# Slides from my intro to Bayesian regression talk

Back in April, I gave a guest lecture on Bayesian regression for the psychology department’s graduate statistics class. This is the same course where I first learned regression—and where I first started using R for statistics instead of for data cleaning. It was fun drawing on my experience in that course and tailoring the materials for the level of training.

Here are the materials:

## Observations (training data)

As I did with my last Bayes talk, I’m going to note some questions from the audience, so I don’t forget what kinds of questions people have when they are introduced to Bayesian statistics.

One theme was frequentist baggage . One person asked about
Type I and Type II error
rates. I did not have a satisfactory (that is, *rehearsed*) answer ready for
this question. I think I said something about how those terms are based on a
frequentist, repeated-sampling paradigm, whereas a Bayesian approach
worries about different sorts of errors.
(Statistical power is still important,
of course, for both approaches.) Next time, I should study up on the
frequentist properties of Bayesian models, so I can field these questions
better.

Other questions:

- Another bit of frequentist baggage . I mentioned that with a
posterior predictive distribution, we can put an uncertainty interval on any
statistic we can calculate, and this point brought up the question of
*multiple comparisons*. These are a bad thing in classical statistics. But for Bayes, there is only one model, and the multiple comparisons are really only the implications of one model. - Someone else said that they had heard that Bayesian models can provide evidence
for a null effect—
*how does that work?*I briefly described the ROPE approach, ignoring the existence of Bayes factors entirely.

For future iterations of this tutorial, I should have a worked example, maybe a blog post, on each of these issues.

It’s kind of amusing now that I think about it. A big part of my enthusiasm for
Bayesian statistics is that I find it much more intuitive than frequentist
statistics. *Yes!* I thought to myself. *I never have to worry about what the
hell a confidence interval is ever again!* Well, actually—no. I need to know
this stuff even more thoroughly than ever if I am going to talk fluently about
what makes Bayes different. ¯\_(ツ)_/¯