## 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

**N**icolas 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.

June 8, 2011 at 2:23 pm

This is really sad. I can’t believe their references are “Statistics” and “Quantum Contextual Sets” and after they conclude “It is not clear why the exact method isn’t mentioned in most textbooks” yeah right, I wonder why you were not able to find it!

Apart from that, we should be thinking how dangerous is to read some literature from Arxiv specially if you are trying to jump into a new area. Better to start somewhere else.

June 8, 2011 at 3:34 pm

Thanks, Rosanna. Great website, by the way!

June 8, 2011 at 5:06 am

[…] end the week, Xi’an’s Og finds a curious paper on the arXiv, The Value of the Variable connects the Kalevala and incompleteness, Series Divergentes remembers […]

June 6, 2011 at 9:20 pm

It appears that this is the same Norman Megill who wrote the Metamath proof checker so it is not surprising that it got by what minimal filtering the ArXiv has. This seems to be a case of someone writing about a subject far outside their area of expertise. The old adage of “a month in the laboratory can save you hours in the library” seems to apply.

June 5, 2011 at 7:16 pm

This post may come as an illustration of “the other Arrow’s theorem” discussed by Andrew here and there. Although I do not know how many times Bayes’ theorem has been proved!