Nearest-Neighbor Non-Gaussian Processes for Geostatistical Modeling

2026-08-23

AI Summary

本文提出了一种最近邻非高斯过程(NNnGP)，通过引入非线性条件均值函数来有效捕捉复杂的非高斯空间特征，采用变分推理方法进行后验计算和预测。

Abstract

We develop a general class of nearest-neighbor non-Gaussian processes (NNnGP) for modeling geostatistical data. By introducing non-linear conditional mean functions into the Vecchia approximation, NNnGP extends the popular nearest-neighbor Gaussian process (NNGP) to effectively capture complex, non-Gaussian spatial characteristics. To ensure coherent spatial predictions from a single realization, we propose a regularized homogeneity condition across the univariate conditionals. We then formulate a Bayesian non-parametric construction of the conditional mean using Gaussian processes and embed the resulting NNnGP as a non-Gaussian spatial prior within a hierarchical regression model. For posterior computation and prediction, we adopt a normalizing flow-based variational inference approach. Numerical experiments on synthetic data and real-world PRISM precipitation anomalies demonstrate that NNnGP captures local non-linear dependencies and significantly mitigates the underestimation of extreme spatial events, all the while maintaining global predictive accuracy.

Problem

• non-Gaussian processes
• geostatistical modeling
• spatial characteristics
• local non-linear dependencies
• extreme spatial events

Innovation

• Nearest-Neighbor Non-Gaussian Processes
• Non-linear Conditional Mean Functions
• Regularized Homogeneity Condition
• Variational Inference with Normalizing Flows