A full scale approximation of covariance functions for large spatial data sets
KAUST Grant NumberKUS-CI-016-04
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AbstractGaussian process models have been widely used in spatial statistics but face tremendous computational challenges for very large data sets. The model fitting and spatial prediction of such models typically require O(n 3) operations for a data set of size n. Various approximations of the covariance functions have been introduced to reduce the computational cost. However, most existing approximations cannot simultaneously capture both the large- and the small-scale spatial dependence. A new approximation scheme is developed to provide a high quality approximation to the covariance function at both the large and the small spatial scales. The new approximation is the summation of two parts: a reduced rank covariance and a compactly supported covariance obtained by tapering the covariance of the residual of the reduced rank approximation. Whereas the former part mainly captures the large-scale spatial variation, the latter part captures the small-scale, local variation that is unexplained by the former part. By combining the reduced rank representation and sparse matrix techniques, our approach allows for efficient computation for maximum likelihood estimation, spatial prediction and Bayesian inference. We illustrate the new approach with simulated and real data sets. © 2011 Royal Statistical Society.
CitationSang H, Huang JZ (2011) A full scale approximation of covariance functions for large spatial data sets. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 74: 111–132. Available: http://dx.doi.org/10.1111/j.1467-9868.2011.01007.x.
SponsorsThe research of Huiyan Sang and Jianhua Z. Huang was partially sponsored by NationalScience Foundation grant DMS-1007618. Jianhua Z. Huang’s work was also partially supported by National Science Foundation grant DMS-09-07170 and National Cancer Institute grant CA57030. Both authors were supported by award KUS-CI-016-04, made by KingAbdullah University of Science and Technology. The authors thank the referees and theeditors for valuable comments. The authors also thank Dr Sudipto Banerjee, Dr ReinhardFurrer and Dr Lan Zhou for several useful discussions regarding this work, and they thankDr Cari Kaufman for providing the precipitation data set.