# Bayes, Thomas

**Bayes, Thomas**(1701-1761): English Mathematician.

Thomas Bayes was probably born in 1701; he died April 7 1761. He was an ordained Nonconformist minister in Tunbridge Wells, a fashionable spa community west of London. He was elected a member of the Royal Society in 1742. Bayes published no mathematical papers during his lifetime; only two were published posthumously. Nonetheless, Bayes contributed significantly to the science of probability, particularly to the debate on logical induction. Hume, David in his *Treatise on Human Nature* (1739-40), had set out to determine whether inductive reasoning could be justified and determined that it could not be. Bayes’ theories were perhaps written in response to Hume. Bayesian subjective approach is different from deductive probability theory: instead of asking, in general, the probability of something happening, Bayes asks:

*Given* the number of times in which an unknown event has happened and failed: *Required* the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be names.

Baysean induction begins with observed events, not with a deduction of general probability. Bayes’ theorem (1763, later discovered independantly by Laplace, Pierre Simon de), in modern notation, is as follows:

where A and B are events.

Further Reading:

Andrew Dale, *Most honourable remembrance: the life and work of Thomas Bayes*, 2003.

**Paul Beidler**