Background and Motivation
- Lecture 1: Motivation and Prototypical Examples (PDF)
Probability and Statistics Background
- Lectures 2: Random variables, estimators and sampling distributions (PDF)
- Lectures 3-5: Statistical models and interval estimators (PDF)
Representation of Random Inputs
- Lecture 6: Representation of random variables and random fields (PDF)
- Lecture 7: Karhunen-Loeve Expansions (PDF)
Parameter Selection Techniques
- Lecture 8: Local Sensitivity Analysis (PDF)
- Lecture 9 and 10: Global Sensitivity Analysis (PDF) and (PDF)
- Lecture 11: Active subspaces (PDF) and (PDF)
- Saltelli Implementation Algorithm (PDF)
Statistical Model Calibration
- Lectures 11 and 12: Frequentist techniques for model calibration (PDF)
- Lectures 13-15: Bayesian techniques for model calibration (PDF)
Uncertainty Propagation in Models
- Lecture 16: Linearly parameterized models (PDF)
- Lectures 17 and 18: Random sampling, perturbation methods and prediction intervals (PDF)
- Lectures 19 and 20: Stochastic spectral methods (PDF)
- Lectures 21 and 22: Sparse grid quadrature and interpolation (PDF)
- Lecture 23: Sparse grid example (PDF)
Surrogate Models
- Lectures 23 and 24: Surrogate and Reduced-Order Models (PDF)
Model Discrepancy and Active Subspace-Based Inference
- Lecture 25: Model discrepancey (PDF)
- Lecture 26: Active subspace-based Bayesian inference (PDF)
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