I was preparing an episode for Engines of Our Ingenuity based on my recent post on Bayes’ Theorem. The example I gave before about calculating the probability of having a disease given a positive test was a bit tired. I therefore replaced it with the following:

Thomas Bayes was interested in how our beliefs about the world should evolve as we accumulate new, but uncertain evidence. Bayes suggested a solution, and the French mathematician Simone de Laplace developed it into a powerful theory. Yet for much of the 20^{th} century Bayes’ idea was dismissed by statisticians.

But an increase in computer power allowed statisticians to apply Bayes’ method to a number of very hard problems. In the 1960s the statisticians Frederick Mosteller and David Wallace turned their attention to the Federalist papers, a series of 85 essays written in 1787 and 1788 by John Jay, Alexander Hamilton and James Madison. The authoship of 12 of the essays was disputed, but the differences in writing style between Hamilton and Madison could decide the issue. Strewn throughout the essays were hints that pointed towards one or the other author. For instance, Hamilton wrote “while” and Madison used “whilst”. But such evidence was not certain: the text could have been edited by others before printing, for instance. Mosteller and Wallace used computers and Bayes’ method to integrate many small bits of uncertain evidence. Their conclusion that James Madison was the author of all disputed essays has been accepted by historians.