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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)

Parameter Selection Techniques

  • Lectures 5-8: Local and Global Sensitivity Analysis (PDF)
  • Complex Step Derivative Approximations (PDF)
  • Lecture 9: Active subspaces (PDF)

Statistical Model Calibration

  • Lectures 10-11: Frequentist techniques for model calibration (PDF)
  • Lectures 12-14: Bayesian techniques for model calibration: Part 1 (PDF)
  • Lectures 15-16: Bayesian techniques for model calibration: Part 2 (PDF)

Uncertainty Propagation in Models

  • Lectures 17-18: Uncertainty Propagation (PDF)

Surrogate Models

  • Lectures 19-21: Numerical Surrugate Models (PDF)
  • Lectures 12-23: Statistical Surrugate Models (PDF)
  • Lectures 24-25 Numerical Surrugate Models for PDE (PDF)

Model Discrepancy and Active Subspace-Based Inference

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