Bayesian Data Analysis, Univ. of Oslo 2014

## Doing Bayesian Data Analysis A workshop at the University of Oslo, Norway June 4 - 6, 2014

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 workshop shows you how to do Bayesian data analysis, hands on (with free software called R and JAGS). The workshop 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 workshop. 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.

Pre-Registration is required; see contact information 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.