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 package or other computing language would be helpful.

Logistics

Time: July 18-19, 8:00 am - 2:30 pm, July 20, 8:00 am - 11:00 am

Place: https://uci.zoom.us/j/99078849451 (check Slack for passcode)

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

Schedule:: mcmc_time_table.pdf

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

Course materials

Course Introduction: intro_video

Introduction to Bayesian inference and Gibbs sampling

Slides/Notes	Practicals	Videos	Code
slides_bayesintro.pdf	PracticalBayes.pdf	bayes_intro_lecture	bayesintro2022.R
	PracticalGibbs.pdf	bayes_intro_lecture_live	chainGibbs_reduced.R
		chain-binomial Gibbs sampler	chainGibbs.R
		chain_binomial_lecture_live
		chain_binomial_lab_live

Classical Monte Carlo and Markov chain theory

Slides/Notes	Practicals	Videos	Code
mc_mcmc2022.pdf (pages 8-14)	import-sampling-lab.pdf	monte_carlo_lecture_live	imp_sampl_reduced.R
		imp_sampl_lecture_lab_live	imp_sampl.R
		imp_sampl_lab_live1
		imp_sampl_lab_live2
		markov_theory_lecture_live1
	ehrenfest_diff-lab.pdf	ehrenfest_live	ehrenfest_diff_reduced.R
		ehrenfest_ergodic_live	ehrenfest_diff.R

Metropolis-Hastings algorithm

Slides/Notes	Practicals	Videos	Code
mc_mcmc2022.pdf (pages 14-18)	mh-lab.pdf	mh_lab_live	norm_mh_reduced.R
			norm_mh.R
		infect_time_gibbs_live	infect_time_reduced.R
			infect_time.R

Gibbs sampling and chain binomial model

Slides/Notes	Practicals	Videos	Code
mc_mcmc2022.pdf (pages 18-20)	PracticalGibbs.pdf		chainGibbs.R

Metropolis-Hastings and Gibbs combined

Slides/Notes	Practicals	Videos	Code
mc_mcmc2022.pdf (pages 20-21)	betabin-lab.pdf	beta_bin_lab_live	beta_bin_reduced.R
			beta_bin.R

Chain binomial model revisited

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

General epidemic (SIR) model

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

Monte Carlo error and MCMC diagnostics

Slides/Notes	Practicals	Videos	Code
mc_mcmc2022.pdf (pages 21-22)	diagnostics-lab.pdf	diagnostics_live	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, 2022.
• 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.