## a glaringly long explanation

Posted in Statistics with tags , , , , , , , , , , on December 19, 2018 by xi'an

It is funny that, when I am teaching the rudiments of Bayesian statistics to my undergraduate students in Paris-Dauphine, including ABC via Rasmus’ socks, specific questions about the book (The Bayesian Choice) start popping up on X validated! Last week was about the proof that ABC is exact when the tolerance is zero. And the summary statistic sufficient.

This week is about conjugate distributions for exponential families (not that there are many others!). Which led me to explain both the validation of the conjugacy and the derivation of the posterior expectation of the mean of the natural sufficient statistic in far more details than in the book itself. Hopefully in a profitable way.

## almost uniform but far from straightforward

Posted in Books, Kids, Statistics with tags , , , , , , , on October 24, 2018 by xi'an

A question on X validated about a [not exactly trivial] maximum likelihood for a triangular function led me to a fascinating case, as exposed by Olver in 1972 in The American Statistician. When considering an asymmetric triangle distribution on (0,þ), þ being fixed, the MLE for the location of the tip of the triangle is necessarily one of the observations [which was not the case in the original question on X validated ]. And not in an order statistic of rank j that does not stand in the j-th uniform partition of (0,þ). Furthermore there are opportunities for observing several global modes… In the X validated case of the symmetric triangular distribution over (0,θ), with ½θ as tip of the triangle, I could not figure an alternative to the pedestrian solution of looking separately at each of the (n+1) intervals where θ can stand and returning the associated maximum on that interval. Definitely a good (counter-)example about (in)sufficiency for class or exam!

## the decline of the French [maths] empire

Posted in Kids, University life with tags , , , , , , , on December 16, 2017 by xi'an

In Le Monde edition of Nov 5, an article on the difficulty of maths departments to attract students, especially in master programs and in the training of secondary school maths teachers (Agrégation & CAPES), where the number of candidates usually does not reach the number of potential positions… And also on the deep changes in the training of secondary school pupils, who over the past five years have lost a considerable amount of maths bases and hence are found missing when entering the university level. (Or, put otherwise, have a lower level in maths that implies a strong modification of our own programs and possibly the addition of an extra year or at least semester to the bachelor degree…) For instance, a few weeks ago, I realised for instance that my third year class had little idea of a conditional density and teaching measure theory at this level becomes more and more of a challenge!

## what is your favorite teacher?

Posted in Kids, Statistics, University life with tags , , , , , , , , on October 14, 2017 by xi'an

When Jean-Louis Foulley pointed out to me this page in the September issue of Amstat News, about nominating a favourite teacher, I told him it had to be an homonym statistician! Or a practical joke! After enquiry, it dawned on me that this completely underserved inclusion came from a former student in my undergraduate Estimation course, who was very enthusiastic about statistics and my insistence on modelling rather than mathematical validation. He may have been the only one in the class, as my students always complain about not seeing the point in slides with no mathematical result. Like earlier this week when after 90mn on introducing the bootstrap method, a student asked me what was new compared with the Glivenko-Cantelli theorem I had presented the week before… (Thanks anyway to David for his vote and his kind words!)

## teachin’ (math?) stat…

Posted in Statistics, Travel, University life with tags , , , , on January 24, 2012 by xi'an

Arthur Charpentier (from the awesome Freakonometrics) pointed out to me those two blogs about teaching statistics. One by Meg Dillon about the joy of teaching statistics in France, of all places!, and entitled Statistics à la Mode. And another one by Douglas Andrews commenting on the first one, entitled the Big Mistake: teaching stat as though it was math… (It appeared on an ASA community blog/forum I did not know about.)

…there is almost invariably a peculiar pair of caveats presented as from on high: Never accept the alternative hypothesis, and ever say the probability is 0.95 that the mean lies in a 95% confidence interval for the mean.” Meg Dillon, After Math

Both blogs managed to bemuse me (this is not going to be a very coherent post, I am afraid!): the first one because it has this condescending tone of pure mathematicians about statistics or at least statistics course (i.e. “anyone can teach statistics!” mixed with “I hate teaching statistics!”) that I meet too often, esp. this side of the pond. Plus it seemed to miss the fundamental distinction between probability and statistics (check the above quote). And it did not say why the contents of the French course was much nicer than the equivalent designed by Meg Dillon at her university (except for the fact that she could use measure theory from the start). Maybe the French idiosyncrasy the author basks in is the fact that statistics is not recognised as a field in French universities (there is no stat department for instance) but is instead a subfield of mathematics…

…stat is a different intellectual discipline.  She longs for a so-called stat course based on sigma-algebras and probability spaces.  Well, that has been tried many times over many years, and it fails miserably at helping students understand the important stat concepts.” Douglas Andrews, ASA Blog Viewer

The second post is making sense in stressing that stat is not math. (Or rather, as it should have been stated, it is not only math.) And that (non-statistician) mathematicians should get some preliminary training or exposure to real data when teaching statistics courses. I can certainly remember a few of my (French) stat teachers who had never approached data in their whole life! However, the comment that “foundation of stat is in empirical science and in learning from observed data, not in math” seems to go overboard. As it echoes in negative the complaint from the math teacher that intro statistics courses were “a hodgepodge of recipes” with no mathematical backbone. My feeling there is that, while we certainly do not need measure theory for the earliest statistics courses (Riemann integration is good enough for my second and third year students), we have to anchor statistical techniques into a mathematical bed to avoid them looking as a bag of tricks. I remember after my first (mathematical) statistics course on being puzzled by the lack of direction and/or the multiplicity, when compared with a standard math course. I was missing the decision-theoretic part that was to come later! Had I been exposed to a non-mathematical intro stat course, I do not think I would have persevered in this field! (And I would have moved to differential geometry instead…)