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

Abstract

Models in risk analysis frequently exhibit nonlinear behavior, thresholds, and regime shifts, which challenge conventional global sensitivity analysis (GSA) paradigms. Classical variance-based methods quantify input importance over the entire output space, which can mask how these sensitivities vary across regions that are most relevant for decision making. Existing regional SA approaches, while capable of revealing such heterogeneity, are typically either qualitative or rely on unitless measures that complicate interpretation. This paper addresses these shortcomings by introducing a regional variance-based sensitivity analysis framework that retains the interpretability of variance-based indices while simultaneously resolving their spatial aggregation. Building on a recently developed efficient variance-based GSA method, we extend its formulation to quantify input importance conditionally within the output- or input-defined regions. The proposed approach operates directly on available input–output samples to circumvent any need for specialized experimental designs. To assess its robustness, we conduct a systematic evaluation across 16 benchmark models and nine metafunctions. We further highlight the method's ability to estimate the overall portion of the output variance explained across its regions. This property enables the study of the phenomenon of regional equifinality, which manifests as reduced overall explainability in the middle regions due to multiple combinations of inputs leading to outputs within the same region. We demonstrate the method's practical value on a canonical flood risk model, which systematically reveals substantial regime-dependent shifts in input variable importance. The results show that this new, regional variance-based SA enables a much deeper, decision-relevant characterization of model behavior that bridges the existing gap between GSA and threshold-focused risk assessment.