Scalable Bayesian Transport Maps for High-Dimensional Non-Gaussian Spatial Fields

• 成果类型: Article
• 署名作者: Katzfuss, Matthias; Schafer, Florian
• 署名单位: Texas A&M University System; Texas A&M University College Station; University System of Georgia; Georgia Institute of Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2197158
• 发表日期: 2024
• 页码: 1409-1423
• 关键词: ensemble kalman filter; nonparametric-estimation; NONSTATIONARY; models; SYSTEM

摘要

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 uncertainty quantification of the map estimation, while resulting in a closed-form and invertible posterior map. We then focus on inferring the distribution of a nonstationary spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible and are motivated by the behavior of a large class of stochastic processes. Our approach is scalable to high-dimensional distributions due to data-dependent sparsity and parallel computations. We also discuss extensions, including Dirichlet process mixtures for flexible marginals. We present numerical results to demonstrate the accuracy, scalability, and usefulness of our methods, including statistical emulation of non-Gaussian climate-model output. for this article are available online.