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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 #317237
Title: Scalable Bayesian Transport Maps for High-Dimensional Non-Gaussian Spatial Fields
Author(s): Matthias Katzfuss* and Florian Schaefer
Companies: Texas A&M University and Caltech
Keywords: Gaussian process; maximin ordering; climate-model emulation; Dirichlet process mixture; sparse triangular transport

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian processes. This enables regularization and accounting for uncertainty in the map estimation, while still resulting in a closed-form invertible posterior map. We then focus on inferring the distribution of a spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible but shrink toward a Gaussian field with Matern-type covariance. The approach is scalable to high-dimensional fields due to data-dependent sparsity and parallel computations. We also discuss extensions, including Dirichlet process mixtures for marginal non-Gaussianity. We present numerical results to demonstrate the accuracy, scalability, and usefulness of our methods, including statistical emulation of non-Gaussian climate-model output.

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

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