  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.
