Shapley Effect Estimation using Polynomial Chaos

TL;DR

This paper introduces a novel method using Polynomial Chaos expansion to efficiently estimate Shapley effects, providing a global sensitivity analysis tool that accurately ranks uncertain model parameters in complex models.

Contribution

The paper proposes a Polynomial Chaos-based approach for estimating Shapley effects, enabling efficient and accurate global sensitivity analysis of complex models.

Findings

Validated on Ishigami function, showing correct variable ranking.

Applied to dynamic models, revealing time-varying parameter importance.

Compared favorably to Sobol indices in ranking accuracy.

Abstract

This paper presents an approach for estimating Shapley effects for use as global sensitivity metrics to quantify the relative importance of uncertain model parameters. Polynomial Chaos expansion, a well established approach for developing surrogate models is proposed to be used to estimate Shapley effects. Polynomial Chaos permits the transformation of a stochastic process to a deterministic model which can then be used to efficiently evaluate statistical moments of the quantity of interest. These moments include conditional variances which are algebraically mapped to Shapley effects. The polynomial chaos based estimates of Shapley effects are validated using Monte Carlo simulations and tested on the benchmark Ishigami function and on the dynamic SEIR epidemic model and the Bergman Type 1 diabetes model. The results illustrate the correct ranking of uncertain variables for the Ishigami function in contrast to the Sobol indices and illustrates the time-varying rank ordering of the model parameters for the dynamic models.