Introduction to MCMC

Online Lab Schedule:

• Monday, June 22, 1:00 - 2:30 PM ET and 3:00 - 4:30 PM ET
• Tuesday June 23, 1:00 - 2:30 PM ET and 3:00 - 4:30 PM ET

Classroom: Virtual

Module Summary:
Bayesian statistical models are frequently applied in scientific research for their flexibility in handling complex systems and sparse data and their convenient implementation. This module aims to introduce the basic Bayesian methodolgy for estimating key epidemiological parameters governing transmission dynamics and control of infectious diseases, with an emphasis on hands-on experience in building and interpreting models for practical problems with real data.

The course includes a gentle introduction to Bayesian statistics and inferential algorithms based on Markov chain Monte Carlo (MCMC) methods (such as Gibbs sampling and the Metropolis-Hastings algorithm) in the context of modeling transmission of infectious diseases at both the population level and the individual level. Model diagnostics and model selection will be discussed. The module will be supplemented with special topics in missing data and forecasting. The sessions will alternate between lectures and labs.

Prerequisites:
This module assumes undergraduate level of probability and inference covered in an introductory statistical course. Students will learn how to use R to analzye and forecast infectious disease transmission dynamics. Students are expected to have basic knowledge of the R computing environment, e.g., load, manipulate and visualize data. Students new to R or R Studio should complete a tutorial before the module (see example below).

https://www.youtube.com/watch?v=_V8eKsto3Ug&ab_channel=freeCodeCamp.org

https://www.youtube.com/watch?v=yZ0bV2Afkjc&ab_channel=EquitableEquations

https://www.youtube.com/watch?v=ANMuuq502rE&ab_channel=GlobalHealthwithGregMartin

Module Content:

• Part I: Basics of Bayesian inference and MCMC
  • Lecture 1: Introduction to Bayesian inference
  • Lecture 2: Conjugate prior distributions
  • Lecture 3: Monte Carlo approximation, posterior predictive distributions, and importance sampling
  • Lecture 4: Metropolis algorithm, Metropolis-Hastings algorithm and Gibbs sampling
  • Lecture 5: MCMC diagnostics and model selection
• Part II: Bayesian modeling for infectious diseases (using Rstan)
  • Case study 1: Estimating distribution of serial interval
  • Case study 2: Poisson and Negative Binomial processes
  • Case study 3: SIR model and R
  • Case study 4: Meta-population transmission model

Each part has a few practice sessions.