题目：How Uncertain are Oil Prices? Bayesian Regularized Distribution Neural Network for Forecasting Oil Prices

作者：He Jiang（江河），Yawei Dong(董亚伟，通讯作者），Shaolong Sun（孙少龙），Shouyang Wang（汪寿阳）

Abstract：Crude oil is an essential energy resource that plays a crucial role in driving global economic growth. Amidst deepening international trade and the backdrop of globalization, the volatility of the crude oil market has a direct impact on the global economic structure and international energy stability. Therefore, measuring oil price volatility has become a key task. In this study, we propose a framework based on Bayesian Regularized Distributed Neural Networks (BRDNN), which integrates econometric probability distribution models with deep learning neural networks. By employing a Gaussian mixture distribution, this framework achieves accurate predictions of crude oil prices. It effectively captures the uncertainty and volatility of oil prices while reducing cumulative errors and computational complexity. Empirical analysis of the Brent and WTI crude oil markets demonstrates that the proposed method outperforms mainstream probability distribution models in terms of predictive performance and robustness. This research provides a new perspective and effective tools for quantifying oil price uncertainty. Additionally, it holds significant value both theoretically and practically in developing scientific energy policies and risk management strategies.