Day 15 (March 20)
Announcements
- Class projects
- Presentations will occur between May 2 and May 9
- Peer review is due May 5
- Report and reproducible analysis is due May 10
- Assignment 7 is posted and due Sunday (March 26)
- Read Ch. 17 on spatial models
Review
- Bayesian hierarchical models
- Data model
- Process model
- Parameter model
- Remember this is the place that you can/should use your creativity!!
- Fitting the model to data
- Use Bayes theorem to find the joint posterior distribution
- Using a sampling based approach to obtain samples from the joint posterior distribution
- Gibbs sampler with analytical full-conditionals or Metropolis-Hastings
- Parameter “estimates” are obtained by finding the marginal posterior
- Discard samples of all other parameters in the the joint posterior distribution that are not of interest (automatic marginalization)
- If you are interested in a function a parameter or multiple parameters, just perform the transformation
- Use mathematical formula to transform samples from the posterior of interest
- Predictions are obtained by finding the
- Use composition sampling to obtain samples from the posterior predictive distribution
- Reporting of results
- Carefully writing out a Bayesian model enables us to precisely report the results
- If you report a single number as a results make sure to use mathematical symbols in the text to communicate what part of the model you are showing (give examples on whiteboard)
- If you report a posterior distribution using a histogram (or simlar plot) make sure to use mathematical symbols o communicate what part of the model you are showing (give examples on whiteboard)
- Important things we have not covered
- More advanced/efficient MCMC algorithms
- Less advance, but easier to program/implement algorithms
- Model checking (how do we know if we have a good or bad model)
- Model comparison (using the data to help determine which model is best)