## Bayes’ Theorem or Price’s Theorem?

I’m indebted to a fellow blogger for drawing my attention to the person shown in the above picture, Dr Richard Price who has been described as “the most original thinker ever born in Wales”, and who has a Society named after him.

Price was a moral philosopher, nonconformist preacher and also a mathematician of some note. Of particular interest to this blog is the role he played in the development of what is now known as Bayes’ Theorem, after the Reverend Thomas Bayes.

However, the paper in the Philosophical Transactions of the Royal Society that contains the first published form of this theorem was not published until 1763, over a year after Bayes’ death and, as you can see if you follow the link, is attributed jointly to “Mr Bayes and Mr Price”. It appears that there was an original manuscript written by Bayes around about 1755 which was communicated to Price when Bayes died in 1761 and then presented for publication over a year later; Price had been asked to act as “literary executor” of Bayes’ estate.

Unfortunately the original manuscript has never been found and it is therefore impossible to say for sure how much Price contributed to the final version. However, a relatively recent and very interesting article raises this question, and argues (reasonably convincingly to my mind) that Bayes’ part stops at page 14 of 32 pages. It is therefore quite possible that Price wrote over half the paper himself although most historical discussions of this matter simple state that Price “edited” Bayes’ work.

It has to be said that the paper is not exactly a model of clarity and pertains only to a particular case of the full theorem. The form in general use today was first published by Laplace in 1812, so it should really be called Laplace’s Theorem, but Laplace did give generous credit to the work of Bayes which is no doubt why the name stuck.

I don’t suppose we will know for sure exactly how much Price contributed to the development of Bayes’ theorem, but this may be yet another example of the law that any result in science or mathematics that has a person’s name attached to it has the wrong name attached to it!

Finally, I will mention that the Richard Price Society has started a petition to the Welsh government. I’m taking the liberty of copying the purpose of this petition here:

We call on the Welsh government to acknowledge the important contribution of Dr Richard Price not only to the eighteenth century Enlightenment, but also to the making of the modern world that we live in today, and develop his birthplace and childhood home into a visitor information centre where people of all nationalities and ages can discover how his significant contributions to theology, mathematics and philosophy have shaped the modern world.

Tynton Farm in Llangeinor, the birthplace and childhood home of Dr Richard Price is for sale. Once derelict, the farm has been sensitively restored and almost all of the original features have been preserved. The Richard Price Society is aware that the house attracts visitors from all corners of the globe and this is attested by the previous owner’s Visitors Book that was signed by visitors to the farm. The position of the farm and its provenance would make it an ideal learning centre where people can find out just what an important person he was and remains. This is an opportunity to buy the property at market value and help celebrate the achievements of Wales’ intellectual giant and apostle of liberty.

I have signed it, and hope you will consider doing likewise!

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December 4, 2015 at 1:11 pm

Both Thomas Bayes and Richard Price were buried in the Bunhill Fields nonconformist cemetery in London, Price next to today’s main road near the entrance gate, Bayes on the extreme other end of the cemetery.

Price got a mention in an article I wrote about the history of astronomy in Wales and Welsh astronomers on account of a paper in the

Philosophical Transactionsabout the effect of the aberration of light on predictions of the time of transits of Venus. So he made a very small contribution to astronomy.December 4, 2015 at 1:32 pm

Ah, thanks Bryn; having visited Bayes’ tomb I was now wondering about Price, but apparently I was close!

December 4, 2015 at 1:38 pm

Yes, you would have been close. I can’t remember how I managed to find both graves. There is an information board in the centre of the cemetery, so Price’s grave might have been indicated there, along with the more famous burials.

December 4, 2015 at 2:06 pm

In the 1980s it was difficult to find Bayes’ grave as it was not included in the booklet about famous burials at Bunhill Fields. The tomb took me some time to find and I had more success than Ed Jaynes, who I think had not left himself long enough on his visit.

In Paris once I visited Pere Lachaise cemetery to look for Laplace, but (unlike Jim Morrison, also buried there) he had been dug up and returned to his original village – which I had visited some time before but without knowing of the Laplace connection.

On the subject of search theory, here is the draft of a book, just released, called “Bayesian methods and the search for MH370” about the flight that went missing:

Click to access Bayesian_Methods_MH370_Search_3Dec2015.pdf

Two of the references are to recent work of LD Stone, who is apparently still active and worked with the people who did a similar search for a lost US submarine a generation ago. They found it and wrote a book, “Theory of Optimal Search”. The MH370 book is pure probability theory, but search theory is a specific example of decision theory, which logically speaking sits on top of probability theory.

December 4, 2015 at 5:29 pm

Things have clearly improved at Bunhill Fields in terms of information. I think Thomas Bayes was listed on the information board, but can’t remember whether Richard Price was.

December 4, 2015 at 1:31 pm

I’d not seen that there had been progress in disentangling Price’s contribution from Bayes’; interesting. Martyn Hooper comes across as slightly out of his depth in the wider aspects of his article on the subject (to which Peter gives a link): calling Edmund Burke an arch-conservative is inaccurate, for Burke supported the American Revolution and he was in the Whig, not the Tory Party. Today he is remembered for being against the French Revolution, and his reasons, given that he supported the American one, are interesting.

Regarding the use of Bayes’ theorem to try to prove the existence of God, how to assign the prior??

December 4, 2015 at 8:01 pm

…and as we all know – prior is everything with bayes.

December 5, 2015 at 12:57 am

Exactly as it should be. If you know the answer with certainty (delta-function prior) and are doing the experiment only because your boss ordered you to then no amount of data will shake you and you will correctly ascribe all of the deviations from the known value to noise. Other methods that “let the data speak for themselves” end up placing some of the probability where you know with certainty that it cannot be – which is barmy.

December 5, 2015 at 6:43 pm

Prior is everything only if you don’t have data to form a likelihood…In which case you might as well talk from your posterior..

December 5, 2015 at 6:37 pm

Spoken like a good fundamentalist Anton.

December 5, 2015 at 9:28 pm

Do you mean Bayesian fundamentalist or religious fundamentalist?

December 6, 2015 at 8:59 am

I realise that Peter’s blog post above did not mention that Price apparently hoped to use Bayes’ theorem to prove the existence of god. Hence my comment.