Aggregated Shapley effects: nearest-neighbor estimation procedure and confidence intervals. Application to snow avalanche modeling

María Belén Heredia (1) , Clémentine Prieur (2) , Nicolas Eckert (1)

1 UR ETGR (ETNA) - Erosion torrentielle neige et avalanches
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows

Dynamic models are simplified representations of some real-world entities that change over time. They are essential analytical tools with significant applications, e.g., in environmental and social sciences. The outputs produced by dynamic models are typically time and/or space dependent. Due to physical constraints, their parameters cannot be considered as independent from each others. Also, they can be significantly sensitive to variations of input parameters. A global sensitivity analysis (GSA) consists in modeling input parameters by a probability distribution which propagates through the model to the outputs. Then, input parameters are ordered according to their contribution on the model outputs by computing sensitivity measures. In this paper, we extend Shapley effects, a sensitivity measure well suited for dependent input parameters, to the framework of dynamic models. We also propose an algorithm to estimate the so-called aggre-gated Shapley effects and to construct bootstrap confidence intervals for the estimation of scalar and aggregated Shapley effects. We measure the performances of the estimation procedure and the accuracy of the probability of coverage of the bootstrap confidence intervals on toy models. Finally, our procedure is applied to perform a GSA of an avalanche flow dynamic model, for which the input/output sample is obtained from an acceptance-rejection algorithm. More precisely, we analyze the sensitivity in two different settings: (i) little knowledge on the input parameter probability distribution, and (ii) well-calibrated input parameter distribution. Probative linkages between local slope 1 and sensitivity indices demonstrate the usefulness of our approach for practical problems.

Domaines: Statistiques [math.ST]

María Belén Heredia, Clémentine Prieur, Nicolas Eckert. Aggregated Shapley effects: nearest-neighbor estimation procedure and confidence intervals. Application to snow avalanche modeling. 2020. ⟨hal-02908480v1⟩