Workshop Day 1 – Tuesday, Sept 25th

This workshop aims to be a general introduction to Bayesian data analysis and how it differs from the more familiar classical approaches to data analysis. We will start by providing a brief historical overview of statistical inference and introduce Bayes’s theorem. The fundamental concepts of Bayesian statistical inference will follow, contrasted with frequentist methods of inference. To provide a bridge between Bayesian and classical methods, we will describe likelihood function approaches to inference and introduce both the likelihood principle and the law of the likelihood as the general precepts of likelihood based inference. During this workshop, there will also be practical exercises including using Bayes’s rule to calculate posterior probabilities and posterior distributions, choosing priors in probabilistic models and illustrating their role on the posterior distributions, calculating likelihood ratios and Bayes factors to compare evidence for different parameters in a probabilistic model, and calculating marginal likelihoods for comparing distinct probabilistic models.

• 09:00 Welcome (tea & coffee)
• 09:30 Introduction and overview of workshop 1
• 10:00 Introduction to likelihood
• 11:30 Introduction to Bayesian inference
• 12:30 Lunch
• 13:30 Bayesian data analysis in action
• 15:30 Break
• 15:45 Bayes factors
• 17:00 Discussion
• 17:30 Close

Workshop Day 2 – Wednesday, Sept 26th

This workshop aims to provide a solid theoretical and practical foundation for real-world Bayesian data analysis in psychology and social sciences. We will begin by focusing on some simple, but nontrivial, statistical inference problems. These problems are simple enough to handle with just a few calculations using R, but can nonetheless illustrate clearly all the major concepts on Bayesian inference including prior distributions, the likelihood function, posterior distributions, high posterior density intervals, posterior predictive distributions, marginal likelihood, Bayesian model comparison, and so on. While these models can be very conceptually informative, their practical value for real world inference is limited by their simplicity. In order to provide more practically valuable tools, we will then turn to looking at regression model, beginning with the linear/normal models. These models, which include t tests, ANOVA, ANCOVA, and mutiple linear regression models, form a foundation for much of data analysis. We will explore these models using Stan, a probabilistic programming language, and brms, an R package that allows us to use Stan easily and efficiently. We then turn to generalized linear models, including logistic regression and Poisson regression, as well as their multilevel counterparts. Together together, the general and generalized linear models and their multilevel counterparts constitute a very powerful and practically valuable set of tools for data analysis.

• 09:00 Welcome (tea & coffee)
• 09:30 Introduction and overview of workshop 2
• 10:00 Bayesian inference in binomial models
• 12:30 Lunch
• 13:30 Bayesian inference in linear and normal models
• 15:30 Break
• 15:45 Bayesian inference in general and generalized multilevel linear models
• 17:00 Discussion
• 17:30 Close

GitHub resources

Further resources for this training course can be found on Github at mark-andrews/bayes-lmu-2018.