SISMID Module 8 2021

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 14, 11:30 am - 2:30 pm, July 15-16, 8:00 am - 2:30 pm

Place: https://uci.zoom.us/j/93113380619

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: pre-recorded video

Introduction to Bayesian inference and Gibbs sampling

Slides/Notes	Practicals	Videos	Code
slides_bayesintro.pdf	PracticalBayes.pdf	bayes_intro_lecture	bayesintro2021.R
	PracticalGibbs.pdf	bayes_intro_lab	chainGibbs_reduced.R
		chain-binomial Gibbs sampler	chainGibbs.R
		bayes_gibbs_live
		gibbs_lab_live1
		gibbs_lab_live2

Classical Monte Carlo and Markov chain theory

Slides/Notes	Practicals	Videos	Code
mc_mcmc2021.pdf (pages 8-14)	import-sampling-lab.pdf	mc_lecture_live	imp_sampl_reduced.R
		imp_sampl_lab_live	imp_sampl.R
	ehrenfest_diff-lab.pdf	markov_theory_live	ehrenfest_diff_reduced.R
		ehrenfest_lab_live	ehrenfest_diff.R

Metropolis-Hastings algorithm

Slides/Notes	Practicals	Videos	Code
mc_mcmc2021.pdf (pages 14-18)	mh-lab.pdf	lecture_and_mh_lab_live	norm_mh_reduced.R
			norm_mh.R
			infect_time_reduced.R
			infect_time.R

Gibbs sampling and chain binomial model

Slides/Notes	Practicals	Videos	Code
mc_mcmc2021.pdf (pages 18-20)	PracticalGibbs.pdf	gibbs_lecture_live	chainGibbs.R

Metropolis-Hastings and Gibbs combined

Slides/Notes	Practicals	Videos	Code
mc_mcmc2021.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_checking 1	checkmodel_reduced.R
		model checking 2	checkmodel.R
		model_check_lec_live	chain_hierarchical_reduced.R
		model_check_lab_live	chain_hierarchical.R
			check_hierarchical.R

General epidemic (SIR) model 🧟

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

Monte Carlo error and MCMC diagnostics

Slides/Notes	Practicals	Videos	Code
mc_mcmc2021.pdf (pages 21-22)	diagnostics-lab.pdf		diagnostics_reduced.R
			diagnostics.R

Useful Books: 📘

• A.A. Johnson, M. Ott, M. Dogucu. Bayes Rules! An Introduction to Bayesian Modeling with R, 2021.
• 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.