Bayes redux

“It is not clear why the exact method isn’t mentioned in most textbooks or, indeed, why it isn’t universally used instead of the standard method. Apparently the exact method is not well known.” N. Megill and M. Pavičić, arxiv:1105.1486

Nicolas Chopin pointed out to me this gem of an arXiv paper where the authors bravely reinvent Thomas Bayes‘ 1763 paper, i.e. they managed to derive the posterior distribution on the probability parameter p of a Bernoulli experiment! Using a limiting discretisation argument, they eventually recovered the Beta(m+1,n-m+1) posterior distribution and derived posterior mean and posterior “confidence” interval on p. They call their method “exact” and wonder why it is not used… The only reference in their paper is the book of Freedman, Pisani, and Purves (1980). which indeed does mention neither Bayes nor Bayesian statistics. So MeGill and Pavičić seem to be genuinely unaware of this “not well known” branch of statistics, which is rather funny!  A kind of statistical version of Borges’ Pierre Ménard, Autor del Quijote. I am a wee surprised, though, that it made it through the arXiv filter. Note also that they argue in favour of the uniform prior on the basis that “[t]his seems to be a reasonable assumption absent any other information”, i.e. for non-informative reasons.