Predictive Uncertainty Quantification via Risk Decompositions for
  Strictly Proper Scoring Rules
Nikita Kotelevskii Maxim Panov
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.