MUMS Fall 2018: Model Uncertainty: Mathematical and Statistical


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.


  • 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: **
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