7 Day 7 (February 7)

7.1 Announcements

Do we need another donut day to find people to work with for the class project?
Assignment 3 is graded
- If you are not happy with your grade please compare your assignment to assignment 3 guide
- If your solution is the same or similar to what I provided you don’t need to do anything.
- If your solution is different than what I provided then please explain in detail why your solution is not correct.
- Re-submit Assignment 3 by 11:59 pm on Sunday Feb. 12.
Please read Ch. 6
- You may want to re-read parts of Ch. 4 about Gibbs sampler (pgs.35 - 37)
- You may want to take a look at Ch. 10 and Ch. 23
Assignment 4 is due Sunday Feb. 12

The backstory
- Bat
- Rabies
Building a statistical model using a likelihood-based (classical) approach
- Specify (write out) the likelihood
- Select an approach to estimate unknown parameters (e.g., maximum likelihood)
- Quantify uncertainty in unknown parameters (e.g., using normal approximation)
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

Dig into the rabies test a bit more….
- Rabies test results
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
- 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