Selection and Adaptation of Computational Models in the Presence of Uncertainty: Predictive Models of Random Heterogeneous Media

ABSTRACT - J. Tinsley Oden

A general Bayesian framework for selecting, calibrating, validating, and optimizing computational models of the behavior of complex, physical systems in the presence of uncertainties is presented. The selection and adaptive control of models is based on the calculation of model plausibilities as weighted values of model evidences, on estimates of sensitivity of outputs to the choice of model parameters, and on a posteriori estimates of modeling and discretization error in quantities of interest. To demonstrate the theory and predictive paradigm the estimation and control of modeling error and adaptive multiscale modeling of random heterogeneous media are also discussed.