Thomas Bayes spent most of his career as a Presbyterian minister overseeing his flock at Tunbridge Wells, Kent, yet in his spare time, he produced a number of intriguing and influential mathematical papers. Of particular interest were two published posthumously by the Royal Society of London. In one of these, Bayes offered the first discussion of asymptotic behavior by series expansions; and in the other—a treatise that continues to exert an influence in a variety of statistical applications—he laid the groundwork for what became known as Bayesian statistical estimation.
The circumstances of Bayes's life, including the exact year of his birth, are a mystery. He was born in 1701 or 1702, either in London or in Hertfordshire. At least the identity of his parents, Joshua and Ann Carpenter Bayes, is known, as is the fact that Thomas was the first of six children. His father was one of the first Nonconformist ministers ordained in England. Just as the Anglicans had broken with Rome in the sixteenth century, in the seventeenth century the Nonconformists had begun splitting with the Anglicans, and this movement would ultimately spawn the Baptist, Methodist, and Congregationalist churches.
The nature of Bayes's education is also open to question, but it appears he attended the University of Edinburgh. In 1727, at about the age of 25, he was ordained, and went to work assisting his father at Leather Lane. Later he took charge of the Presbyterian meeting house called Mount Sion in Tunbridge Wells, where he would remain for the rest of his career.
In 1742 Bayes was elected a Fellow of the Royal Society of London, which might seem an unusual honor for a rural minister, but Bayes was no ordinary country pastor. He is widely credited with the authorship of An Introduction to the Doctrine of Fluxions and Defence of the Mathematicians Against the Objections of the Author of the Analyst, a tract written in response to The Analyst by George Berkeley (1685-1753) Berkeley's 1734 publication attacked Isaac Newton (1642-1727) and his writings on differentials or fluxions. It was in honor of this work, wherein Bayes defined the "business of the mathematician" as one of making deductions rather than propounding a specific theory, that Bayes received his election to the Royal Society.
Bayes lived his life quietly, but in secret he recorded a number of fascinating observations, as demonstrated by a notebook of his that offers a model for an electrifying machine and other intriguing ideas. He retired from the ministry in 1750, and died on April 17, 1761, after which a Unitarian minister and friend of the family, Richard Price (1723-1791), went through his papers.
Thanks to Price's efforts, in 1764 the Philosophical Transactions of the Royal Society included a paper by Bayes on the subject of series expansions. According to Price, Bayes wrote the paper in an effort to underscore what philosophers typically call the "argument from design": that is, the defense of God's existence on the basis of his creation and its intricacy.
In the same issue of the Philosophical Transactions was a second Bayes piece, "An Essay Towards Solving a Problem in the Doctrine of Chances." In this tract, Price explained, Bayes sought "to find out a method by which we might judge concerning the probability that an event has to happen, in given circumstances, upon supposition that we know nothing concerning it but that, under the same circumstances, it has happened a certain number of times, and failed a certain other number of times." This helped lay the foundations for statistics in general, and for Bayesian statistical estimation—still used today for a variety of applications—in particular. Price further developed Bayes's ideas in "A Demonstration of the Second Rule in the Essay . . .", published in 1765 by the Royal Society.