In probabilistic risk assessment (PRA), epistemic uncertainties associated with input elements of the system are propagated through the model and represented as probability distributions of the resulting risk metrics. Uncertainty importance measures quantify how input uncertainties influence output uncertainty, and can provide a rational basis for safety-related decision-making as well as for prioritizing data acquisition and model improvements aimed at reducing epistemic uncertainty.

Various uncertainty importance measures have been proposed for PRA, including variance-based and moment-independent measures. However, when input uncertainty causes both a shift in the location of the output distribution and a change in its shape, existing measures often have difficulty distinguishing these effects and interpreting their practical significance. From the viewpoint of uncertainty characterization, these two types of distributional change correspond to bias and variance, respectively, where “variance” is defined here in a broad sense as the non-bias component of the distributional difference, arising mainly from discrepancies in distributional shape. Distinguishing them is important for safety-related decision-making, because they may imply different priorities for uncertainty reduction and risk management.

To address this issue, this study investigates an uncertainty importance evaluation method based on the Wasserstein distance, an optimal transport metric between probability distributions. Specifically, by using a decomposition of the squared Wasserstein-2 distance, we construct a framework that separates distributional differences into bias and variance components. Through numerical analyses, we demonstrate that the proposed method can quantify uncertainty effects that are difficult to capture with existing measures, and can more rationally support the prioritization of data acquisition and model improvements for reducing epistemic uncertainty in PRA.