Modeling nonstationary spatial processes with normalizing flows
stat.ME, stat.ML
Submitted: 2025-09-16
Updated: 2026-09-21
Code: https://github.com/pratiknag/Spatial_NormalizingFlows_
License: http://creativecommons.org/licenses/by/4.0/
The gist: Nonstationary spatial processes can often be represented as stationary processes on a warped spatial domain.
Terminology
Abstract
Nonstationary spatial processes can often be represented as stationary processes on a warped spatial domain. Selecting an appropriate spatial warping function for a given application is often difficult and, as a result of this, warping methods have largely been limited to two-dimensional spatial domains. In this paper, we introduce a novel approach to modeling nonstationary, anisotropic spatial processes using neural autoregressive flows (NAFs), a class of invertible mappings capable of generating complex, high-dimensional warpings. Through simulation studies we demonstrate that a NAF-based model has greater representational capacity than other commonly used spatial process models. We apply our proposed modeling framework to a subset of the 3D Argo Floats dataset, highlighting the utility of our framework in real-world applications.
Sources
- NICE: Non-linear Independent Components Estimation
- Review: Nonstationary Spatial Modeling, with Emphasis on Process Convolution and Covariate-Driven Approaches
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