STAMPS@CMU presents:

Non-Gaussian Emulation of Climate Models via Scalable Bayesian Transport Maps

by Matthias Katzfuss (University of Wisconsin, Madison)

Online webinar March 22, 2024 at 1:30-2:30 PM ET.
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Abstract
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 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 present numerical results to demonstrate the accuracy, scalability, and usefulness of our generative methods, including emulation of non-Gaussian climate-model output.

Bio

Matthias Katzfuss is a Professor in the Department of Statistics at University of Wisconsin–Madison. His research interests include computational spatial and spatio-temporal statistics, Gaussian processes, uncertainty quantification, and data assimilation, with applications to environmental and satellite remote-sensing data. His research has been funded by NSF, NASA, NOAA, USDA, Sandia National Laboratory, Jet Propulsion Laboratory, and Texas A&M Institute of Data Science. Matthias is the recipient of an NSF Career Award, a Fulbright Scholarship, and an Early Investigator Award from the American Statistical Association’s Section on Statistics and the Environment.