A2 Copula-Driven Spatial Bayesian Neural Network For Modeling Non-Gaussian Dependence: A Simulation Study

TL;DR

This paper introduces A2-SBNN, a novel spatial Bayesian neural network that incorporates a dual-tail Archimedean copula to effectively model complex and extreme dependencies in spatial data, outperforming traditional Gaussian models.

Contribution

The paper presents the first integration of A2 copula into a Bayesian neural network for spatial modeling, enabling better capture of non-Gaussian dependencies and extreme co-movements.

Findings

High accuracy across various dependency strengths

Effective modeling of extreme spatial dependencies

Outperforms traditional Gaussian-based methods

Abstract

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.