Reverend Bayes is dead; long live Bayesian thinking!

Rev. Thomas Bayes died on this day in 1761 at the age of 59. Below the fold is a summary of his life and work via the editors of the Encyclopaedia Britannica [with edits by us in brackets]:

Thomas Bayes, (born 1702, London, England—died April 17, 1761, Tunbridge Wells, Kent), English Nonconformist theologian and mathematician who was the first to use probability inductively and who established a mathematical basis for probability inference … [ Probability inference is a method for estimating, from the frequency with which an event has occurred in the past, the probability that it will occur in the future].

Bayes set down his findings on probability in “Essay Towards Solving a Problem in the Doctrine of Chances” (1763), published posthumously in the Philosophical Transactions of the Royal Society. That work became the basis of a statistical technique, now called Bayesian estimation, for calculating the probability of the validity of a proposition on the basis of a prior estimate of its probability and new relevant evidence. Disadvantages of the method … include the different ways of assigning prior distributions of parameters and the possible sensitivity of conclusions to the choice of distributions. [So Bayes’ theorem can apply to itself!]

The only works that Bayes is known to have published in his lifetime are Divine Benevolence; or, An Attempt to Prove That the Principal End of the Divine Providence and Government Is the Happiness of His Creatures (1731) and An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of The Analyst (1736), which was published anonymously and which countered the attacks by Bishop George Berkeley on the logical foundations of Sir Isaac Newton’s calculus.

Bayes was elected a fellow of the Royal Society in 1742.

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