Bayes’ theorem began as a defense of Christianity

Jordana Cepelewicz, Nautilus, December 20, 2016, on the Christian roots of Bayesian statistics:

Presbyterian reverend Thomas Bayes had no reason to suspect he’d make any lasting contribution to humankind. Born in England at the beginning of the 18th century, Bayes was a quiet and questioning man. … Yet an argument he wrote before his death in 1761 would shape the course of history. It would help Alan Turing decode the German Enigma cipher, the United States Navy locate Soviet subs, and statisticians determine the authorship of the Federalist Papers. Today it has helped unlock the secrets of the brain.

It all began in 1748, when the philosopher David Hume published An Enquiry Concerning Human Understanding, calling into question, among other things, the existence of miracles. According to Hume, the probability of people inaccurately claiming that they’d seen Jesus’ resurrection far outweighed the probability that the event had occurred in the first place. This did not sit well with the reverend.

Inspired to prove Hume wrong, Bayes tried to quantify the probability of an event. He came up with a simple fictional scenario to start: Consider a ball thrown onto a flat table behind your back. You can make a guess as to where it landed, but there’s no way to know for certain how accurate you were, at least not without looking. Then, he says, have a colleague throw another ball onto the table and tell you whether it landed to the right or left of the first ball. If it landed to the right, for example, the first ball is more likely to be on the left side of the table (such an assumption leaves more space to the ball’s right for the second ball to land). With each new ball your colleague throws, you can update your guess to better model the location of the original ball. In a similar fashion, Bayes thought, the various testimonials to Christ’s resurrection suggested the event couldn’t be discounted the way Hume asserted.

In 1767, Richard Price, Bayes’ friend, published “On the Importance of Christianity, its Evidences, and the Objections which have been made to it,” which used Bayes’ ideas to mount a challenge to Hume’s argument. “The basic probabilistic point” of Price’s article, says statistician and historian Stephen Stigler, “was that Hume underestimated the impact of there being a number of independent witnesses to a miracle, and that Bayes’ results showed how the multiplication of even fallible evidence could overwhelm the great improbability of an event and establish it as fact.”