We started by learning that probability is hard and not always quantifiable. For instance, I imagine many of you would have judged it more likely than not that the Supreme Court would have invalidated at least the “mandate” portion of Obamacare. Clearly, many of us had the wrong premises.
Just as many of us have new incorrect premises about what the Roberts’ ruling means. As to that, follow my Twitter stream from yesterday (see the panel to the right), where I sequentially pull out what I think are relevant quotes from the ruling. However, this is a topic for another time.
I’ve taught this class at Cornell for several years. The in-class version is, naturally, quite different than the on-screen presentation, so don’t be misled by what you’ve seen here the past fortnight. After many (but not infinite) repetitions teaching, I have learned three things.
Lesson One: try not to do too much. The book/class notes was originally designed for a semester-length course for undergraduates. It works for that, but not as well for a class meant to teach fundamentals of analysis. For instance, I could leave out all the stuff on counting and how to build a binomial distribution. Basic probability rules might stay, because they’re easy and useful. But to even learn to compute the chance of winning the (say) Mega Millions requires learning some basic combinatorics. Can’t have it all, though.
So I think it better to stop after Bayes’s rule and present everything else as a “given”, like I do with the ubiquitous, and ubiquitously inappropriate, normal distribution. This would allow more time to discuss ideas instead of mechanics. More time to cover how things go wrong, and why there is so much over-certainty produced using classical statistical methods.
This means a re-write of the book/notes is in order. Which I have been doing slowly, but now must finish to get it ready in time for next year.
Lesson Two: red wine does not go with white linen.
Lesson Three: there are churches left that still have hat clips in the backs of pews. I had tremendous fun snapping these during mass at Divine Child when I was a kid, usually during homilies. Just for the sake of the good old days, I did so last weekend. But only once. It might have been twice.