An Efficient Surrogate Modeling Approach in Bayesian Uncertainty Analysis

We develop an efficient sparse-grid Bayesian approach for quantifying parametric and predictive uncertainties of physical systems constrained by stochastic PDEs. An accurate surrogate posterior distribution is constructed using sparse-grid interpolation and integration. It improves the simulation efficiency by accelerating the evaluation of the posterior distribution without losing much accuracy, and by determining an appropriate importance density for importance sampling which is easily sampled and captures the main features of the exact posterior distribution.