Bayes and Blake at Bunhill

One of my holiday treks this year was across town to visit Bunhill Fields, final resting place of two of my favorite Londoners: William Blake and Thomas Bayes.

Blake is of course one of the most famous poets in the English language, but most people know him only from short poems like The Tiger [sic] (“Tyger, Tyger burning bright/ In the forests of the night/ What immortal hand or eye/ Could frame thy fearful symmetry”) and Jerusalem, sung in Anglican churches each week. But most of Blake’s work is much too weird to make it into church. It is peopled by gods and monsters, illuminated by Blake’s own wonderful over-the-top illustrations. (For example, America: A Prophecy, his poetic interpretation of the American Revolutionary War, begins “The shadowy Daughter of Urthona stood before red Orc/When fourteen suns had faintly journey’d o’er his dark abode” — George Washington and Thomas Jefferson don’t make Blake’s version.)

Blake’s gravestone sits right on the pavement in the middle of Bunhill Fields, and as such unfortunately has been slightly damaged.

I don’t read Blake every day or even every week, but I probably do use Bayes’s famous theorem at least that often. As I and other bloggers have gone on and on about, Bayes’s theorem is the mathematical statement of how we ought to rigorously and consistently incorporate new information into our model of the world. Bayes himself wrote down only a version appropriate for a restricted version of this problem, and used words, rather than mathematica symbols. Nowadays, we usually write it mathematically, and in a completely general form, as

Which means, very roughly, that the so-called posterior probability, P(H|D) — the probability of some hypothesis, H, given data, D — is equal to P(H) — the prior probability of the hypothesis, H — times the likelihood, P(D|H) — the probability of observing the actual data that we obtained given that hypothesis; finally, all of this needs to be normalized by the quantity P(D). This seems pretty obscure, but it really is a model for learning: the prior represents our knowledge in the absence of the new data, and the theorem tells us how to update this in the face of new data. And it really is a theorem: a statement of mathematical fact. So this statement really is the foundation for the use of probability in reasoning about the world, which is the science of statistics (despite the internecine wars within the statistics community about exactly how one ought to make sense of the concept of “probability” itself), or more broadly, science itself. So Bayes is a man whose life is well worth celebrating by all of us interested in and affected by science.

Bayes is buried in his family tomb, now bearing the moss-covered Inscription: “Rev. Thomas Bayes, son of the said Joshua and Ann Bayes, 7 April 1761. In recognition of Thomas Bayes’s important work in probability this vault was restored in 1960 with contributions received from statisticians throughout the world.” (With restoration and upkeep since by Bayesian Efficient Strategic Trading of Hoboken, NJ, USA –across the Hudson River from New York City– and ISBA, the International Society for Bayesian Analysis.)