Bayesian Data Analysis, ICPSR 2014

July 8 - July 11, 2014 University of Michigan, Ann Arbor

Many fields of science are transitioning from null hypothesis significance testing (NHST) to Bayesian data analysis. Bayesian analysis provides complete information about the relative credibilities of all candidate parameter values for any descriptive model of the data. 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 course shows you how to do Bayesian data analysis, hands on (with free software called R and JAGS). The course will use new programs and examples.

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 course. 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.

This course is offered through the Interuniversity Consortium for Political and Social Research (ICPSR) Summer Program. Registration is required and links are provided below.

Course Topics include the following. There will be updated software and examples for 2014!
 A posterior probability distribution for parameters that describe two groups, showing complete distributions of the difference of means (right middle), the difference of standard deviations, the effect size (right bottom), and posterior predictive check (right upper).

Day 1:
• Overview / Preview:
• Bayesian reasoning generally.
• 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.
Day 2:
• 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 or regression coefficients in multiple regression.
Day 3:
• 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.
Day 4:
• Model comparison as hierarchical model. The Bayes factor. Doing it in JAGS.
• Two Bayesian ways to assess null values: Estimation vs model comparison.
• 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.
• Advanced topics as time permits: Censored data in JAGS. Mixture of normals. Other data distributions in JAGS using beta 1's trick. Stan an Hamiltonian Monte Carlo.