TY - JOUR
T1 - Hierarchical Low Rank Approximation of Likelihoods for Large Spatial Datasets
AU - Huang, Huang
AU - Sun, Ying
N1 - KAUST Repository Item: Exported on 2021-02-23
Acknowledgements: 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.
PY - 2017/9/21
Y1 - 2017/9/21
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/631117
UR - https://www.tandfonline.com/doi/full/10.1080/10618600.2017.1356324
UR - http://www.scopus.com/inward/record.url?scp=85041442432&partnerID=8YFLogxK
U2 - 10.1080/10618600.2017.1356324
DO - 10.1080/10618600.2017.1356324
M3 - Article
AN - SCOPUS:85041442432
VL - 27
SP - 110
EP - 118
JO - Journal of Computational and Graphical Statistics
JF - Journal of Computational and Graphical Statistics
SN - 1061-8600
IS - 1
ER -