Originally published in The Reasoner Volume 10, Number 2 – February 2016
The Cross-Check blog of the Scientific American, published recently a post titled Bayes’s Theorem: What’s the Big Deal?
From the social media, to rather specialised mailing lists, this piece has clearly reached a considerably wide public. Indeed chances are that you have already come across it. If you haven’t, here’s a quick fix, for the subtitle really says it all: “Bayes’s theorem, touted as a powerful method for generating knowledge, can also be used to promote superstition and pseudoscience.”
So, yes, this is yet another piece discussing, with splendid shallowness, why so many seemingly learned people call themselves Bayesians, and why equally learned masses get offended by the label. The stated goal is clarificatory: “the Bayes fever has become too pervasive to ignore”, so the author takes upon himself the burden “to get to the bottom of Bayes, once and for all”. I refer the interested reader to the original post to find out how the bottom of Bayes ultimately looks like.
Be it as it may, this Scientific American post does raise an interesting question. The Bayes Theorem is a mathematically trivial consequence of the so-called “product rule” of probability functions and the commutativity of conjunction (or intersection). And yet it’s rather easy to be impressed by its counterintuitive consequences. This is wonderfully illustrated by this scene from the film “21”,
where the outstanding student astonishes Professor –and professional gambler– Kevin Spacey with his effortless solution of the Monty Hall problem. Now compare this with, say Modus Ponens in classical logic. You can certainly see it as following trivially from the definitions of classical consequence and the truth table for “material implication”. Of course there is a good deal of arbitrariness (i.e. mathematical convenience) in defining this truth table, but this is hardly more arbitrary than the product rule for probability. And yet Modus Ponens fails to impress. Its use in causing a variety of evils, from Finance to Terrorism, doesn’t seem to fuel much discussion. No blog post on Modusponianism appears to be (academically) viral on social media. Why is that?
