Uncertainty Quantification and Predictive Computational Science: A Foundation for Physical Scientist

Part I Fundamentals1. Introduction1.1. What is Uncertainty Quantification1.2. Selecting Quantities of Interest (QoIs)1.3. Identifying Uncertainties1.4. Physics-based uncertainty quantification1.5. From simulation to prediction1.6. Notes and References1.7. Exercises
2. Probability and Statistics Preliminaries2.1. Random Variables2.2. Moments and Expectation Values 2.3. Sampling Random variables2.4. Notes and References2.5. Exercises
3. Input Parameter Distributions3.1. Principle Components Analysis3.2. Copulas3.3. Choosing input parameter distributions3.4. Implications of distribution selection3.5. Notes and References3.6. Exercises
Part  II Local Sensitivity Analysis4. Derivative Approximations4.1. First-order approximations4.2. Scaled Sensitivity Coefficients4.3. Sensitivity Indices4.4. Automatic Differentiation4.5. Notes and References4.6. Exercises
5. Regression Approximations5.1. Sensitivity analyses with many parameters5.2. Least-squares regression5.3. Regularized regression5.4. Notes and References5.5. Exercises
6. Adjoint-based Local Sensitivity Analysis6.1. Adjoint equations for linear, steady-state models6.2. Adjoints for nonlinear, time-dependent models6.3. Notes and References6.4. Exercises
Part III Parametric Uncertainty Quantification7. From Sensitivity Analysis to UQ7.1. Applying distributions to SA results7.2. Limitations of SA for UQ7.3. Approximate QoI variance due to covariance of inputs7.4. Variable Selection 7.5. Notes and References7.6. Exercises
8. Sampling-Based UQ8.1. Basic Monte Carlo Method8.2. Pseudo-Monte Carlo  8.3. Quasi-Monte Carlo8.4. Notes and References8.5. Exercises9. Reliability Methods9.1. General Statement of Reliability Analysis9.2. First-Order Reliability Methods9.3. First-Order Second-Moment Reliability Methods9.4. Higher-Order approaches 9.5. Notes and References9.6. Exercises
10. Polynomial Chaos Methods10.1. The Polynomial Chaos Expansion10.2. Estimating Expansion Parameters using Quadrature10.3. Sparse Quadrature Rules10.4. Regression-based PCE10.5. Stochastic Finite Elements 10.6. Notes and References10.7. ExercisesPart IV Predictive Science11. Emulators and Surrogate Models11.1. Simple Surrogate Models11.2. Markov Chain Monte Carlo11.3. Gaussian Process Regression11.4. Bayesian MARS11.5. Notes and References11.6. Exercises
12. Reduced Order Models12.1. Proper Orthogonal Decomposition12.2. Active Subspace Methods 12.3. Notes and References12.4. Exercises
13. Predictive Models13.1. The Kennedy-O'Hagan Model13.2. Calibration and Data Assimilation13.3. Hierarchical Models13.4. Notes and References13.5. Exercises
14. Epistemic Uncertainties14.1. Horsetail Plots14.2. The Minkowski Metric14.3. Dempster-Shafer Theory14.4. Kolmogorov-Smirnoff Confidence Bounds14.5. The Method of Cauchy Deviates14.6. Notes and References14.7. Exercises
AppendicesA. A cookbook of distributions