gaussian process models. Another important objective was the development of appropriate statistical models for specific spatiotemporal processes arising in the physical sciences.