Schedule
Tuesdays 4:30 pm-7:00pm at SAMSI, Research Triangle Park, NC, beginning Tuesday, August 28, 2018
No class during week of Thanksgiving (November 20, 2017)
Last class: Tuesday, December 4, 2018
Instructors: This course was jointly taught by multiple instructors; lead instructor is Ralph Smith, Professor of Mathematics, N.C. State University. Additional Instructor is: Jim Berger, Arts and Sciences, Statistics Professor, Duke University
Course Outline:
This course was offered in conjunction with the SAMSI year-long research program on Model Uncertainty: Mathematical and Statistical.
This course introduced statistical and mathematical sensitivity analysis and uncertainty quantification techniques for large-scale models arising in current applications. This included the construction and verification of surrogate models and emulators for complex simulation models, frequentist and Bayesian inference techniques, and techniques to quantify uncertainties associated with statistical quantities of interest. Examples were drawn from applications in materials science, biology and biomedical sciences, and nuclear engineering.
Registration:
- NCSU – MA 810.001
- UNC-CH – STOR 894.1 / MATH 892.1
- Duke – STA 790.01 / Math 790-71.01
Class Materials
| Date | Lecture Topic | Speaker | Slides |
|---|---|---|---|
| Aug 28 | Introduction to statistical and mathematical model uncertainty, with motivating examples | Jim Berger | |
| Sept 4 | Essentials of Bayesian hypothesis testing | Jim Berger | |
| Sept 11 | Essentials of Bayesian model uncertainty | Jim Berger | |
| ** Problem Set 1 (Attachment for Sept. 11th Lecture) ** | |||
| Sept 18 | Conventional priors for Bayesian model uncertainty | Jim Berger | |
| Sept 25 | Approximations, computation and model criticism | Jim Berger | |
| Oct 2 | Statistical representation of model inputs and quantities of interest in UQ | Ralph Smith | |
| ** For more material, visit Ralph Smith’s website at: http://www4.ncsu.edu/~rsmith/MA810_f18.html ** | |||
| Oct 9 | ** NO CLASS – October Break ** | ||
| Oct 16 | Bayesian inference for model calibration in UQ | Ralph Smith | |
| Oct 23 | Gaussian processes | Jim Berger | |
| Oct 30 | Statistical surrogate models | Jim Berger | |
| Nov 6 | Mathematical surrogate and reduced-order models | Ralph Smith | |
| Nov 13 | Sampling-based techniques for uncertainty propagation in UQ | Ralph Smith | |
| Nov 20 | ** NO CLASS – Thanksgiving Week ** | ||
| Nov 27 | Statistical and mathematical techniques for sensitivity and parameter subspace analysis | Ralph Smith | |
| Dec 4 | Model discrepancy in uncertainty quantification | Ralph Smith |
Questions: email Jim Berger or Ralph Smith