Learning Global Sensitivity Indices from Observational Data: A Metamodel-Based Approach

Giulia Vannucci

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arXiv · 2609.40342

Learning Global Sensitivity Indices from Observational Data: A Metamodel-Based Approach

Giulia Vannucci

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Abstract

Classical variance-based Global Sensitivity Analysis (GSA) assumes that the input--output mechanism can be repeatedly evaluated under a designed sampling scheme, which is infeasible when only a given sample of observations is available. We propose MM--GSA, a metamodel-based approach to GSA from observational data, in which supervised learning approximates the systematic input--output relationship. MM--GSA combines two complementary perspectives on input relevance: a model-agnostic estimator of the first-order Sobol' index, quantifying the contribution of an input to the variability of the systematic response, and a new trigger-based structural index, quantifying how predictive performance depends on the availability of a predictor across alternative predictor subsets. We establish consistency for both estimators and a variable-selection property for the structural index under input independence. Monte Carlo experiments and an NHANES application illustrate their finite-sample behavior and show that the two measures provide complementary information on input relevance.

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Giulia Vannucci. 2026-09-30. Learning Global Sensitivity Indices from Observational Data: A Metamodel-Based Approach. https://arxiv.org/abs/2609.40342

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