## Bayes-250

**M**y fourth Bayes-250 and presumably the last one, as it starts sounding like groundhog day!

**S**tephen Stigler started the day with three facts or items of inference on Thomas Bayes: the first one was about The Essay and its true title, a recent research I made use of in Budapest. As reported in his Statistical Science paper, Stigler found an off-print of Bayes’ Essay with an altogether different title:* “A Method of Calculating the Exact Probability of All Conclusions founded on Induction”*, which sounds much better than the title of the version published in the Proceedings of the Royal Society,* “An Essay toward solvi**ng a Problem in the Doctrine of Chances”*, and appears as part of a larger mathematical construct in answering Hume’s dismissal of miracles… (Dennis Lindley in a personal communication to Stephen acknowledged the importance of the title and regretted “as an atheist” that the theorem was intended for religious usage!)

**S**tephen then discussed Bayes’s portrait, which (first?) appeared in June 1933 in *The American Conservationist*. Herein acknowledged as taken from the Wing collection of the Newberry library in Chicago (where Stephen has not yet unearthed the said volume!) My suggestion would be to use a genealogy algorithm to check whether or not paternity cannot be significantly rejected by comparing the two portraits. The more portraits from Bayes’ family, the better.

**S**teven Fienberg took over for another enjoyable historical talk about the neo-Bayesian revival of the 50s. In connection with his BA paper on the appearance of the term *Bayesian*. Giving appropriately a large place to Alan Turing. And Jimmy Savage (whose book does not use the term *Bayesian*). He also played great videos of Howard Raiffa explaining how he became a (closet) Bayesian. And of Jack Good being interviewed by Persi Diaconis. *(On a highly personal level, I wonder who in my hotel has named his or her network “Neo Bayesian Revival”!)*

**I**n a very unusual format, Adrian Smith and Alan Gelfand ran an exchange around a bottle of Scotch (and a whole amphitheatre), where Adrian recollected his youth at Cambridge and the slow growth of Bayesian statistics in the UK (“a very unorthodox form of inference” in Dennis’ words). I liked very much the way he explained how Dennis Lindley tried to build for statistics the equivalent of the system of axioms Kolmogorov had produced for probability. And even more how Dennis came to the Bayesian side for decision-theoretic reasons. (The end of the exchange was more predictable as being centred on the MCMC revolution.)

**M**ichael Jordan completed the day with a talk oriented much more towards the future. About the growing statistical perspective on document analysis. Document as data indeed. Starting with the bag of words representation. (A side remark was that his paper Latent Dirichlet allocation got more citations than classics like Jim Berger’s 1985 book or Efron’s 1984 book.) The central theme of the talk was that there is much work left to be done to address real problems. Really real problems with computational issues orders of magnitude away from what we can propose today. Michael took linguistics as a final example. Linking with Adrian’s conclusion in that respect.

December 18, 2013 at 1:50 pm

With all due respect to Stigler, I think he is incorrect assuming that Bayes was responding to Hume. He has argued that Bayes completed the bulk of his calculations sometime prior to 1750 and may have discussed this with David Hartley (Hartley’s ingenious friend). However, Hume’s work was published in the Spring of 1748. Hartley completed his work in December 1748. For Stigler’s argument to work, Bayes would have needed to have read Hume, understood that Hume was discussing induction (a word Hume did not use in his 1748 work), completed his incomplete beta calculations, and have shown this to Hartley all within in less than six months. This is improbable. Instead, if Bayes was responding to Hume, he could not have been Hartley’s friend. If he was Hartley’s friend, he could not have been responding to Hume.

December 18, 2013 at 12:51 pm

You’ve basically done a Bayes1000 now! ;-)