Merci, Simone! [in Strasbourg]

I posted this picture on the ‘Og last June, when I went to Rouen. At the time Simone Veil had just passed away and I wanted to recall her single-handed fight for making abortion legal in France… I received last week an email I first took for a spam, email from a curator of the European Parliament, in Strasbourg (where Simone Veil was for a while a European deputy and its President, its first female President), preparing a permanent exhibit in her memory and wishing to use my picture in the exhibit, to illustrate another perspective on her, away from official and family photographs. Completely unexpected, but I obviously gave immediately my agreement.

Merci, Simone!

a trip back in time [and in Rouen]

On Monday, I took part in a celebration of the remarkable career of a former colleague of mine in Rouen, Gérard Grancher, who is retiring after a life-long position as CNRS engineer in the department of maths of the University of Rouen, a job title that tells very little about the numerous facets of his interactions with mathematics, from his handling of all informatics aspects in the laboratory to his support of all colleagues there, including fresh PhD students like me in 1985!, to his direction of the CNRS lab in 2006 and 2007 at a time of deep division and mistrust, to his numerous collaborations on statistical projects with local actors, to his Norman federalism in bringing the maths departments of Caen and Rouen into a regional federation, to an unceasing activism to promote maths in colleges and high schools and science fairs all around Normandy, to his contributions to professional training in statistics for CNRS agents, and much, much more… Which explains why the science auditorium of the University of Rouen was packed with mathematicians and high schools maths teachers and friends! (The poster of the day was made by Gérard’s accomplices in vulgarisation, Élise Janvresse and Thierry Delarue, based on a sample of points randomly drawn from Gérard’s picture, maybe using a determinantal process, and the construction of a travelling salesman path over those points.)

This was a great day with mostly vulgarisation talks (including one about Rasmus’ socks..!) and reminiscences about Gérard’s carreer at Rouen. As I had left the university in 2000 to move to Paris-Dauphine, this was a moving day as well, as I met with old friends I had not seen for ages, including our common PhD advisor, Jean-Pierre Raoult.

This trip back in time was also an opportunity to (re-)visit the beautifully preserved medieval centre of Rouen, with its wooden houses, Norman-style, the numerous churches, including Monet‘s cathedral, the Justice Hall… Last time I strolled those streets, George Casella was visiting!

more Rouen noir [jatp]

Rouen noir [jatp]

Bayesian decision riddle

The current puzzle on The Riddler is a version of the secretary problem with an interesting (?) Bayesian solution.

Given four positive numbers x¹, x², x³, x⁴, observed sequentially, the associated utility is the value of x at the stopping time. What is the optimal stopping rule?

While nothing is mentioned about the distribution of the x’s, I made the assumption that they were iid and uniformly distributed over (0,M), with M unknown and tried a Bayesian resolution with the non-informative prior π(M)=1/M. And failed. The reason for this failure is that the expected utility is infinite at the first step: while the posterior expected utility is finite with three and two observations, meaning I can compare stopping and continuing at the second and third steps, the predicted expected reward for continuing after observing x¹ does not exist because the expected value of max(x¹,x²) given x¹ does not exist. As the predictive density of x² is max(x¹,x²)⁻²…  Several alternatives are possible to bypass this impossible resolution, from changing the utility function to picking another reference prior.

For instance, using a prior like π(M)=1/M² l(and the same monetary return utility) leads to a proper optimal solution, namely

1. always wait for the second observation x²
2. stop at x² if x²>11x¹/12, else wait for x³
3. stop at x³ if x³>23 max(x¹,x²)/24, else observe x⁴

obtained analytically on a bar table in Rouen (and checked numerically later).

Another approach is to try to optimise the probability to pick the largest amount of the four x’s, but this is not leading to an interesting solution, since it corresponds to picking the first maximum after x¹, while picking the largest among remaining ones leads to a somewhat convoluted solution I have no patience to produce here! Plus this is not a really pertinent loss function as it does not discriminate enough against waiting…

GG Day in Rouen

[Notice: This post is fairly “local” in that it is about a long-time friend being celebrated by his university. Nice poster though and an opportunity to stress his essential contributions to the maths department there!]

Next June, I will spend the day in Rouen for a conference celebrating the career and dedication of Gérard Grancher to mathematics and the maths department there. (When I got invited I had not realised I was to give the research talk of the day!) Gérard Granger is a CNRS engineer and a statistician who is indissociable from the maths department in Rouen, where he spent his whole career, now getting quite close to [mandatory] retirement! I am very happy to take part in this celebration as Gérard has always been an essential component of the department there, driving the computer structure, reorganising the library, disseminating the fun of doing maths to high schools around and to the general public, and always a major presence in the department,  whom I met when I started my PhD there (!) Working on the local computers in Pascal and typing my thesis with scientific word (!!)