Discrepancies observed in practice between experimental and computational provide the basic motivation for performing quantitative model verification, validation, calibration through data assimilation, and predictive estimation. Estimation of the validation domain requires computation of contours of constant uncertainty in the high-dimensional space that characterizes the application of interest. Model calibration involves the integration (assimilation) of new experimental and-or computational data for updating (i.e., calibrating or adjusting) the parameters underlying the respective model. Also, the experimental facility must be adequately designed and instrumented in order to facilitate a comprehensive and accurate characterization of the operating, initial, and boundary conditions together with the accompanying experimental uncertainties. (Note here that often the required degree of detail was not routinely reported in published data ) Predictive estimation incorporates all of these activities, aiming at a probabilistic description of possible future computational and experimental outcomes, based on all recognized errors and uncertainties. Computational results almost always depend on inputs that are uncertain, rely on approximations that introduce errors, and are based on mathematical models1 that are imperfect representations of reality. Hence, given some calculated quantity of interest (QOI) from the computational model, the corresponding true physical QOI is uncertain. If this uncertaintythe relationship between the true value of the QOI and the prediction of the computational modelcannot be quantified or bounded, then the computational results have limited value .