Bayesian Zig-Zag Webinar
On February 13 I presented a webinar for the ACM Learning Center, entitled “The Bayesian Zig Zag: Developing Probabilistic Models Using Grid Methods and MCMC“. Eric Ma served as moderator, introducing me and joining me to answer questions at the end.
The example I presented is an updated version of the Boston Bruins Problem, which is in Chapter 7 of my book, Think Bayes. At the end of the talk, I generated a
Does that mean I was right? Maybe.
According to the good people at the ACM, there were more than 3000 people registered for the webinar, and almost 900 who watched it live. I’m glad I didn’t know that while I was presenting 🙂
If you did not watch it live, you can view the recorded webinar at no cost other than registering and providing contact information.
Here are the slides I presented. And here is a static view of the Jupyter notebook with all of the code and results. You can also run the notebook on Binder.
Thanks to the ACM Learning Center for inviting me, to Eric for moderating, and to Chris Fonnesbeck and Colin Carroll for their help developing the example I presented.
Nelis Willers “wrote a 510 page book with LaTeX, using 
For the first 9 months, from September to May, we see what we would expect if at least some of the excess diagnoses are due to age-related behavior differences. For each month of difference in age, we see an increase in the number of diagnoses.
This pattern breaks down for the last three months, June, July, and August. This might be explained by random variation, but it also might be due to parental intervention; if some parents hold back students born near the deadline, the observations for these months include some children who are relatively old for their grade and therefore less likely to be diagnosed.
We could test this hypothesis by checking the actual ages of these students when they started school, rather than just looking at their months of birth. I will see whether that additional data is available; in the meantime, I will proceed taking the data at face value.
I fit the data using a Bayesian logistic regression model, assuming a linear relationship between month of birth and the log-odds of diagnosis. The following figure shows the fitted models superimposed on the data.
Most of these regression lines fall within the credible intervals of the observed rates, so in that sense this model is not ruled out by the data. But it is clear that the lower rates in the last 3 months bring down the estimated slope, so we should probably consider the estimated effect size to be a lower bound on the true effect size.
To express this effect size in a way that’s easier to interpret, I used the posterior predictive distributions to estimate the difference in diagnosis rate for children born in September and August. The difference is 21 diagnoses per 10,000, with 95% credible interval (13, 30).
As a percentage of the baseline (71 diagnoses per 10,000), that’s an increase of 30%, with credible interval (18%, 42%).
However, if it turns out that the observed rates for June, July, and August are brought down by red-shirting, the effect could be substantially higher. Here’s what the model looks like if we exclude those months:
Of course, it is hazardous to exclude data points because they violate expectations, so this result should be treated with caution. But under this assumption, the difference in diagnosis rate would be 42 per 10,000. On a base rate of 67, that’s an increase of 62%.
Here is the notebook with the details of my analysis:
Here’s another Bayes puzzle: