托马斯·贝叶斯1702—1761

Thomas Bayes ( BAYZ; c. 1701 – 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for formulating a specific case of the theorem that bears his name: Bayes' theorem.

Bayes never published what would become his most famous accomplishment; his notes were edited and published posthumously by Richard Price.

Biography

Thomas Bayes was the son of London Presbyterian minister Joshua Bayes, and was possibly born in Hertfordshire. He came from a prominent nonconformist family from Sheffield. In 1719, he enrolled at the University of Edinburgh to study logic and theology. On his return around 1722, he assisted his father at the latter's chapel in London before moving to Tunbridge Wells, Kent, around 1734. There he was minister of the Mount Sion Chapel, until 1752.

He is known to have published two works in his lifetime, one theological and one mathematical:

Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures (1731)

An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of The Analyst (published anonymously in 1736), in which he defended the logical foundation of Isaac Newton's calculus ("fluxions") against the criticism by George Berkeley, a bishop and noted philosopher, the author of The Analyst

Bayes was elected as a Fellow of the Royal Society in 1742. His nomination letter was signed by Philip Stanhope, Martin Folkes, James Burrow, Cromwell Mortimer, and John Eames.

Bayes' theorem

Bayes's solution to a problem of inverse probability was presented in An Essay Towards Solving a Problem in the Doctrine of Chances, which was read to the Royal Society in 1763 after Bayes's death. Richard Price shepherded the work through this presentation and its publication in the Philosophical Transactions of the Royal Society of London the following year. This was an argument for using a uniform prior distribution for a binomial parameter and not merely a general postulate. This essay gives the following theorem (stated here in present-day terminology). ((n+1)!)/(S!(n-S)!)r^(S)(1-r)^(n-S) dr for 0≤ r≤ 1, where S=X₁+⋯ +Xₙ.

Thus, for example, （公式略）

This is a special case of the Bayes' theorem.

In the first decades of the eighteenth century, many problems concerning the probability of certain events, given specified conditions, were solved. For example: given a specified number of white and black balls in an urn, what is the probability of drawing a black ball? Or the converse: given that one or more balls has been drawn, what can be said about the number of white and black balls in the urn? These are sometimes called "inverse probability" problems.

Bayes's Essay contains his solution to a similar problem posed by Abraham de Moivre, author of The Doctrine of Chances (1718).

In addition, a paper by Bayes on asymptotic series was only published posthumously.

Bayesianism

Bayesian probability is the name given to several related interpretations of probability as an amount of epistemic confidence – the strength of beliefs, hypotheses etc. – rather than a frequency. This allows the application of probability to all sorts of propositions rather than just ones that come with a reference class. "Bayesian" has been used in this sense since about 1950. Since its rebirth in the 1950s, advancements in computing technology have allowed scientists from many disciplines to pair traditional Bayesian statistics with random walk techniques. The use of the Bayes' theorem has been extended in science and in other fields.

Bayes himself might not have embraced the broad interpretation now called Bayesian, which was in fact pioneered and popularised by Pierre-Simon Laplace; it is difficult to assess Bayes's philosophical views on probability, since his essay does not go into questions of interpretation. There, Bayes defines probability of an event as "the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon its happening" (Definition 5).