9 Day 9 (February 14)

9.1 Announcements

  • My zoom office hours will be 2-3pm today (not the usual 1-2 pm).

  • Valentine’s day gift

  • See Tips and tricks (pgs. 541) and Glossary (pg. 543)

  • Assignment 5 is posted and due Sunday Sunday, February 19.

  • Class project proposal is due Friday

  • Assignment #4

    • Metropolis-Hastings ratio
      • Don’t forget about the support!
    • What does rnorm(1,2,3) do? (i.e., \(\sigma^2\) vs. \(\sigma\))
    • Question 7 and algorithm efficiency
      • Optimal proposal (work out on whiteboard)
      • Requires no tuning

9.2 Our second statistical model

  • Dig into the rabies test a bit more….
  • What statistical model should I use if I know/estimate if I have rabies?
    • Remember that with our first statistical model we were trying to estimate if probability a randomly sampled bat has rabies.
  • Building a statistical model using a hierarchical Bayesian approach
    • Specify (write out) the data model (you may want to take a look at Ch. 10 and Ch. 23)
    • Specify the process model
    • Specify the parameter model (or prior) including hyper-parameters
    • Select and approach to obtain the posterior distribution
      • Gibbs sampler (re-read parts of Ch. 4 about Gibbs sampler; pgs.35 - 37)
      • Derive full conditionals
      • Discussion of trade-offs with Gibbs sampler with analytical full conditionals vs. Metropolis-Hastings
    • Live example (download)