Adaptive Bayesian Nonstationary Modeling for Large Spatial Datasets Using Covariance Approximations

Type
Article

Authors
Konomi, Bledar A.
Sang, Huiyan
Mallick, Bani K.

KAUST Grant Number
KUS-CI-016-04

Date
2014

Abstract
Gaussian process models have been widely used in spatial statistics but face tremendous modeling and computational challenges for very large nonstationary spatial datasets. To address these challenges, we develop a Bayesian modeling approach using a nonstationary covariance function constructed based on adaptively selected partitions. The partitioned nonstationary class allows one to knit together local covariance parameters into a valid global nonstationary covariance for prediction, where the local covariance parameters are allowed to be estimated within each partition to reduce computational cost. To further facilitate the computations in local covariance estimation and global prediction, we use the full-scale covariance approximation (FSA) approach for the Bayesian inference of our model. One of our contributions is to model the partitions stochastically by embedding a modified treed partitioning process into the hierarchical models that leads to automated partitioning and substantial computational benefits. We illustrate the utility of our method with simulation studies and the global Total Ozone Matrix Spectrometer (TOMS) data. Supplementary materials for this article are available online.

Citation
Konomi, B. A., Sang, H., & Mallick, B. K. (2014). Adaptive Bayesian Nonstationary Modeling for Large Spatial Datasets Using Covariance Approximations. Journal of Computational and Graphical Statistics, 23(3), 802–829. doi:10.1080/10618600.2013.812872

Acknowledgements
The research of Huiyan Sang was partially sponsored by National Science Foundation grant DMS-1007618 and the research of Bani Mallick was partially supported by NSF DMS 0914951. Bani Mallick and Huiyan Sang were also partially supported by award KUS-CI-016-04, made by King Abdullah University of Science and Technology. The authors thank the referees and the editors for valuable comments.

Publisher
Informa UK Limited

Journal
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS

DOI
10.1080/10618600.2013.812872

Additional Links
http://www.tandfonline.com/doi/full/10.1080/10618600.2013.812872

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