Bayesian Data Analysis, Cog Sci 2011 Tutorial

## Doing Bayesian data analysis with R and BUGS

### Tutorial at the Conference of the Cognitive Science Society, Wednesday, July 20, 2011, Boston, Massachusetts.

 Figure 1. Why you should attend the tutorial. (Notice that the Bayesian analysis reveals many credible regression lines, for which the slopes and intercepts trade off, instead of just one "best" line.)

This tutorial introduces you to doing Bayesian data analysis, hands on. The intended audience is graduate students and other researchers who want a ground-floor introduction to Bayesian data analysis. No mathematical expertise is presumed. Complete computer programs will be provided. The software is free; see installation instructions, below, before arriving at the tutorial.

Agenda: The full-day tutorial progresses through the following topics.

• 9:00-10:30 Bayes' Rule, Grid Approximation, and R. We start with the basics of conditional probabilities, the meaning of Bayes' rule, and simple examples of Bayes' rule graphically illustrated with grid approximation in the programming language R.
10:30-11:00 Break
• 11:00-12:30 Markov Chain Monte Carlo (MCMC) and BUGS; Linear Regression. We explain the idea of approximating distributions by large representative samples, and MCMC methods for generating them. The BUGS language is introduced and used to do Bayesian linear regression.
• 1:30-3:00 Hierarchical Models and Model Comparison. Bayesian methods and the BUGS language make hierarchical modeling straight forward. Hierarchical models are tremendously useful for analyzing individual differences, repeated measures, and structural constraints across conditions. Model comparison is a case of hierarchical modeling.
3:00-3:30 Break
• 3:30-5:00 Bayesian ANOVA; Power Analysis. We use hierarchical analysis of variance with Bayesian parameter estimates, for rich and flexible inferences about differences between groups. We conclude with a brief look at power analysis from a Bayesian perspective.

Why go Bayesian? See Figure 1. But beyond that, modern Bayesian methods are the best approach to empirical data analysis because Bayesian methods yield richer inferences than traditional methods and without use of ill-defined p values. Sciences from astronomy to zoology are changing from 20th-century null-hypothesis significance testing to Bayesian data analysis. Read more:

• An open letter explaining why it's time to go Bayesian.
• An article* that explains a critical flaw of p-values in null hypothesis significance testing, and two different Bayesian approaches to assessing null values.
Kruschke, J. K. (2010). Bayesian data analysis. Wiley Interdisciplinary Reviews: Cognitive Science, 1(5), 658-676. (doi:10.1002/wcs.72)
• An article* that emphasizes advantages of Bayesian data analysis and the fact 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. (doi:10.1016/j.tics.2010.05.001)
*Your click on this link constitutes your request to the author for a personal copy of the article exclusively for individual research.

 Figure 2. Concepts of Bayesian data analysis (left) transfer to Bayesian models of mind (right), but Bayesian data analysis with generic descriptive models will be useful even when specific Bayesian models of mind fail to fit real behavior.

Bayesian data analysis uses generic descriptive models such as linear regression, without any assertions about the processes that generated the data. Bayesian methods infer credible values of parameters in the descriptive models, such as credible slopes and intercepts in linear regression, as suggested in the left side of Figure 2.

... but concepts and methods of Bayesian data analysis transfer to Bayesian models of cognition.

Because the Bayesian approach to inference is the normative approach, some cognitive scientists posit that cognitive processing itself is based on Bayesian inference by the mind, as suggested in the right side of Figure 2.

When you learn about concepts and methods of Bayesian data analysis, it is easier to understand Bayesian models of mind. But Bayesian data analysis will always be useful, even if particular Bayesian models of mind fail to accurately mimic cognition.

Who is the instructor?

John Kruschke is five-time winner of Teaching Excellence Recognition Awards from Indiana University, where he is Professor of Psychological and Brain Sciences, and Adjunct Professor of Statistics. He has written an introductory textbook on Bayesian data analysis; see also the articles linked above. He has presented many well-received workshops on Bayesian data analysis.

His research interests include the science of morality, applications of Bayesian methods to adaptive teaching and learning, and models of attention in learning, which he has developed in both connectionist and Bayesian formalisms. He received the Troland Research Award from the National Academy of Sciences. He chaired the Cognitive Science Conference in 1992.