Bayesian Regression: Theory & Practice

Session 2: Priors, prior & posterior predictions, and categorical predictors

Part 1: Priors and predictives

Priors are an essential part of Bayesian data analysis. There are different approaches to specify priors:

• we can try to be feign maximal uncertainty;
• we can try to commit strongly to prior knowledge we think is relevant;
• we can use priors to make the model “well-behaved” (e.g., help training / fitting)
• we can try to use priors that are as “objective” and “non-committal”.

Whatever approach to specifying priors we adopt, all (proper) priors generate predictions. So here we look at prior and posterior predictives of a Bayesian model. This is helpful because you might not have intuitions about how to select priors, but you will likely have intuitions about what counts are reasonable /a priori/ predictions.

Here are slides for session 2.

Part 2: Categorical predictors

In the second part of this session, we look at categorical predictors in simple linear regression models.

More on this topic can be found in this chapter of the webbook.