Sequential Bayesian Polynomial Chaos Model Selection for Estimation of Sensitivity Indices

Global sensitivity analysis for expensive-to-evaluate functions can be conveniently performed with a polynomial chaos metamodel of the function. This paper proposes a sequential Bayesian approach that incorporates the effect sparsity and hierarchy principles to identify sparse polynomial chaos metamodels. A hierarchical Bayesian model is employed for model selection, and the best metamodel is identified by optimizing the posterior model probability. Explicit expressions for important posterior quantities are derived. A sequential procedure is proposed in which experiment runs are added until changes in the posterior mean of the coefficients of the polynomial metamodel are small. Point and interval estimates of sensitivity indices are obtained via simulation from the posterior distribution of the model coefficients conditioned on the highest posterior probability model. Examples show that the proposed approach can identify high degree metamodels that give accurate estimates of sensitivity indices with a small number of runs. MATLAB code implementing the proposed method is available upon request.