P533/P534 is a tutorial introduction to doing Bayesian statistics for data analysis. The course is intended to make advanced Bayesian methods genuinely accessible to real graduate students, and even unreal undergraduates (see pre-req's below). Many complete computer programs are provided for you do adapt to your own research.
• In P533, we start from the basics of probabilities and Bayes' theorem, and gradually work our way through contemporary Monte Carlo methods in the context of simple analyses, building up to simple linear regression and Bayesian versions of single-factor analysis of variance (ANOVA).
• In P534, we contrast null hypothesis significance testing with Bayesian approaches to null value assessment, as well as Bayesian approaches to power. Then we do a variety of more complicated realistic applications, covering the Bayesian versions of multiple linear regression, logistic regression, analysis of variance, etc., including a look at repeated-measures designs.
• The order of topics (as just described) is different from previous years, so that students who can only enroll in P533 (without continuing into P534) nevertheless learn about basic applications such as simple linear regression and single-factor ANOVA. More details about the schedule are provided in tabular form below, in the context of chapters from the course textbook.
Why go Bayesian? See Figure 1, above. But beyond that, sciences from astronomy to zoology are changing from 20th-century null-hypothesis significance testing to Bayesian data analysis, because Bayesian analysis provides rich information with flexible application to numerous models. Read more:
*Your click on this link constitutes your request to the author for a personal copy of the article exclusively for individual research, and the author's delivery of that copy. Any other use is prohibited.
- An article that shows the rich information provided by Bayesian estimation in the context of analyzing data from two groups: Kruschke, J. K. (2012). Bayesian estimation supersedes the t test. Journal of Experimental Psychology: General *. More info, including links to videos, is here.
- An overview article: Kruschke, J. K. (2010). Bayesian data analysis. Wiley Interdisciplinary Reviews: Cognitive Science *, 1(5), 658-676.
- An article that emphasizes that Bayesian data analysis is appropriate regardless of the status of Bayesian models of cognition: Kruschke, J. K. (2010). What to believe: Bayesian methods for data analysis. Trends in Cognitive Sciences *, 14(7), 293-300.
- An article that explains two Bayesian methods to assess null values, and which one is typically more informative: Kruschke, J. K. (2011). Bayesian assessment of null values via parameter estimation and model comparison. Perspectives on Psychological Science *, 6(3), 299-312.
|Week of semester||Course||Book Chapters|
|1||P533||Ch. 1, 2, 3: Intro; probability; R|
|2||P533||Ch. 4: Bayes' rule|
|3||P533||Ch. 5, 6: Beta distribution|
|4||P533||Ch. 7, 8: Markov chain Monte Carlo (excluding 7.3.3 and 7.4.3)|
|5||P533||Ch. 9: Hierarchical models|
|6||P533||Ch. 14: Generalized linear model|
Ch. 15: Normal distribution.
|7||P533||Ch. 16: Linear regression|
|8||P533||Ch. 18: Oneway ANOVA|
Ch. 23: How to report an analysis
|9||P534||Ch. 10: Model comparison (including 7.3.3 and 7.4.3)|
|10||P534||Ch. 11: Null hypothesis significance testing|
Ch. 12: Bayesian approaches to null value assessment
|11||P534||Ch. 13: Power|
|12||P534||Ch. 17: Multiple linear regression|
|13||P534||Ch. 20: Logistic regression|
Ch. 21: Ordinal regression
|14||P534||Ch. 19: Two factor ANOVA|
|15||P534||Ch. 22: Contingency table analysis|
Discussion: Please discuss the assignments and lectures on Oncourse under the "Forums" link. If you are attending the class but cannot get access to the Oncourse page, please e-mail Prof. Kruschke.
Grading; Homework; Exams: There are homework exercises assigned every week or so. No exams or projects. Grades will be determined by performance on the homework assignments. All assignments are mandatory. There will be penalties for late homework unless you have a cogent excuse. These penalties are designed as an incentive to you because the material is cumulative; the penalties also help keep things fair to all students. If you must be late with an assignment, please notify the professor immediately.
How does this course (P533/P534) differ from S626? The Dept. of Statistics offers S626, Bayesian theory and data analysis. S626 has a prerequisite of "two statistics courses at the graduate level", and provides a mathematical treatment of Bayesian data analysis. Students are encouraged to consider S626 after taking P533/P534.
Disclaimer: All the information here is subject to
change. Changes will announced in class.
This web page is at URL = http://www.indiana.edu/~jkkteach/P533/