8 Day 8 (February 9)

8.1 Announcements

  • Statistics seminar today at 4pm on Bayesian methods (link)

  • Questions about homework or other things?

8.2 Our first statistical model

  • Building a statistical model using a Bayesian approach
    • Specify (write out) the likelihood/data model
    • Specify the parameter model (or prior) including hyper-parameters
    • Select an approach to obtain the posterior distribution
      • Analytically (i.e., pencil and paper)
      • Live example Metropolis-Hastings

8.3 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)