By Steve Bishop

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**Thomas Bayes (1702-1761)**

**Thomas Bayes (1702-1761)** was the minister of the Presbyterian Chapel in the English spa town of Tunbridge Wells from around late 1733. By all accounts he was a better mathematician than he was a church minister! The *Protestant Dissenter’s Magazine* of 1814 describes Bayes as a respected minister, however, he was not according to Timpson (writing in 1859) a popular preacher (Bellhouse, 2004).

As a non-conformist he was prevented from attending the English universities, so he began study in 1719 at Edinburgh University in Scotland.

In 1731 he published a work entitle *Divine Benevolence* and in 1742 he was made a fellow of the Royal Society after defending Isaac Newton against Bishop Berkeley in a ‘pamphlet war’.

Bayes did work with fluxions, infinite series as well as in probability. In the late 1740s Bayes set out his theory of probability that eventually bore his name. His theorem was discovered after his death. It had no practical applications in his lifetime. He didn’t even bother to publish it. It was his friend and fellow mathematician and church minister Richard Price who discovered it among Bates’ effects after his death and had it published as “An Essay towards solving a problem in the doctrine of chances,” *Philosophical Transactions of the Royal Society of London* 53 (1763): 370–418. Available here: http://rstl.royalsocietypublishing.org/content/53/370.full.pdf+html

Price suggested that the theory could be used to defend Christianity against the skepticism of David Hume. Price was at the time the minister of the non-conformist chapel in Newington Green, England.

Laplace re-rediscovered it and modified it into the form we largely recognise today.

The statistical community who largely accepted the frequentist view of statistics rejected it; they thought that the bayseian approach was subjective and hence ‘unscientific’. It is only in the last few decades that the bayesian approach is starting to be dominant. McGrayne (2011) writes:

In discovering its value for science, many supporters underwent a near-religious conversion yet had to conceal their use of Bayes’ rule and pretend they employed something else. It was not until the twenty-first century that the method lost its stigma and was widely and enthusiastically embraced.

Today it is used among other things to forecast weather, to identify e-mail spam, to improve low-res images on computers and has been used to identify forgeries.

The formula is known today in this form:

P(A|B)=P(B|A)P(A)/P(B)

where P(A) denotes the probability of A and P(A|B) is the probability of A given that B has occurred.

Sharon Bertsch McGrayne’s (2011) book title summarises its impact: *The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines & Emerged Triumphant from Two Centuries of Controversy* (Yale University Press, 2011)

A recent book by Andrew Hartley, *Christian and Humanist Foundations for Statistical Inference* (Resource, 2008), suggests that a subjective bayesian approach comports well with a Christian perspective on statistics.

Interestingly, Bayes’ theorem has been used by philosophers of religion such as Richard Swinburne to try and prove God’s existence and by others such as philosopher John Mackie and the atheist evangelist Richard Dawkins in an attempt to disprove God’s existence.

Bill Bryson on Thomas Bayes:

**References**

Bellhouse, D. R. 2004. “The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth,” *Statistical Science *19 (1) 3–43.

Sharon Bertsch McGrayne (2011) *The Theory That Would Not Die* (Yale University Press, 2011)

*Steve Bishop is the compiler of *A Bibliography for a Christian Approach to Mathematics *and the author of several articles on the relationship between faith and math. Look for future posts from him in this series on Christian Mathematicians.*

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