# Bayes, Thomas

### From Enlightenment Revolution

**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. Bayesâ€™ 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. Bayesâ€™ 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**