Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statistics face tremendous challenges due to the prohibitive computational burden. Various approximation methods have been introduced to reduce the computational cost. However, most of them rely on unrealistic assumptions for the underlying process and retaining statistical efficiency remains an issue. We develop a new approximation scheme for maximum likelihood estimation. We show how the composite likelihood method can be adapted to provide different types of hierarchical low rank approximations that are both computationally and statistically efficient. The improvement of the proposed method is explored theoretically; the performance is investigated by numerical and simulation studies; and the practicality is illustrated through applying our methods to two million measurements of soil moisture in the area of the Mississippi River basin, which facilitates a better understanding of the climate variability. Supplementary material for this article is available online.
Bibliographical noteFunding Information:
The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). The authors thank the anonymous reviewers for their valuable comments.
© 2018 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
- Gaussian process models
- Likelihood approximation
- Matérn covariance function
- Soil moisture
- Statistical efficiency
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Statistics and Probability
- Statistics, Probability and Uncertainty