## abstract for “Bayes’ Theorem: then and now”

**H**ere is my abstract for the invited talk I will give at EMS 2013 in Budapest this summer (the first two banners were sites of EMS 2013 conferences as well, which came above the European Meeting of Statisticians on a Google search for EMS 2013):

What is now called Bayes’ Theorem was published and maybe mostly written by Richard Price in 1763, 250 ago. It was re-discovered independently (?) in 1773 by Pierre Laplace, who put it to good use for solving statistical problems, launching what was then called inverse probability and now goes under the name of Bayesian statistics. The talk will cover some historical developments of Bayesian statistics, focussing on the controversies and disputes that marked and stil mark its evolution over those 250 years, up to now. It will in particular address some arguments about prior distributions made by John Maynard Keynes and Harold Jeffreys, as well as divergences about the nature of testing by Dennis Lindley, James Berger, and current science philosophers like Deborah Mayo and Aris Spanos, and misunderstandings on Bayesian computational issues, including those about approximate Bayesian computations (ABC).

**I** was kindly asked by the scientific committee of EMS 2013 to give a talk on Bayes’ theorem: then and now, which suited me very well for several reasons: first, I was quite interested in giving an historical overview, capitalising on earlier papers about Jeffreys‘ and Keynes‘ books, my current re-analysis of the Jeffreys-Lindley’s paradox, and exchanges around the nature of Bayesian inference. (As you may guess from the contents of the abstract, even borrowing from the article about Price in Significance!) Second, the quality of the programme is definitely justifying attending the whole conference. And not only for meeting again with many friends. At last, I have never visited Hungary and this is a perfect opportunity for starting my summer break there!

March 19, 2013 at 3:30 pm

Christian/Thanks a lot for reminding us about the famous paper for the 250th anniversary of its presentation by Richard Price.

I only read it two years ago and I am still puzzled by two things in it:

i) the strange definition by Bayes of probability as a ratio of two expected values;

ii) the will of Bayes to substitute at the end of the paper (his “scholium” between propositions 9 & 10) the assumption of a uniform distribution on the probability of the event M (abscissa of the position of the first ball thrown on the billard table) by the assumption of the equiprobability of the numbers of successes M in n trials before any experiment (ie a uniform prior predictive distribution=1/(n+1) value following from the corollary of proposition 8 on the marginal of the no of occurrences of M).

I would be curious to hear your comments on these historical aspects of Bayes’ contribution.