Thomas Bayes

Incandio publishes no likeness of Thomas Bayes: no photograph exists that is out of copyright or offered under a licence this product may use, and every candidate found was refused rather than stretched. In place of a face the app shows a deliberate cipher — a monogram set on a ruled manuscript page — because a missing photograph must never quietly demote the person. The life below is complete; only the picture is missing.

The Question Turned Round · Presbyterian Minister & Mathematician · c. 1701–1761

The Tunbridge Wells minister who asked probability's other question — not how the throws will fall given the chance, but what the chance may be given the throws — and never published the answer.

Who was Bayes?

Thomas Bayes was born around 1701, the son of Joshua Bayes, one of the first Nonconformist ministers publicly ordained in England after the Toleration Act. As a Dissenter he could not attend Oxford or Cambridge, so he was educated at Edinburgh, where he studied logic and theology. He became minister of the Presbyterian meeting-house at Tunbridge Wells around 1734 and stayed for most of his working life. He published two works in his lifetime and neither carried his name on the title page: Divine Benevolence (1731), on the problem of evil, and An Introduction to the Doctrine of Fluxions (1736), a defence of Newton's calculus against Bishop Berkeley's attack in The Analyst. Berkeley had argued that the method's foundations were incoherent — that its vanishing quantities were 'ghosts of departed quantities' — and Bayes answered him carefully and at length. It was probably that pamphlet which got him elected to the Royal Society in 1742. The paper he is famous for he did not publish at all. The problem it addresses had not been asked in that form. Everyone could compute, given a known chance, how a run of throws was likely to come out: de Moivre's Doctrine of Chances is full of it. Bayes asked the inverse. Suppose you do NOT know the chance, and have only the throws. What may then be said about the chance itself? His method of attacking it is characteristic: instead of arguing in generalities he sets up a physical arrangement. A ball is rolled across a level table and comes to rest somewhere; its position fixes an unknown chance. Further balls are thrown, and each is recorded as falling to the left or right of the first. From those records he reasons back to where the first ball must be. He died in 1761. His friend Richard Price, going through his papers, found the essay, judged it important, added a preface and an appendix of his own, and read it to the Royal Society in December 1763. Laplace independently developed the same inverse reasoning a decade later and made far more of it. For most of the nineteenth and twentieth centuries the approach was contested and often derided; it is now central to statistics, machine learning and much of science. No authentic portrait of him is known to exist.

Major achievements

Life in brief

Explore the life of Bayes — five chapters

  1. Shut Out — A Dissenter's education
  2. The Ghosts of Departed Quantities — Answering Bishop Berkeley, 1736
  3. The Table and the Ball — The question nobody had asked
  4. Richard Price Finds It — 1763, two years too late
  5. Two Centuries of Argument — Derided, then indispensable

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