9 Day 9 (February 18)

9.1 Announcements

• The material I talk about today will come from Chapters 4, 6, and 23.

• Activity 3 questions?

9.2 Introduction to Metropolis-Hastings algorithm

• Note this material is in Ch. 4

• What is a Metropolis-Hastings algorithm?

• Why use a Metropolis-Hastings algorithm?

  • Only need to know a function that is proportional to the PDF/PMF
  • Why this is such a big deal for Bayesian statistics?
  • What else do we need to unlock the power of Bayesian?

• What we loose by using a Metropolis-Hastings algorithm

  • Requires a bit more programming and supervision/checking
  • Correlated samples vs. independent samples
  • Burn-in interval

• Live example using bat and coin data/model

  • See pg. 25 in book for algorithm
  • Download R script

• Automated software

  • All of this in R (WinBugs, OpenBugs, JAGS, NIMBLE, STAN, etc)

9.3 Our second statistical model

• Dig into the rabies test a bit more….
  • Rabies test results
  • Building a statistical model using a hierarchical Bayesian approach
  • Specify (write out) the data model
  • Specify the process model
  • Specify the parameter model (or prior) including hyper-parameters
  • Select an approach to obtain the posterior distribution
    • Gibbs sampler
    • Derive full conditionals
    • Discussion of trade-offs with Gibbs sampler with analytical full conditionals vs. Metropolis-Hastings