oh wait that was for the credible interval (which is not shown by subgroup in this table). the confidence interval shown in the table is as you say (and by definition) non-bayesian.

The study notes that they used Bayesian beta-binomial model for the confidence intervals. Who knows how they parameterized the prior distribution though…

The conclusions are parallel to yours: good evidence in the overall and 18-64 cohorts, marginal evidence in the 65-74 cohort, no real evidence in the 75+ cohort, and the 16-17 cohort is a joke that probably should have been removed. It does explain, however, why some VRBPAC members voted against it, because of the lack of evidence in 16-17 year olds when the approval question included them.

I don’t really understand the linked post very clearly. Would you mind helping out? What does it mean to say once we see the interval we can know?

looks to me like ~800 in each group.

Your comment is obviously well taken and absolutely correct. I added a footnote and updated the post to clarify. However, in my defense, I found that when trying to explain this stuff to laypeople or when I was teaching it to freshman being a little bit sloppy and saying “this isn’t quite right but it is basically the way it works” was often a better approach! After all thinking of it as “the odds” is true on average.