Regional Variance-Based Sensitivity Analysis and a Study of Regional Equifinality

Two major things came out of this paper.

First, we developed a regional sensitivity analysis based on variance-based measures. Existing regional sensitivity analysis commonly relies on distance-based measures, which can be harder to interpret and do not give the same additive decomposition of importance. Our approach computes sensitivity indices separately across regions of the output distribution, showing not only which inputs matter, but where in the output space they matter. Because the indices are variance-based, their contributions can also be combined to show how much of the output variance is explained within each region.

Second, this led us to an interesting phenomenon: regional equifinality. In many models, the total explained variance drops sharply in the middle regions of the output space. Why? The same output values can be produced by different combinations of inputs. Their effects become partly indistinguishable 😶‍🌫️, almost as if several parallel worlds were playing out simultaneously but arriving at the same outcome.

The paper develops and validates the method across benchmark models and then demonstrates it on a flood-risk model. Regional analysis reveals changes in input importance and interaction structure that are hidden by global sensitivity indices, while the summed regional indices provide a direct diagnostic of where the model becomes more or less explainable.