Introduction to Bayesian Analysis in R and Stan

Bayesian analysis is a probabilistic data analysis approach that produces powerful but intuitive inference from your data. A Bayesian approach helps us ask and answer probability statements about data. For example:

• What is the probability that treatment A is more cost effective than treatment B for a specific health care provider?
• Do most people rate product A higher than product B? How much higher is product A’s rating likely to be?
• What is the probability that a patient’s blood pressure decreases if they are prescribed drug A? By how much is their blood pressure likely to decrease?

We will introduce fundamental concepts and approaches to Bayesian data analysis. We will then practice applications of these concepts and approaches using the Stan programming language through R.

By the end of the one-day workshop, you will be able to describe what Bayesian analysis is, why you would use it, and the general workflow of Bayesian data analysis. You will learn how to specify, run, and interpret linear, logistic, ordinal, and hierarchical linear models using Stan. You will be able to use these fundamental tools for basic analyses and know where to look for guidance on more advanced analyses.

Prerequisites: Basic understanding of regression, probability, and statistical analysis principles. We assume no or minimal prior experience with Bayesian analysis. Basic understanding of R, such as object assignment, data frames and how to subset them, and using functions in R, is helpful but not required.

• Why use Bayesian analysis
• Comparison with frequentist analysis
• Bayes theorem, probability and use in data analysis
• Overview of Markov Chain Monte Carlo methods
• Overview of steps in Bayesian analysis and regression
• Introduction to Stan
• Creating, running and drawing inference from Bayesian regression models
• Selecting priors for models
• Assessing model performance
• Expressing posterior distributions as effect sizes with visualization
• Introduction to distributional models

Fully virtual teaching with interactive examples and exercises. Question periods and breaks will be given during the workshop.

Slides, exercises, and solutions will be made available to all participants.