Talk Title
Bayesian Transport Maps with Flexible Marginal Regressions for Non-Gaussian High-Dimensional Spatial Fields
Abstract
In Bayesian transport maps as introduced by Katzfuss and Schaefer (2023), a multivariate distribution is described by a triangular map from the target distribution to the standard normal distribution through a set of independent Gaussian process regressions. These regressions assume additive Gaussian errors. Previous work indicates that this assumption may be overly restrictive for complex applications like the emulation of climate models. We present a multi-stage inference approach to overcome this assumption: after an initial fit of the transport map, we correct for non-Gaussianity in the marginal error distributions by applying penalized transformation models. Regularizing priors govern the deviations from Gaussianity, and the computations are fully parallel. The approach can be used to evaluate the target distribution and to generate new random samples. We present numerical results to demonstrate the feasibility of the method and illustrate its use in the emulation of non-Gaussian climate model output.
"Johannes Brachem is a PhD student in applied statistics at the University of Goettingen, where he works on the development of penalized transformation models, a form of flexible semi-parametric distributional regression. Specifically, his research is focused on relaxing assumptions on the shape of the response distribution, while preserving interpretability for quantities of interest like its location and scale. He is particularly passionate about Bayesian modeling.
Bio
Currently, Johannes is visiting the University of Wisconsin-Madison on a 6-month scholarship awarded by the German Academic Exchange Service. At UW-Madison, he works with Matthias Katzfuss on the integration of penalized transformation models with Bayesian transport maps to relax distributional assumptions in the modeling of high-dimensional spatial fields.
Prior to specializing in statistics, Johannes obtained a Master's degree in Psychology from the University of Goettingen, where he focused on experiment design and research reproducibility, driven by the so-called replication crisis in Psychology. This experience fueled his pursuit of a Master's degree in Applied Statistics, also at the University of Goettingen.
An important aspect of Johannes' work is the development of research software. He is a part of the development team for the probabilistic programming framework Liesel (liesel-project.org) and developed extensions of Liesel for conditional transformation models as well as penalized transformation models. He also works on the development of alfred3, a Python framework for the creation of computer experiments in the social sciences.
Website: www.jobrachem.com"