8 Day 8 (February 13)

8.1 Announcements

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

  • Final project is posted

    • Short lecture with donuts/meet people today

  • Activity 3 is posted

8.2 Introduction to Metropolis-Hastings algorithm

  • Note this material is in Ch. 4

  • What is a Metropolis-Hastings algorithm?

  • Why use a Metropolis-Hastings algorithm?

    • Original work (see link and link)
    • Wikipedia page
    • 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

  • Automated software

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

8.3 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