## a probabilistic proof to a quasi-Monte Carlo lemma

Posted in Books, Statistics, Travel, University life with tags , , , , , on November 17, 2014 by xi'an

As I was reading in the Paris métro a new textbook on Quasi-Monte Carlo methods, Introduction to Quasi-Monte Carlo Integration and Applications, written by Gunther Leobacher and Friedrich Pillichshammer, I came upon the lemma that, given two sequences on (0,1) such that, for all i’s,

$|u_i-v_i|\le\delta\quad\text{then}\quad\left|\prod_{i=1}^s u_i-\prod_{i=1}^s v_i\right|\le 1-(1-\delta)^s$

and the geometric bound made me wonder if there was an easy probabilistic proof to this inequality. Rather than the algebraic proof contained in the book. Unsurprisingly, there is one based on associating with each pair (u,v) a pair of independent events (A,B) such that, for all i’s,

$A_i\subset B_i\,,\ u_i=\mathbb{P}(A_i)\,,\ v_i=\mathbb{P}(B_i)$

and representing

$\left|\prod_{i=1}^s u_i-\prod_{i=1}^s v_i\right| = \mathbb{P}(\cap_{i=1}^s A_i) - \mathbb{P}(\cap_{i=1}^s B_i)\,.$

Obviously, there is no visible consequence to this remark, but it was a good way to switch off the métro hassle for a while! (The book is under review and the review will hopefully be posted on the ‘Og as soon as it is completed.)

## Statistics slides (4)

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , on November 10, 2014 by xi'an

Here is the fourth set of slides for my third year statistics course, trying to build intuition about the likelihood surface and why on Earth would one want to find its maximum?!, through graphs. I am yet uncertain whether or not I will reach the point where I can teach more asymptotics so maybe I will also include asymptotic normality of the MLE under regularity conditions in this chapter…

## the new museum ruining my views!

Posted in pictures, Travel, University life with tags , , , , , , , , , , on November 8, 2014 by xi'an

In the past years, I have see a construction grow and grow under my office windows in Paris-Dauphine, ruining my views of the towers of La Défense, as seen on the above picture. This huge building designed by architect Frank Gehry has now opened as the Fondation Louis Vuitton museum, exposing artworks owned by LVMH and Bernard Arnault. Since I am very close to it and could not get an idea of what it looked like from my office, I took a Vélib yesterday and biked the kilometer between Porte Dauphine and the museum. As it had just opened, it was fairly crowded but I could still take a few pictures of this elegant sail-boat made of glass panels, without entering the art gallery itself…

Once the novelty has worn out and the crowds thinned down, I will be back to look at the exhibits. In the meanwhile, I for sure will not forget its presence…!

## postdoc in Paris?

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

There is an open call of the Fondation Sciences Mathématiques de Paris (FSMP) about a postdoctoral funding program with 18 position-years available for staying in Université Paris-Dauphine (and other participating universities). The net support is quite decent  (wrt French terms and academic salaries) and the application form easy to fill. So, if you are interested in coming to Paris to work on ABC, MCMC, Bayesian model choice, &tc., feel free to contact me (or another Parisian statistician) and to apply! The deadline is December 01, 2014.  And the decision will be made by January 15, 2015. The starting date for the postdoc is October 01, 2015.

## art brut

Posted in Kids, pictures, Travel with tags , , , , on October 18, 2014 by xi'an

## impression, soleil couchant

Posted in pictures, Running with tags , , , , , , on October 11, 2014 by xi'an

As the sunset the day before had been magnificent [thanks to the current air pollution!], I attempted to catch it from a nice spot and went to the top of the nearby hill. The particles were alas (!) not so numerous that evening and so I only got this standard view of the sun going down. Incidentally, I had read a few days earlier in the plane from Vienna that the time and date when Monet’s Impression, Soleil Levant was painted had been identified by a U.S. astronomer as 7h35 on the 13th of Novembre 1872. In Le Havre, Normandy. An exhibit in the nearby Musée Marmottan retraces this quest…

## Statistics slides (3)

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , on October 9, 2014 by xi'an

Here is the third set of slides for my third year statistics course. Nothing out of the ordinary, but the opportunity to link statistics and simulation for students not yet exposed to Monte Carlo methods. (No ABC yet, but who knows?, I may use ABC as an entry to Bayesian statistics, following Don Rubin’s example! Surprising typo on the Project Euclid page for this 1984 paper, by the way…) On Monday, I had the pleasant surprise to see Shravan Vasishth in the audience, as he is visiting Université Denis Diderot (Paris 7) this month.