## MCMSki IV, Jan. 6-9, 2014, Chamonix (news #13)

Posted in Mountains, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on December 9, 2013 by xi'an

Now, most poster abstracts have been received (or at least 63 of them),  even though newcomers can still send them to my wordpress address (if they realise the message gets posted immediately!, so the format Subject: firstname secondname (affiliation): title and text: abstract must be respected! No personal message or query please!). We have now above 200 registered participants, with all sessions remaining miraculously full (after a few permutations in the program).

S0 it is time to mention a wee bit of the “ski” side of MCMski. Chamonix has two types of ski passes, Chamonix Le Pass, and Mont Blanc Unlimited, the later allowing a wide access to the Mont Blanc area, up to 3800 meters and in France, Italy, and Switzerland, but presumably harder to exploit to the fullest on a 4 hour afternoon break. (You have to arrange renting skis and buying passes on your own! The conference centre may answer moderate queries but not make any booking.)  The temperature in the town of Chamonix is currently between -7 and 0 (centigrades), with ten centimetres of snow in town. All ski areas will be open by Dec. 21. If you plan to ski the Vallée Blanche from Aiguille du Midi, at 3800m, I strongly advise renting a guide for this ultimate skiing experience!

Big news: not only the ski race will take place on Wed., Jan. 08, afternoon, organised by ESF Chamonix, but Antonietta Mira managed to secure one or two pairs of skis for the winner(s) of the race! I doubt there will be other opportunities of that magnitude for winning a magnificent pair of skis made in Italy by Blossom skis. Thanks a lot to Anto!!! And to Blossom skis (whose collection includes a series called FreeTibet.)

## La Défense, soleil couchant [#4]

Posted in pictures, Travel, University life with tags , , , on December 7, 2013 by xi'an

## La Défense, soleil couchant [#3]

Posted in pictures, Travel, University life with tags , , on December 6, 2013 by xi'an

## simulating determinantal processes

Posted in Statistics, Travel with tags , , , , , , , , , , on December 6, 2013 by xi'an

In the plane to Atlanta, I happened to read a paper called Efficient simulation of the Ginibre point process by Laurent Decreusefond, Ian Flint, and Anaïs Vergne (from Telecom Paristech). “Happened to” as it was a conjunction of getting tipped by my new Dauphine colleague (and fellow blogger!) Djalil Chaffaï about the paper, having downloaded it prior to departure, and being stuck in a plane (after watching the only Chinese [somewhat] fantasy movie onboard, Saving General Yang).

This is mostly a mathematics paper. While indeed a large chunk of it is concerned with the rigorous definition of this point process in an abstract space, the last part is about simulating such processes. They are called determinantal (and not detrimental as I was tempted to interpret on my first read!) because the density of an n-set (x1x2,…,xn) is given by a kind of generalised Vandermonde determinant

$p(x_1,\ldots,x_n) = \dfrac{1}{n!} \text{det} \left( T(x_i,x_j) \right)$

where T is defined in terms of an orthonormal family,

$T(x,y) = \sum_{i=1}^n \psi_i(x) \overline{\psi_i(y)}.$

(The number n of points can be simulated via an a.s. finite Bernoulli process.) Because of this representation, the sequence of conditional densities for the xi‘s (i.e. x1, x2 given x1, etc.) can be found in closed form. In the special case of the Ginibre process, the ψi‘s are of the form

$\psi_i(z) =z^m \exp\{-|z|^2/2\}/\sqrt{\pi m!}$

and the process cannot be simulated for it has infinite mass, hence an a.s. infinite number of points. Somehow surprisingly (as I thought this was the point of the paper), the authors then switch to a truncated version of the process that always has a fixed number N of points. And whose density has the closed form

$p(x_1,\ldots,x_n) = \dfrac{1}{\pi^N} \prod_i \frac{1}{i!} \exp\{-|z_i|^2/2\}\prod_{i

It has an interestingly repulsive quality in that points cannot get close to one another. (It reminded me of the pinball sampler proposed by Kerrie Mengersen and myself at one of the Valencia meetings and not pursued since.) The conclusion (of this section) is anticlimactic, though,  in that it is known that this density also corresponds to the distribution of the eigenvalues of an Hermitian matrix with standardized complex Gaussian entries. The authors mentions that the fact that the support is the whole complex space Cn is a difficulty, although I do not see why.

The following sections of the paper move to the Ginibre process restricted to a compact and then to the truncated Ginibre process restricted to a compact, for which the authors develop corresponding simulation algorithms. There is however a drag in that the sequence of conditionals, while available in closed-form, cannot be simulated efficiently but rely on a uniform accept-reject instead. While I am certainly missing most of the points in the paper, I wonder if a Gibbs sampler would not be an interesting alternative given that the full (last) conditional is a Gaussian density…

## La Défense, soleil couchant [#2]

Posted in pictures, Travel, University life with tags , , , on December 5, 2013 by xi'an