## Bayes at the Bac’ [again]

Posted in Kids, Statistics with tags , , , , , , , , on June 19, 2014 by xi'an

When my son took the mathematics exam of the baccalauréat a few years ago, the probability problem was a straightforward application of Bayes’ theorem.  (Problem which was later cancelled due to a minor leak…) Surprise, surprise, Bayes is back this year for my daughter’s exam. Once again, the topic is a pharmaceutical lab with a test, test with different positive rates on two populations (healthy vs. sick), and the very basic question is to derive the probability that a person is sick given the test is positive. Then a (predictable) application of the CLT-based confidence interval on a binomial proportion. And the derivation of a normal confidence interval, once again compounded by  a CLT-based confidence interval on a binomial proportion… Fairly straightforward with no combinatoric difficulty.

The other problems were on (a) a sequence defined by the integral

$\int_0^1 (x+e^{-nx})\text{d}x$

(b) solving the equation

$z^4+4z^2+16=0$

in the complex plane and (c) Cartesian 2-D and 3-D geometry, again avoiding abstruse geometric questions… A rather conventional exam from my biased perspective.

## do novel writers need to make exceptional beings of their characters?

Posted in Books, Kids with tags , , , , , , , , on June 26, 2013 by xi'an

In the French literature part of the baccalauréat exam my daughter (and 170,000 other French students) took on Tuesday, the essay was about the above. It was quite a congenial theme and she seems to have enjoyed the opportunity to review her favourite books to argue the point. (She however declined to write a shorter version for the ‘Og, even in French..!) I wish I had time to expand on this, as it is a fairly rich field for arguing both ways, from Rabelais’ Gargantua and Dumas’ D’Artagnan to Melville’s Bartelby and Raymond Carver‘s characters (who often even remain unnamed). Opposing Flaubert’s Emma Bovary and Maupassant’s Jeanne for instance. Although my daughter considered Emma was in the “ordinary” camp… And discussing the characters in The Grapes of Wrath since this was one of the included texts. In my conclusion, despite advices not to answer the question in a definitive manner, I would however lean towards the quantum physics analogy that writers impact on the exceptional nature of their characters, since they become exceptional if only by appearing in the novel… (Check a mediocre online correction.)

## Bayes on the radio (regrets)

Posted in Books, Kids, Running, Statistics with tags , , , , , on November 13, 2012 by xi'an

While running this morning I was reconsidering (over and over) my discussion of Bayes’ formula on the radio and thought I should have turned the presentation of Bayes’ theorem differently. I spent much too much time on the math side of Bayes’ formula and not enough on the stat side. The math aspect is not of real importance as it is a mere reformulation of conditional probabilities. The stat side is what matters as introducing a (prior) distribution on the parameter (space) is the #1 specificity of Bayesian statistics…. And the focus point of most criticisms, as expressed later by the physicist working on the Higgs boson, Dirk Zerwas.

I also regret not mentioning that Bayes’ formula was taught in French high schools, as illustrated by the anecdote of Bayes at the bac. And not reacting at the question about Bayes in the courtroom with yet another anecdote of Bayes’ formula been thrown out of the accepted tools by an English court of appeal about a year ago. Oh well, another argument for sticking to the written world.

## Uneducated guesses

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , on January 12, 2012 by xi'an

I received this book, Uneducated Guesses: Using Evidence to Uncover Misguided Education Policies by Howard Wainer, from Princeton University Press for review in CHANCE. Alas, I am presumably one of the least likely adequate reviewers for the book in that

• having done all of my academic training in France (except for my most useful post-doctoral training in Purdue and in Cornell), I never took any of those ACT/SAT/&tc tests (except for the GRE at the very end of my Ph.D. towards a post-doctoral grant I did not get!);
• teaching in a French university, I never used any of those tests to compare undergraduate or graduates applicants;
• I am very marginally aware of the hiring process in US universities at the undergraduate, even though I knew about the early admission policy;
• there is no equivalent in the French high school system, given that high school students have to undergo a national week-long exam, le baccalauréat, to enter higher education and that most curricula actually decide on the basis of the high school record, prior to [but conditional on] the baccalauréat.

Thus, this review of Wainer’s Uneducated Guesses is to be taken with pinches (or even tablespoons) of salt. And to be opposed to other reviews. Esp. in Statistics journals (I could not find any).

My role in this parallels Spock’s when he explained `Nowhere am I so desperately needed as among a shipload of illogical humans.‘” (page 157)

First, the book is very pleasant to read, with a witty and whimsical way of pushing strong (and well-argued) opinions. Even as a complete bystander, I found the arguments advanced for keeping SAT as the preferential tool for student selection quite engaging, as were the later ones against teacher and college rankings equally making sense. So the book should appeal to a large chunk of the public, as prospective students, parents, high school teachers or college selection committees. (Scholars on entrance tests may already have seen the arguments since most of the chapter are based on earlier papers of  Howard Wainer.) Second, and this is yet another reason why I feel remote from the topic, the statistical part of the analysis is simply not covered in the book. There are tables and there are graphs, there are regressions and there are interpolation curves, there is a box-plot and there are normal densities, but I am missing a statistical model that would push us further than the common sense that permeates the whole book. After reading the book, my thirst about the modelling of education tests and ranking is thus far from being quenched! (Note I am not saying the author is ignorant of such matters, since he published in psychometrics, educational statistics and other statistics journals, and taught Statistics at Wharton. The technical side of the argument does exist, but it is not included in the book. The author refers to Gelman et al., 1995, and to the fruitful Bayesian approach on page 69.)

## Bayes at the Bac’ [and out!]

Posted in Kids, Statistics with tags , , , , , , on June 24, 2011 by xi'an

In the mathematics exam of the baccalauréat my son (and 160,000 other students) took on Tuesday, the probability problem was a straightforward application of Bayes’ theorem. Given a viral test with 99% positives for infected patients and 97% negatives for non-infected patients, in a population with 2% of infected patients, what is the probability that the patient is infected given that the test is positive? (It looks like another avatar of Exercise 1.7  in The Bayesian Choice!) A lucky occurrence, given that I had explained to my son Bayes’ formula earlier this year (neither the math book nor the math teacher mentioned Bayes, incidentally!) and even more given that, in a crash revision Jean-Michel Marin gave him the evening before, they went over it once again! The other problems were a straightforward multiple choice about complex numbers (with one mistake!), some calculus around the functional sequence xne-x, and some arithmetic questions around Gauss’s and Bezout’s theorems. A few hours after I wrote the above, the (official) news came that this question had been posted on the web prior to the exam by someone and thus that it would be canceled from the exam by the Ministry for Education! The grade will then be computed on the other problems, which is rather unfair for the students. (On the side, the press release from the Ministry contains a highly specious argument that regulation allows for three to five exercises in the exam, hence that there is nothing wrong with reducing the number of exercises to three!) Not so lucky an occurrence, then, and I very deadly hope this will not impact in a drastic manner my son’s result! (Most likely, the grading will be more tolerant and students will not unduly suffer from the action of a very few….)