kwebtransPreview
Open in TheBrain

Bayes, Thomas

Name: Thomas Bayes

Achievements: Established a mathematical basis for probability inference

Born: 1702; London, England   

Died: April 17, 1761; Tunbridge Wells, Kent, England (Aged about 59)

Field & Discipline: Mathematics

Language: English

Father: Joshua Bayes

Mother: Ann Carpenter

Siblings: 3 brothers, 3 sisters

Spouse: None

Children: None

Education: University of Edinburgh

Major Work:

"Essay Towards Solving a Problem in the Doctrine of Chances"

Life & Times:

Bayes may have been tutored by [taught by] De Moivre*, who was giving private math lessons in London in the early 1700s.  In 1727, Bayes was ordained and appointed to the Presbyterian Chapel in Tunbridge Wells, outside London, where he stayed the rest of his life.

In 1731, Bayes published his first work, "Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government Is the Happiness of His Creatures".  Five years later, his first mathematical work, "An Introduction to the Doctrine of Fluxions", countered Bishop [disputed] Berkeley*'s attacks on the logical foundations of  [defended] Newton*'s calculus.  Bayes counted  among his friends theologian/philosopher [a pal of] Price* and mathematician [a pal of] Whiston*.  In 1742, he was elected a fellow of the Royal Society, partly because of a piece in wrote in 1736 defending Newton.

Bayes's theory of probability, which he developed late in life, was set out in "Essay Towards Solving a Problem in the Doctrine of Chances", a paper that Price submitted to the Royal Society and which was published in the "Philosophical Transactions of the  Royal Society of London" in 1763, two years after Bayes died.  The paper was the first to establish a foundation for statistical inference.

The basis of probability theory had already been established in the early 18th century by Jakob Bernoulli and de Moivre, who spelled out the logical principles for inferring the probabilities of related events given the probability of one event ("a  priori" probabilities.) Bayes set himself the converse problem, reasoning backwards from effect to cause, and estimating the "a posteriori" probabilities.

Bayes's principle can be illustrated using his often-used example of urns and balls: "Let there be an urn containing white and black balls in an unknown proportion.  A ball is drawn and replaced again m times.  Of these balls n prove to be white and m-nto be black.  If M is the total number of balls in the urn, what is the probability in the light of the given evidence that the urn contains N white and M-N black balls?"

To Bayes, his task was to find a way to calculate the probability of statistical hypotheses in the light of data.  Given that an unknown event has, under the same circumstances, happened a certain number of times and failed to happen a certain number of times, Bayes set himself to finding a method to estimate the probability of its happening in a single trial.

Noting that sometimes the probability of a statistical hypothesis is given prior to any particular events being observed, he showed how to compute the probability of the hypothesis after some observations are made, leading to probabilities for which it is more or less probable that they have calculable values within two certain intervals, limits or "degrees.”

Bayes proceeded from this to a new supposition: that if there is no information about the prior probability of a statistical hypothesis, then (he argued by analogy) our ignorance is neither more nor less than if prior probabilities were known to be entirely uniform (equal).

Bayes's conclusion of uniform prior probability distributions 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 combination of a prior estimate of its probability and new relevant evidence.

The influential French mathematician/astronomer [influenced] Laplace* wholly accepted Bayes's argument, and from 1774 regularly assumed uniform prior probability distributions. Laplace's support made Bayes's ideas generally accepted until they were seriously  challenged in 1854 in George Boole's "Laws of Thought".

Assessment: Best known for making "a posteriori" probability suppositions by working backward from effect to cause

Oneliner: Thomas Bayes, expert on probability

Bibliography:

Attachments