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 :date:

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

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

Schedule:: mcmc_time_table.pdf :alarm_clock:

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

Course materials :open_book:

Course Introduction: pre-recorded video :movie_camera:

Introduction to Bayesian inference and Gibbs sampling :telescope:

Slides/Notes :green_book: Practicals :microscope: Videos :movie_camera: Code :computer:
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 :diamonds: :spades: :hearts: :clubs: :game_die:

Slides/Notes :green_book: Practicals :microscope: Videos :movie_camera: Code :computer:
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 :frog:

Slides/Notes :green_book: Practicals :microscope: Videos :movie_camera: Code :computer:
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 :chains:

Slides/Notes :green_book: Practicals :microscope: Videos :movie_camera: Code :computer:
mc_mcmc2021.pdf (pages 18-20) PracticalGibbs.pdf gibbs_lecture_live chainGibbs.R

Metropolis-Hastings and Gibbs combined :octopus:

Slides/Notes :green_book: Practicals :microscope: Videos :movie_camera: Code :computer:
mc_mcmc2021.pdf (pages 20-21) betabin-lab.pdf beta_bin_lab_live beta_bin_reduced.R
      beta_bin.R

Chain binomial model revisited :chains:

Slides/Notes :green_book: Practicals :microscope: Videos :movie_camera: Code :computer:
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 :green_book: Practicals :microscope: Videos :movie_camera: Code :computer:
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 :woman_mechanic:

Slides/Notes :green_book: Practicals :microscope: Videos :movie_camera: Code :computer:
mc_mcmc2021.pdf (pages 21-22) diagnostics-lab.pdf   diagnostics_reduced.R
      diagnostics.R

Useful Books: 📘

Other Resources: 🗒️