After successful completion of the course, students are able to learn the foundations of Bayesian inference, as well as a high-level overview of a wide range of other topics. The students will learn the computational tools that will aide them in designing Bayesian models and applying Bayesian methods in the R software.
I. Fundamentals of Bayesian Inference
1. Probability and inference
2. Single-parameter models
3. Multiple-parametermodels
4. Asymptotics and connections to non-Bayesian approaches
5. Hierarchical models
II. Fundamentals of Bayesian Data Analysis
1. Model checking
2. Evaluating, comparing, and expanding models
3. Modeling accounting for data collection
4. Decision analysis
III. Advance Computation
1. Introduction to Bayesian computation
2. Basics of Markov chain simulation
3. Computationally efficient Markov chain simulation
IV. Regression Models (if time allows)
1. Introduction to regression models
2. Hierarchical linear models
3. Generalized linear models
Most of the course will be taught using lecture slides in conjunction with derivations on board. Aditional parts will be done in computer lab sessions.
Course information and materials, including sylabus and grading policy will be posted in TUWEL.
Two reference books are used:
-
Bayesian Data Analysis. Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., & Rubin, D.B.(2013). CRCpress
- The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation. Robert, C.P.(2001). Springer Texts in Statistics.
The statistical software we want to use is R. It can be downloaded from the R home page . RStudio offers a GUI R platform.
Proposed grading policy (this can be discuss with students at the beginning of the term)
Data analysis project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30%
Presentation of the project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20%
Final exam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50%
