Abstract:
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Advances in high performance computing have enabled detailed simulations of real world physical processes, and these simulations produce large datasets. Even as detailed as they are, these simulations are only approximations of imperfect mathematical models, and furthermore, their outputs depend on inputs that are themselves uncertain. The main goal of a validation and uncertainty quantification methodology is to determine the uncertainty, that is, the relationship between the true value of a quantity of interest and its prediction by the simulation. A principled approach to building hierarchical models, even relatively shallow, but informed by the available understanding of physics and statistics is a required step towards useful and rigorous uncertainty quantification of complex physics-based models, and addresses three main concerns: interpretability, probabilistic rigor and bounding of false discovery.
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