### BIOGRAPHY 23.1* Thomas Bayes* (1702 -1761)

Thomas Bayes was born in London, England, as the eldest son of the Rev. Joshua Bayes, one of the first nonconformist ministers to be publicly ordained in England. (Nonconformists refused to be bound by the beliefs, customs, and practices of the Church of England.) Bayes was privately educated (as was the usual practice among nonconformists at the time); the focus was on languages, literature, and science. Quite possibly, he was tutored in mathematics by Abraham de Moivre (Biography 8.2). Like his father, Thomas Bayes also became a Presbyterian minister and spent 30 years in that capacity. In that period, he published (nonmathematical) treatises under the pseudonym of John Noon, and they got him elected a Fellow of the Royal Society. Bayes' mathematical work is contained in two papers published posthumously due to the efforts of a friend, Richard Price.

One of the papers, "An Essay Towards Solving a Problem in the Doctrine of Chances" reversed de Moivre's focus of reasoning from the population to the sample and dealt with inferences from the sample to the population. The paper put forth a number of mathematical propositions; as "Proposition 9," it presented what is now known as Bayes' theorem (first discussed in Chapter 8 of the text). The essay is, perhaps, one of the least understood but most famous and controversial contributions ever made in the history of science. Many call it a masterpiece of mathematical elegance. In the words of Ronald Fisher (Biography 13.1), Bayes' "mathematical contributions.... show him to have been in the first rank of independent thinkers." Certainly, Bayes has become, through his famous theorem, the father of modern decision theory. For this reason, the optimal strategy selected in expected-payoff-optimizing decision making problems is universally referred to as *Bayes' strategy*.

*Sources:* Adapted from *Biometrika*, December 1958, pp. 293-315 (which includes a reproduction of the famous essay); *International Encyclopedia of Statistics*, vol.1 (New York: Free Press, 1978), pp. 7-9; Ronald Fisher, *Statistical Methods and Scientific Inference*, 2nd ed., rev. (New York: Hafner, 1959), p. 8.