Titlebook: Uncertainty Quantification and Predictive Computational Science; A Foundation for Phy Ryan G. McClarren Textbook 2018 Springer Nature Switz

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Probability and Statistics Preliminariesjection. The use of the Box-Mueller transform to sample a normal random variable and the Cholesky factorization technique for sampling a multivariate normal are presented. The chapter concludes with a discussion of Bayesian statistics.

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Input Parameter Distributions of realizations of finitely many RV as well as the analogue for stochastic processes, the Karhunen-Loève expansion. Section 3.6 closes with some remarks on the delicate issue of choosing input distributions.

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Regression Approximations to Estimate Sensitivitiesful solutions also for the case where fewer QoI evaluations than parameters are available; sparsity-promoting regularization (1-norm, LASSO) and a combination of 1-norm and 2-norm (elastic net) are considered. Section 5.3 adds cross-validation techniques for selecting the regularization parameters.

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Introduction to Uncertainty Quantification and Predictive Sciencen to define the task of uncertainty quantification. The concept of a quantity of interest is defined, and the use of uncertainty information to answer questions regarding safety and design is presented.

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