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Activity Number: 197 - New Methods for Scalable Nonstationary Spatial Statistics
Type: Topic-Contributed
Date/Time: Tuesday, August 10, 2021 : 1:30 PM to 3:20 PM
Sponsor: Section on Statistics and the Environment
Abstract #317241
Title: Geostatistics Meets Variable Selection: Multi-Scale Models for Nonstationary Spatial Fields
Author(s): Bruno Sansó * and Daniel Kirsner
Companies: University of California, Santa Cruz and Chase Bank
Keywords: Geostatistics; Variable Selection; Bayesian Methods

To model random fields whose variability changes at differing scales we use multiscale kernel convolution models that rely on nested grids of knots at different resolutions. Thus, lower order terms capture large scale features, while high order terms capture small scale ones. To accommodate the space-varying nature of the variability we consider models where the coefficients of the kernel expansion vanish adaptively as the resolution grows. We develop an approach that relies on knot selection, to achieve parsimony, and discuss how this induces a field with spatially varying resolution. We extend shotgun stochastic search to the multi resolution model setting. Alternatively, we consider maximization methods for the estimation of the optimal model. These consist of using a sparsity inducing regularization term that, using an overlapping group penalty incorporates information about the structure of a recursive partitioning of the domain. We demonstrate that the proposed methods are computationally competitive and produce excellent fit to both synthetic and real datasets.

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

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