Distinguishing sources of predictive uncertainty is of crucial importance in the application of forecasting models across various domains. Despite the presence of a great variety of proposed uncertainty measures, there are no strict definitions to disentangle them. Furthermore, the relationship between different measures of uncertainty quantification remains somewhat unclear. In this work, we introduce a general framework, rooted in statistical reasoning, which not only allows the creation of new uncertainty measures but also clarifies their interrelations. Our approach leverages statistical risk to distinguish aleatoric and epistemic uncertainty components and utilizes proper scoring rules to quantify them. To make it practically tractable, we propose an idea to incorporate Bayesian reasoning into this framework and discuss the properties of the proposed approximation.

翻译：区分预测不确定性的来源在各个领域预测模型的应用中至关重要。尽管已有多种不确定性度量方法被提出，但缺乏严格的定义来厘清它们之间的关系。此外，不同不确定性量化度量之间的关联仍不明确。本文提出一个基于统计推理的通用框架，该框架不仅能构建新的不确定性度量，还能阐明它们之间的相互关系。我们的方法利用统计风险来区分偶然不确定性和认知不确定性成分，并采用适当评分规则对其进行量化。为使该框架具有实际可操作性，我们提出将贝叶斯推理融入该框架的思路，并讨论了所提近似的性质。