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Activity Number: 190 - Contributed Poster Presentations: Section on Statistics and the Environment
Type: Contributed
Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistics and the Environment
Abstract #304132
Title: Bayesian Covariance Estimation for Large Spatial Data
Author(s): Brian Kidd* and Matthias Katzfuss
Companies: Texas A&M University and Texas A & M University
Keywords: modified Cholesky; sparsity; screening effect

Spatial statistics often assumes that the spatial field of interest is stationary and its covariance has a simple parametric form, but these strong assumptions are not appropriate in many applications. We propose nonstationary and nonparametric Bayesian inference on the covariance matrix for a spatial field, with a prior distribution that shrinks toward popular Matern-type covariances. Our prior is motivated by recent results on the so-called screening effect for such covariances, which ensures exponential decay of the entries of the Cholesky factor of the precision matrix under a specific ordering scheme. This decay also results in approximate sparsity of the Cholesky factor, so that the number of nonzero entries to be estimated and the resulting computational complexity are both linear in the number of spatial locations. We apply our methodology to output from global climate models, enabling cheap statistical emulation of these computationally expensive physical models.

Authors who are presenting talks have a * after their name.

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