This class is an introduction to Bayesian statistics including subjective probability, Renyi axiom system, Savage axioms, coherence, Bayes theorem, credibility intervals, Lindley paradox, empirical Bayes estimation, natural conjugate priors, de Finetti’s theorem, approximation methods, Bayesian bootstrap, Bayesian computer programs.
The class will be taught in the R language.
There will approximately eight participation / presentation exercises, five homework, and a final exam. Grades will be calculated as follows:
Strongly recommended books:
Other books that may be helpful:
There are many online resources for learning about it and working with it, in addition to the textbooks:
You are encouraged to discuss course material, including assignments, with your classmates. All work you turn in, however, must be your own. This includes both writing and code. Copying from other students, from books, or from websites (1) does nothing to help you learn, (2) is easy to detect, and (3) has serious negative consequences.
| Date | Lecture | Topic |
|---|---|---|
| 1/9/18 | 1 | Introduction and Fundamental Ideas, Slides |
| 1/11/18 | 2 | Fundamentals, Slides and Why isn’t everyone a Bayesian? |
| 1/16/18 | 3 | Ch. 3 - Integration Versus Simulation, Slides |
| 1/18/18 | 4 | Prior Selection, Slides |
| 1/23/18 | 5 | Ch.5 - Comparing Populations, Slides |
| 1/25/18 | 6 | Slides |
| 1/30/18 | 7 | Diasorin Example and Inference for Rates, Slides |
| 2/1/18 | 8 | Ch. 6 - Simulations, Slides |
| 2/1/18 | - | mcmcse Software Tutorial, Slides and R Markdown |
| 2/6/18 | 9 | Sampling Algorithms, Slides |
| 2/8/18 | 10 | Lauren (Rmd and pdf) and Mi (txt and pdf) Software Tutorials |
| 2/13/18 | 11 | Ch. 8 - Binomial Regression, Slides |
| 2/15/18 | 12 | Slides |
| 2/20/18 | 13 | Binomial Mixed Models, Slides |
| 2/22/18 | 14 | Sajjad (pdf), Huiling (Rmd and html), and Song (Rmd and pdf) Software Tutorials |
| 2/27/18 | 15 | Group Presentations |
| 3/1/18 | 16 | Samantha (Rmd and pdf), Jinhui (Rmd and html), and Ying (py and pdf) Software Tutorials |
| 3/6/18 | 17 | Ch. 9 - Linear Regression, Slides |
| 3/8/18 | 18 | Linear Regression II, Slides and R Markdown |
| 3/13/18 | 19 | Group Presentations |
| 3/15/18 | 20 | Final Exam Handout |