用新型非高斯依赖模型提升空间预测精度
A2 Copula-Driven Spatial Bayesian Neural Network For Modeling Non-Gaussian Dependence: A Simulation Study
- 将A2 copula嵌入神经网络权重初始化，捕捉极端共变关系
- 在多种依赖强度下均保持高精度，优于传统高斯方法
- 适合处理极端事件频发的空间数据建模任务
本文提出A2 Copula空间贝叶斯神经网络（A2-SBNN），一种用于将坐标映射为连续场的预测性空间模型，可同时捕捉典型空间模式与极端依赖关系。通过将新型双尾阿基米德copula（A2）直接嵌入网络权重初始化，A2-SBNN自然建模复杂空间关系，包括数据中罕见的共变行为。模型采用基于校准的训练过程，结合Wasserstein损失、矩匹配和相关性惩罚，以优化预测并管理不确定性。仿真结果表明，A2-SBNN在多种依赖强度下均保持高精度，为超越传统高斯方法的空间数据建模提供了新而有效的解决方案。
原文摘要 · Abstract (English)
In this paper, we introduce the A2 Copula Spatial Bayesian Neural Network (A2-SBNN), a predictive spatial model designed to map coordinates to continuous fields while capturing both typical spatial patterns and extreme dependencies. By embedding the dual-tail novel Archimedean copula viz. A2 directly into the network's weight initialization, A2-SBNN naturally models complex spatial relationships, including rare co-movements in the data. The model is trained through a calibration-driven process combining Wasserstein loss, moment matching, and correlation penalties to refine predictions and manage uncertainty. Simulation results show that A2-SBNN consistently delivers high accuracy across a wide range of dependency strengths, offering a new, effective solution for spatial data modeling beyond traditional Gaussian-based approaches.
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