Statistical Methods Seminar Description
Overview: Many fields of science are transitioning from null hypothesis significance testing (NHST) to Bayesian data analysis. Bayesian analysis provides rich information about the relative credibilities of all candidate parameter values for any descriptive model of the data, without reference to p values. Bayesian analysis applies flexibly and seamlessly to complex hierarchical models and realistic data structures, including small samples, large samples, unbalanced designs, missing data, censored data, outliers, etc. Bayesian analysis software is flexible and can be used for a wide variety of data-analytic models. This seminar shows you how to do Bayesian data analysis, hands on.
Mike Kalish is a Professor of Psychology at Syracuse University. He earned a PhD in Cognitive Science from UC San Diego and has held academic positions in both the US and Australia. His primary research area is the psychology of category learning, which has led him to work on areas of methodology including State-Trace Analysis and Bayesian estimation and model selection. He frequently teaches postgraduate level seminars on Bayesian statistics.
The intended audience is advanced students, faculty, and other researchers, from all disciplines, who want a ground-floor introduction to doing Bayesian data analysis.
No specific mathematical expertise is presumed. In particular, no matrix algebra is used in the seminar. Some previous familiarity with statistical methods such as a t-test or linear regression can be helpful, as is some previous experience with programming in any computer language, but these are not critical.
(Exact content, ordering, and durations may change due to student interests)
- Overview / Preview:
- Bayesian reasoning generally. (See this introductory chapter)
- Robust Bayesian estimation of difference of means. Software: R, JAGS, etc.
- NHST t test: Perfidious p values and the con game of confidence intervals.
- Bayes’ rule, grid approximation, and R. Example: Estimating the bias of a coin.
- Markov Chain Monte Carlo and JAGS. Example: Estimating parameters of a normal distribution.
- HDI, ROPE, decision rules, and null values.
- Hierarchical models: Example of means at individual and group levels. Shrinkage.
- Examples with beta distributions: therapeutic touch, baseball, meta-analysis of extrasensory perception.
- The generalized linear model.
- Simple linear regression. Exponential regression. Sinusoidal regression, with autoregression component.
- How to modify a program in JAGS & rjags for a different model.
- Robust regression for accommodating outliers, for all the models above and below.
- Multiple linear regression.
- Logistic regression.
- Ordinal regression.
- Hierarchical regression models: Estimating regression parameters at multiple levels simultaneously.
- Hierarchical model for shrinkage of regression coefficients in multiple regression.
- Variable selection in multiple linear regression.
- Model comparison as hierarchical model. The Bayes factor. Doing it in JAGS.
- Two Bayesian ways to assess null values: Estimation vs model comparison.
- Bayesian hierarchical oneway “ANOVA”. Multiple comparisons and shrinkage.
- Example with unequal variances (“heteroscedasticity”).
- Bayesian hierarchical two way “ANOVA” with interaction. Interaction contrasts.
- Split plot design.
- Log-linear models and chi-square test.
- Bayesian generalized linear models in other statistical software packages
- Power: Probability of achieving the goals of research. Applied to Bayesian estimation of two groups.
- Sequential testing.
- The goal of achieving precision, instead of rejecting/accepting a null value.
- How to report a Bayesian analysis.
- Catch-up and individual consultations
Highly recommended textbook:
Doing Bayesian Data Analysis, 2nd Edition: A Tutorial with R, JAGS, and Stan. The book is a genuinely accessible, tutorial introduction to doing Bayesian data analysis. The software used in the seminar accompanies the book, and many topics in the seminar are based on the book. (The seminar uses the 2nd edition, not the 1st edition.) Further information about the book can be found at https://sites.google.com/site/doingbayesiandataanalysis/.
Install software before arriving.
It is important to bring a notebook computer to the seminar, so you can run the programs and see how their output corresponds with the presentation material. Please install the software before arriving at the seminar. The software and programs are occasionally updated, so please check here a week before the seminar to be sure you have the most recent versions.
For complete installation instructions, please go to https://sites.google.com/site/doingbayesiandataanalysis/software-installation
Below are links to seminar files for those who enrolled in the seminar. Please download these files onto your computer before the first day of the seminar. The files are password protected to respect the intellectual property rights of the instructors. By using your login information you agree not to share your login information or the content protected by it.
After May 1st: Click Here to Access Bayesian Data Analysis Seminar Files