Advanced: offering specialized and in-depth knowledge on the topic; the target group is RM2 students who have previously written a paper on the topic and PhD students whose research relates to the topic.
In recent years, Bayesian methods have come to be widely adopted in all areas of science. This is in large part due to the development of sophisticated software for probabilisic programming; a recent example is the astonishing computing capability afforded by the language Stan (mc-stan.org). However, the underlying theory needed to use this software sensibly is often inaccessible because end-users don’t necessarily have the statistical and mathematical background to read the primary textbooks (such as Gelman et al’s classic Bayesian data analysis, 3rd edition). In this course, we seek to cover this gap, by providing a relatively accessible and technically non-demanding introduction to the basic workflow for fitting different kinds of linear models using a powerful front-end R package for Stan called brms.
After completing this course, participants will have become familiar with the foundations of Bayesian inference using brms, and will be able to fit a range of multiple regression models and hierarchical models. They will know how to calibrate their models using prior and posterior predictive checks; and to carry out model comparison using Bayes factors.
- Probability theory and Bayes-Price-Laplace’s rule
- Probability distributions
- Understanding and eliciting priors
- Analytical Bayes: Beta-Binomial
- introduction to brms
- linear models
- Generating prior predictive distributions using RStan and R
- Fake-data simulation for model evaluation
- Hierarchical linear models
- More hierarchical linear models
- Bayes factors
Background and preparatory readings: