December 23, 2013 marks the 250th anniversary of the reading of Thomas Bayes’ essay on inverse probability by Richard Price to the Royal Society of London. As mentioned in previous posts, Thomas Bayes (1702-1761) was an English dissenting minister and Fellow of the Royal Society. In 1763, two years after Bayes’ death, Richard Price submitted to the Society Bayes’ posthumous work in which Price added and authored a lengthy introduction and detailed appendix. That work, An Essay towards Solving a Problem in the Doctrine of Chances, represents more or less the beginning of Bayesian statistics.
Viewed within a contemporary perspective, we tend to see Bayes’ and Price’s paper for what it eventually became, not for what it was at the time it was written. That is, we see it as a first attempt at inverse probability. In modern terms, we see Bayes struggling with the incomplete beta integral. To us, it is a mathematical essay.
Yet, it is much more than that. It is also a theological essay. It uses math to make a point — that God underlies all events and we might, perhaps imperfectly, estimate God’s handiwork through logic and probability. Put another way, for Price (and we assume Bayes), events are a result of divine cause and that cause can be inferred through events.
Price argues that Bayes’ method provides evidence for the intelligent design of events. However, that conclusion is not intuitively obvious in Bayes’ method or Price’s conclusion (at least when viewed from a modern perspective). Although not referred to by name in Bayes’ and Price’s essay, some have argued that the writings of David Hume may represent the possible impetus behind Bayes’ and Price’s paper and the intent of Price’s theological argument.
David Hume was a Scottish philosopher who published Philosophical Essays Concerning Human Understanding (later retitled, An Enquiry Concerning Human Understanding) in 1748. This free-wheeling treatise considered a number of topics and included Hume’s discussion regarding the reliability of reports by those who had witnessed events that were essentially miraculous in nature. Because Hume’s essay focused on events reported in scripture and questioned their validity, Hume’s work would have been inflammatory among Christian clergy such as Bayes and Price.
In 1767, Price did directly challenge Hume in Price’s publication, Four Dissertations. In the fourth and final dissertation of this work, Price expounded on the importance of Christianity, and on the nature of historical evidence and miracles. While discussing Hume’s arguments, Price makes reference to Bayes’ method in a vast footnote. Based on this, some historical researchers have argued that Price’s dissertation provides the rationale for the theological tone of Bayes’ and Price’s earlier essay. In essence, Bayes’ essay serves as a prelude to Price’s penultimate argument against Hume.
In his recent paper, Stephen Stigler presents this exact argument and suggests that Bayes and Price may have met around the time of Hume’s publication and worked together devising a mathematical challenge to Hume.
Who is Stephen Stigler, you ask?
Stephen Stigler is the Ernest DeWitt Burton Distinguished Service Professor in the Department of Statistics at the University of Chicago. For over four decades Stigler has been researching and publishing in the area of the history of statistics. He is thorough and erudite and has that rare gift of explaining complex topics in understandable terms. I recommend two of his books in particular: The History of Statistics: The Measurement of Uncertainty before 1900 and Statistics on the Table: The History of Statistical Concepts and Methods.
Yet, with some trepidation, I am going to argue against Stigler’s premise. Now, keep in mind, if you had to choose between someone who has made it his profession and life’s work to research the history of statistics or some random anonymous blogger, I know whom I would choose.
With that caveat in mind, I will boldly go forth with my argument. Well at least I will boldly do that in my next post regarding this topic.
- Hume, D. (1748). Philosophical essays concerning human understanding. London: A. Millar.
- Price, R. (1772). Four dissertations (3rd ed.). London: T. Cadell.