Sublime

The core of Bayesian thinking (or Bayesian updating, as it can be called) is this: given that we have limited but useful information about the world, and are constantly encountering new information, we should probably take into account what we already know when we learn something new.

Bayes’s much more famous work, “An Essay toward Solving a Problem in the Doctrine of Chances,”24 was not published until after his death, when it was brought to the Royal Society’s attention in 1763 by a friend of his named Richard Price. It concerned how we formulate probabilistic beliefs about the world when we encounter new data.

Thomas Bayes was an English minister who was probably born in 1701—although it may have been 1702. Very little is certain about Bayes’s life, even though he lent his name to an entire branch of statistics and perhaps its most famous theorem.

On its face Bayes’ rule is a simple, one-line theorem: by updating our initial belief about something with objective new information, we get a new and improved belief. To its adherents, this is an elegant statement about learning from experience.

Bayes’ genius was to take the idea of narrowing down the range of positions for the cue ball and—based on this meager information—infer that it had landed somewhere between two bounds. This approach could not produce a right answer. Bayes could never know precisely where the cue ball landed, but he could tell with increasing confidence that it was