Course Description

This module is an introduction to Markov chain Monte Carlo (MCMC) methods with some simple applications in infectious disease studies. The course includes an introduction to Bayesian statistics, Monte Carlo, MCMC, some background theory, and convergence diagnostics. Algorithms include Gibbs sampling, Metropolis-Hastings and their combinations. Familiarity with the R statistical environment or other computing language is important.

Logistics

Time: July 17-18, 8:30 am - 5:00 pm, July 19, 8:30 am - 12:00 pm

Place: FSH 107

Instructors: Kari Auranen, M. Elizabeth Halloran, Volodymyr Minin

Teaching Assistant: Isaac Goldstein

Schedule:: mcmc_time_table.pdf

R tutorials: R for Beginners, Swirl (Learn R, in R), SISMID/SISG Introduction to R

Stan installation: Stan Installation Instructions

Course materials

Introduction to Bayesian inference and Gibbs sampling

Slides/Notes	Practicals	Code
slides_bayesintro.pdf	PracticalBayes.pdf	bayesintro2023.R
	PracticalGibbs.pdf	chainGibbs_reduced.R
		chainGibbs.R

Classical Monte Carlo and Markov chain theory

Slides/Notes	Practicals	Code
mc_mcmc2023.pdf (pages 8-14)	import-sampling-lab.pdf	imp_sampl_reduced.R
		imp_sampl.R
	ehrenfest_diff-lab.pdf	ehrenfest_diff_reduced.R
		ehrenfest_diff.R
		beta_monte_carlo.R

Metropolis-Hastings algorithm

Slides/Notes	Practicals	Code
mc_mcmc2023.pdf (pages 14-18)	mh-lab.pdf	norm_mh_reduced.R
		norm_mh.R
		infect_time_reduced.R
		infect_time.R

Gibbs sampling and chain binomial model

Slides/Notes	Practicals	Code
mc_mcmc2023.pdf (pages 18-20)	PracticalGibbs.pdf	chainGibbs.R

Metropolis-Hastings and Gibbs combined

Slides/Notes	Practicals	Code
mc_mcmc2023.pdf (pages 20-21)	betabin-lab.pdf	beta_bin_reduced.R
		beta_bin.R

Chain binomial model revisited

Slides/Notes	Practicals	Code
chain_bin_revisited.pdf	chain-bin-revisit-lab.pdf	checkmodel_reduced.R
		checkmodel.R
		chain_hierarchical_reduced.R
		chain_hierarchical.R
		check_hierarchical.R

Hamiltonian Monte Carlo and stan

Slides/Notes	Practicals	Code
intro_to-stan.pdf	Beta-binomial in Stan	beta_binomial_example.Rmd
		beta_binom.stan
bayes_ode.pdf	SIR ODE in Stan	stan_sir_example.Rmd
		SIR.stan

General epidemic (SIR) model

Slides/Notes	Practicals	Code
sir_lecture.pdf	sir-lab.pdf	SIRaugmentation_reduced.R
		SIRaugmentation.R

Monte Carlo error and MCMC diagnostics

Slides/Notes	Practicals	Code
mc_mcmc2023.pdf (pages 21-22)	diagnostics-lab.pdf	diagnostics_reduced.R
		diagnostics.R

SIS model

Slides/Notes	Practicals	Videos	Code
sis_lecture.pdf	sis-lab.pdf		simulateSIS_N.R
			MH_SIS.R

Useful Books: 📘

• A.A. Johnson, M. Ott, M. Dogucu. Bayes Rules! An Introduction to Bayesian Modeling with R, 2023.
• C.P. Robert and G. Casella. Monte Carlo statistical methods, 2nd edition, Springer-Verlag, 2004.
• C.P. Robert and G. Casella. Introducing Monte Carlo methods with R, Springer-Verlag, 2009. (a more hands-on version of the first book by the same authors)
• J. Albert. Bayesian computation with R, 2nd edition, Springer-Verlag, 2009.
• P. Brémaud. Markov chains: Gibbs fields, Monte Carlo simulation, and queues, Springer-Verlag, 1999.

Other Resources: 🗒️

• L. Tierney. Markov Chains for Exploring Posterior Distributions, Annals of Statistics, 22, 1701-1762, 1994.
• S. Chib. and E. Greenberg. Understanding the Metropolis-Hastings Algorithm, The American Statistician, 49, 327-335, 1995.
• G. Casella and E.I. George. Explaining the Gibbs Sampler, The American Statistician, 46, 167-174, 1992.