## Archive for mathematics

## {Monte Carlo}²

Posted in Kids with tags comics, logic, mathematics, Monte Carlo methods, SMBC on May 1, 2012 by xi'an## teachin’ (math?) stat…

Posted in Statistics, Travel, University life with tags France, mathematics, Statistics, teaching, undergraduates on January 24, 2012 by xi'an**A**rthur 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

**B**oth 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

**T**he 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…)

## Fellowships in Stat only: good news?!

Posted in Statistics, University life with tags EPSCR, fellowships, funding, mathematics on October 3, 2011 by xi'an**A**s reported in Nature newsblog, the UK funding body, EPSRC (Engineering and Physical Sciences Research Council), “has scrapped fellowships in all but two areas of mathematical sciences, namely statistics and applied probability”. This decision may sound like a bonanza for statisticians and applied probabilists, however, when thinking about it a bit more widely, it is close to a disaster. Choosing to fund fellowships only in a narrow subset of the field is indeed unfair, unwise, and inefficient. ** Unfair** because the topics were chosen w/o consultation with mathematicians. It could have been numerical analysis or cryptography instead. In which case it would have impacted statisticians and applied probabilists as well. Thus, top UK statisticians like Peter Donnelly and Peter Green rightly signed a protest letter along colleagues from other mathematical fields. (Maybe the RSS has likewise reacted. I have not seen it.)

**, because, as noted in the letter sent a week ago by twenty-five top UK mathematicians to their Prime Minister, cutting funds in most of mathematics will mean that most UK PhD students will leave the UK to get fellowships abroad. With a fair chance of never returning. (Maybe a bonanza for France? Not really, either, as the funding has not increased here and the current French PhDs need to be funded as well. Even though they most often get hired within a few months of their defense. Or leave for a postdoc abroad…)**

*Unwise***, because the decision is taken without prior notice and cannot expect to impact the area of research of future PhD’s. Nor does it bring a solution for the future of current PhD’s in**

*Inefficient***…**

*Not!{statistics and applied probability}*## The foundations of Statistics [reply]

Posted in Books, R, Statistics, University life with tags blog, foundations, introductory textbooks, linguistics, mathematics, R, simulation, Statistics Forum on July 19, 2011 by xi'an**S**hravan Vasishth has written a response to my review both published on the Statistics Forum. His response is quite straightforward and honest. In particular, he acknowledges not being a statistician and that he “should spend more time studying statistics”. I also understand the authors’ frustration at trying “to recruit several statisticians (at different points) to join [them] as co-authors for this book, in order to save [them] from [them]selves, so to speak. Nobody was willing to do join in.” (Despite the kind proposal to join as a co-author to a new edition, I would be rather unwilling as well, mostly because of the concept to avoid calculus at all cost… I will actually meet with Shravan at the end of the month to discuss specifics of the statistical flaws in this book.)

**H**owever, I still do not understand why the book was published without a proper review from a statistician. Springer is a/my serious scientific editor and book proposals usually go through several reviews, prior to and after redaction. Shravan Vasishth asks for alternative references, which I personally cannot provide for lack of teaching at this level, but this is somehow besides the point: even if a book at the intended level and for the intended audience did not exist, this would not justify the publication of a book on statistics (and only statistics) by authors not proficient enough in the topic.

**O**ne point of the response I do not get is the third item about the blog and letting my “rage get the better of [myself] (the rage is no doubt there for good reason)”. Indeed, while I readily acknowledge the review is utterly negative, I have tried to stick to facts, either statistical flaws (like the unbiasedness of *s*) or presentation defects. The reference to a blog in the book could be a major incentive to adopt the book, so if the blog does not live as a blog, it is both a disappointment to the reader and a sort of a breach of advertising. I perfectly understand the many reasons for not maintaining a blog (!), but then the site should have been advertised as a site rather than a blog. This was the meaning of the paragraph

The authors advertise a blog about the book that contains very little information. (The last entry is from December 2010: “The book is out”.) This was a neat idea, had it been implemented.

that does not sound full of rage to me… Anyway, this is a minor point.

## The foundations of Statistics: a simulation-based approach

Posted in Books, R, Statistics, University life with tags blog, Emacs, foundations, hypothesis testing, introductory textbooks, LaTeX, linguistics, mathematics, Python, R, simulation, Statistics Forum on July 12, 2011 by xi'an

“We have seen that a perfect correlation is perfectly linear, so an imperfect correlation will be `imperfectly linear’.”page 128

**T**his book has been written by two linguists, Shravan Vasishth and Michael Broe, in order to teach statistics “in areas that are traditionally not mathematically demanding” at a deeper level than traditional textbooks “without using too much mathematics”, towards building “the confidence necessary for carrying more sophisticated analyses” through R simulation. This is a praiseworthy goal, bound to produce a great book. However, and most sadly, I find the book does not live up to expectations. As in Radford Neal’s recent coverage of introductory probability books with R, there are statements there that show a deep misunderstanding of the topic… *(This post has also been published on the Statistics Forum.)* Continue reading

## Mathematics and realism

Posted in Books with tags Anathem, cosmology, Kurt Gödel, Liberation, mathematics, perspectivism, physics, platonicism, Pythagorean theorem, realism, Stephen Hawking, The Guardian on November 27, 2010 by xi'an**I** read in ** Liberation** a rather surprising tribune (in French) by “Yann Moix, writer”. The starting point is a criticism of Stephen Hawking (and Leonard Mlodinow)’s recent book

**, With regards to its conclusion that a god is not necessary to explain the creation and the working of the Universe: “**

*The Grand Design**It is not necessary to invoke God to light the blue touch paper and set the universe going*.” I haven’t read Hawking’s book (although I briefly considered buying it in London last time I was there, here is a Guardian review), I had never heard before of this (controversial) writer, and I do not see the point in debating about supernatural beings (except when reviewing a fantasy book!). However, the arguments of Moix are rather limited from a philosophical viewpoint.

## Mathematics looking for mathematicians

Posted in Statistics, University life with tags graduate course, mathematics, Maths à venir, students on December 6, 2009 by xi'an**T**his is on the cover of * Le Monde* today! In association with the workshop “Maths à venir“, i.e. “Maths to come”, jointly supported by the Société Mathématique de France, the Société Francaise de Statistique and the Société de Mathématiques Appliquées et Industrielles, there were several newshots in Mathematics this week on the national chanels, including a roundtable on the national public radio

**(with Jean-Pierre Bourguignon and the statistician Claudine Schwartz, also signing as C. Robert!) and this piece is an illustration of the efforts of the mathematicians. to reach the medias… The decrease in the number of math (and science) students in universities is a global trend in Western countries and France is not spared by this phenomenon. Till very recently, mathematical finance graduate programs were able to partly compensate for this decline but the subprime crisis has also impacted this flow. While the paper argues that the crisis has degraded the image of mathematics among students, I am quite skeptical about this, because financial mathematics are only taught in the final year of graduate programs. My own observation is that the last year saw instead a surge in the number of PHD students in mathematics (and statistics) as a result of lesser positions in banks and companies.**

*France Inter*