Archive for Bernoulli distribution

reading classics (#1,2)

Posted in Books, Kids, Statistics, University life with tags , , , , , , on December 4, 2014 by xi'an

La Défense from Paris-Dauphine, Nov. 15, 2012Today was the second session of our Reading Classics Seminar for the academic year 2014-2015. I have not reported on this seminar so far because it has had starting problems, namely hardly any student present on the first classes and therefore several re-starts until we reach a small group of interested students. Actually, this is the final year for my TSI Master at Paris-Dauphine, as it will become integrated within the new MASH Master next year. The latter started this year and drew away half of our potential applicants, presumably because of the wider spectrum between machine-learning, optimisation, programming and a tiny bit of statistics… If we manage to salvage [within the new Master] our speciality of offering the only Bayesian Statistics training in France, this will not be a complete disaster!

Anyway, the first seminar was about the great 1939 Biometrika paper by Pitman about the best invariant estimator appearing magically as a Bayes estimator! Alas, the student did not grasp the invariance part and hence focussed on less relevant technical parts, which was not a great experience (and therefore led me to abstain from posting the slides here). The second paper was not on my list but was proposed by another student as of yesterday when he realised he was to present today! This paper, entitled “The Counter-intuitive Non-informative Prior for the Bernoulli Family”, was published in the Journal of Statistics Education in 2004 by Zu and Liu, I had not heard of the paper (or of the journal) previously and I do not think it is worth advertising any further as it gives a very poor entry to non-informative priors in the simplest of settings, namely for Bernoulli B(p) observations. Indeed, the stance of the paper is to define a non-informative prior as one returning the MLE of p as its posterior expectation (missing altogether the facts that such a definition is parameterisation-invariant and that, given the modal nature of the MLE, a posterior mode would be much more appropriate, leading to the uniform prior of p as a solution) and that the corresponding prior was made of two Dirac masses at 0 and 1! Which again misses several key points like defining properly convergence in a space of probability distributions and using an improper prior differently from a proper prior. Esp. since in the next section, the authors switch to Haldane’s prior being the Be(0,0) distribution..! A prior that cannot be used since the posterior is not defined when all the observations are identical. Certainly not a paper to make it to the list! (My student simply pasted pages from this paper as his slides and so I see again no point in reposting them here. )

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