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)_/¯
Last knitted on 2021-02-15. Source code on GitHub.1
-
sessioninfo::session_info() #> - Session info --------------------------------------------------------------- #> setting value #> version R version 4.0.3 (2020-10-10) #> os Windows 10 x64 #> system x86_64, mingw32 #> ui RTerm #> language (EN) #> collate English_United States.1252 #> ctype English_United States.1252 #> tz America/Chicago #> date 2021-02-15 #> #> - Packages ------------------------------------------------------------------- #> package * version date lib source #> assertthat 0.2.1 2019-03-21 [1] CRAN (R 4.0.2) #> cli 2.3.0 2021-01-31 [1] CRAN (R 4.0.3) #> crayon 1.4.1 2021-02-08 [1] CRAN (R 4.0.3) #> emo 0.0.0.9000 2020-07-06 [1] Github (hadley/emo@3f03b11) #> evaluate 0.14 2019-05-28 [1] CRAN (R 4.0.2) #> generics 0.1.0 2020-10-31 [1] CRAN (R 4.0.3) #> git2r 0.28.0 2021-01-10 [1] CRAN (R 4.0.3) #> glue 1.4.2 2020-08-27 [1] CRAN (R 4.0.2) #> here 1.0.1 2020-12-13 [1] CRAN (R 4.0.3) #> knitr * 1.31 2021-01-27 [1] CRAN (R 4.0.3) #> lubridate 1.7.9.2 2020-11-13 [1] CRAN (R 4.0.3) #> magrittr 2.0.1 2020-11-17 [1] CRAN (R 4.0.3) #> purrr 0.3.4 2020-04-17 [1] CRAN (R 4.0.2) #> ragg 0.4.1 2021-01-11 [1] CRAN (R 4.0.3) #> Rcpp 1.0.6 2021-01-15 [1] CRAN (R 4.0.3) #> rlang 0.4.10 2020-12-30 [1] CRAN (R 4.0.3) #> rprojroot 2.0.2 2020-11-15 [1] CRAN (R 4.0.3) #> sessioninfo 1.1.1 2018-11-05 [1] CRAN (R 4.0.2) #> stringi 1.5.3 2020-09-09 [1] CRAN (R 4.0.2) #> stringr 1.4.0 2019-02-10 [1] CRAN (R 4.0.2) #> systemfonts 1.0.0 2021-02-01 [1] CRAN (R 4.0.3) #> textshaping 0.2.1 2020-11-13 [1] CRAN (R 4.0.3) #> withr 2.4.1 2021-01-26 [1] CRAN (R 4.0.3) #> xfun 0.20 2021-01-06 [1] CRAN (R 4.0.3) #> #> [1] C:/Users/Tristan/Documents/R/win-library/4.0 #> [2] C:/Program Files/R/R-4.0.3/library
Leave a comment