## S626: Bayesian Theory And Data Analysis

### Class Description

The course covers an introduction to the theory and practice of Bayesian inference. Topics covered include: Prior and posterior distributions, Bayes theorem, model formulation, Bayesian computation, model checking and sensitivity analysis. This is a general class on Bayesian methods. Some basic knowledge of probability distributions, calculus and linear algebra is assumed.

### Class Information

**Semester(s): **Fall

**Semester(s) Offered: ** Fall

**Class time: **
Tuesday, Thursday : 11:15-12:30

**Capacity: ** 40

### Contact Information

**Instructor: **Jianyu Wang - jw257@indiana.edu

**Other Contact(s): ** Jianyu Wan - jw257@indiana.edu

### Other Details

**Sequence: ** no specific sequence.

**Prerequisites: ** Two courses at the graduate level or consent by the instructor. A course equivalent to MATH-M 463 (Introduction to Probability Theory) is ideal.

**Algebra Required?: ** Some preliminary knowledge of matrix algebra is needed to discuss some ideas about performing regression analysis from a Bayesian point-of-view.

**Calculus Required?: ** Some notions of integration are needed. Specially dealing with integrals that arise from working with known probability distributions. Some basic knowledge of differentiation is needed too.

**Recommended follow-up classes: ** Any topics course in advanced statistical methods that involve some form of Bayesian methodology.

**Substantive Orientation: ** This course accommodates students from a variety of disciplines. In past semesters, S626 has been attended by students in Statistics, Computer Science, Economics, Biological Sciences, and Political Science, among others.

**Books used: ** Required:
*Hoff, Peter (2009) "A first Course in Bayesian Statistical Methods". New York: Springer. ISBN 978-0-387-92299-7.
(strongly) recommended:
*Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., Rubin, D. B. (2003), Bayesian data analysis, Second Edition, Chapman and Hall/CRC. ISBN 978-1-4398-4095-5.
*Marin, J. M. and Robert, C. (2007), Bayesian Core: A Practical Approach to Computational Bayesian Statistics. New York: Springer. ISBN 978-0-387-38979-0.

**Applied/Theoretical: ** Historically this course had a theoretical focus. This semester we are pursuing more of a balance between theory and practice.

**Formal Computing Lab?: ** No

**Software Used: **
R

**How the software is used: ** The software is mainly used for computation and data analysis for in-class examples and homework assignments. Only a reasonably low level of programming is required for both R and Winbugs.

**Problem Sets: ** in the range of 5-6 homeworks a semester

**Data Analysis: ** Yes, typically involving actual data sets. Examples of proportions, count data and estimation of rates are considered. Along with some regression models.

**Presentations: ** No

**Exams: ** Historically, a midterm test and a final exam.

**Keywords: ** Prior and posterior distributions, Bayes theorem, model formulation, Bayesian computation, model checking and sensitivity analysis.