Bayes' Theorem - making the connections


(Andy Wootton) #1

I hadn’t had anything to do with Bayes until a few weeks ago but his theorem kept coming up at Brum AI then people did hard sums and I got lost. It’s been mentioned more on Brumtech Slack and then I stumbled upon his grave in https://en.wikipedia.org/wiki/Bunhill_Fields burial ground, while looking for William Blakes’ and we talked about that too. It’s a short walk from my daughters flat in That London so I’ve started to think of him as a neighbour.

I’ve noticed how much great work in the Enlightement and Industrial Revolution was done by Non-Conformists and Thomas Bayes was the son of London Presbyterian minister Joshua Bayes, originally from Sheffield. Thomas became a statistician, philosopher and a minister himself and wrote 2 books: the 1st was thoeological but in 1736 he wrote a defence of Isaac Newton’s calculus, against the criticism of George Berkeley (arguably the reason for the existence of Unix BSD.) This paper probably led to him being elected a Fellow of the Royal Society in 1742.

The thing that interested me most was that Bayes wrote one special case of his theorem in his notebook then appears to have ignored it until he died. Luckily, his widow asked his friend Richard Price, himself a FRS, moral philosopher, nonconformist preacher and mathematician to read his notes and he edited and published the idea, having identified the importance of the idea. Price read (https://en.wikipedia.org/wiki/An_Essay_towards_solving_a_Problem_in_the_Doctrine_of_Chances)" to the Royal Society in 1763.

I didn’t understand the importance of Bayesian probability but I’ve learned it is now considered to include several related interpretations of probability as an amount of epistemic confidence – the strength of beliefs, hypotheses etc., rather than just a frequency, so it greatly increased the applicability of probability theory. It sounds like it might be applicable to estimating.

You may have noticed that I like the interconnections between everything. Price was a political pamphleteer, active in radical, republican, and liberal causes such as the American Revolution. He was well-connected and communicated between a large number of people, including several of the Founding Fathers of the United States.

Price spent most of his adult life as minister of Newington Green Unitarian Church, which my daughter also lived near. What are the chances of that happening twice in one post?


(Marc Cooper) #2

Yeah, Bayes theorem was published posthumously. Mainly due to his friend, Richard Price.

Bayes, T., & Price, R. (1763). An essay towards solving a problem in the doctrine of chances. http://dx.doi.org/10.1098/rstl.1763.0053

It’s understood that Bayes himself was unaware of the importance of his own work. Most folk attribute the advances to Laplace.