Adaptive Bayesian Nonstationary Modeling for Large Spatial Datasets Using Covariance Approximations

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

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)802-829
Number of pages28
JournalJOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
Volume23
Issue number3
DOIs
StatePublished - 2014
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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