S626: Bayesian Theory And Data Analysis
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 time: Tuesday, Thursday : 11:15-12:30
Instructor: Jianyu Wang - email@example.com
Other Contact(s): Jianyu Wan - firstname.lastname@example.org
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.
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.