MCMC I For Infectious Diseases

Meeting Times:

• Monday, July 22, 8:30 AM – 5:00 PM
• Tuesday July 23, 8:30 AM – 5:00 PM
• Wednesday July 24, 8:30 AM – 12:00 PM

Classroom: Randall Rollins Building (RR 200)

Module Summary:
Mathematical models based on systems of ordinary differential equations (ODEs) are frequently applied in various scientific fields to assess hypotheses, estimate key model parameters, and generate predictions about the system's state. To support their application, this module introduces frequentist and Bayesian methods for estimating parameters and generating short-term forecasts with quantified uncertainty from dynamical models. Motivating practical examples will be based on epidemic models with varying levels of complexity. The course includes a general introduction to Bayesian statistics, Monte Carlo, and MCMC.

The course includes a general introduction to Bayesian statistics, Monte Carlo, and MCMC. Some relevant facts from the Markov chain theory are reviewed. Algorithms include Gibbs sampling and Metropolis-Hastings. A practical introduction to convergence diagnostics is included. The module will alternate between lectures and computer labs.

Prerequisites:
This module assumes knowledge of probability and inference covered in an introductory statistical course. Students will learn to use R and MATLAB toolboxes designed for parameter estimation and forecasting using dynamic models. Students are expected to have basic knowledge of the R computing environment. Students new to R should complete a tutorial before the module.

Module Content:

• Brief review of ordinary differential equation models applied to infectious disease transmission and control.
• Introduction to parameter identifiability
• Introduction to uncertainty quantification using parametric bootstrapping
• Model selection and assessing the quality of model fit
• Introduction to Bayesian statistics, Monte Carlo, and MCMC
• Bayesian modeling framework for fitting and forecasting epidemic trajectories in Stan
• Model-based forecasts with quantified uncertainty
• Metrics for assessing calibration and forecasting performance