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MA 797

Uncertainty Quantification for Physical and Biological Models





Background and Motivation

  • Lecture 1: Motivation and Prototypical Examples (PDF)

Probability and Statistics Background

  • Lectures 2-4: Statistical models and interval estimators (PDF)
  • Supplemental Material: Random variables, estimators and sampling distributions (PDF)

Representation of Random Inputs

  • Lectures 5-7: Representation of random variables and random fields (PDF)
  • Revised Version of Chapter 5 (PDF)

Parameter Selection Techniques

  • Lectures 8-11: Local and Global Sensitivity Analysis (PDF)
  • Lecture 12-13: Active subspaces (PDF)
  • Saltelli Implementation Algorithm (PDF)

Statistical Model Calibration

  • Lectures 13-14: Frequentist techniques for model calibration (PDF)
  • Lectures 15-18: Bayesian techniques for model calibration (PDF)

Uncertainty Propagation in Models

  • Lecture 19: Linearly parameterized models (PDF)
  • Lectures 19 and 20: Random sampling, perturbation methods and prediction intervals (PDF)
  • Lectures 21-23: Stochastic spectral methods (PDF)
  • Lectures 24-26: Sparse grid quadrature and interpolation (PDF)
  • Lecture 26: Sparse grid example (PDF)

Surrogate Models

  • Lectures 27-28: Surrogate and Reduced-Order Models (PDF)

Model Discrepancy and Active Subspace-Based Inference

  • Lecture 29: Model discrepancey (PDF)
  • Lecture 29: Active subspace-based Bayesian inference (PDF)