Archive for Valencia conferences

reading classics (#4,5,6)

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

La Défense from Paris-Dauphine, Nov. 15, 2012This week, thanks to a lack of clear instructions (from me) to my students in the Reading Classics student seminar, four students showed up with a presentation! Since I had planned for two teaching blocks, three of them managed to fit within the three hours, while the last one nicely accepted to wait till next week to present a paper by David Cox…

The first paper discussed therein was A new look at the statistical model identification, written in 1974 by Hirotugu Akaike. And presenting the AIC criterion. My student Rozan asked to give the presentation in French as he struggled with English, but it was still a challenge for him and he ended up being too close to the paper to provide a proper perspective on why AIC is written the way it is and why it is (potentially) relevant for model selection. And why it is not such a definitive answer to the model selection problem. This is not the simplest paper in the list, to be sure, but some intuition could have been built from the linear model, rather than producing the case of an ARMA(p,q) model without much explanation. (I actually wonder why the penalty for this model is (p+q)/T, rather than (p+q+1)/T for the additional variance parameter.) Or simulation ran on the performances of AIC versus other xIC’s…

The second paper was another classic, the original GLM paper by John Nelder and his coauthor Wedderburn, published in 1972 in Series B. A slightly easier paper, in that the notion of a generalised linear model is presented therein, with mathematical properties linking the (conditional) mean of the observation with the parameters and several examples that could be discussed. Plus having the book as a backup. My student Ysé did a reasonable job in presenting the concepts, but she would have benefited from this extra-week in including properly the computations she ran in R around the glm() function… (The definition of the deviance was somehow deficient, although this led to a small discussion during the class as to how the analysis of deviance was extending the then flourishing analysis of variance.) In the generic definition of the generalised linear models, I was also reminded of the
generality of the nuisance parameter modelling, which made the part of interest appear as an exponential shift on the original (nuisance) density.

The third paper, presented by Bong, was yet another classic, namely the FDR paper, Controlling the false discovery rate, of Benjamini and Hochberg in Series B (which was recently promoted to the should-have-been-a-Read-Paper category by the RSS Research Committee and discussed at the Annual RSS Conference in Edinburgh four years ago, as well as published in Series B). This 2010 discussion would actually have been a good start to discuss the paper in class, but Bong was not aware of it and mentioned earlier papers extending the 1995 classic. She gave a decent presentation of the problem and of the solution of Benjamini and Hochberg but I wonder how much of the novelty of the concept the class grasped. (I presume everyone was getting tired by then as I was the only one asking questions.) The slides somewhat made it look too much like a simulation experiment… (Unsurprisingly, the presentation did not include any Bayesian perspective on the approach, even though they are quite natural and emerged very quickly once the paper was published. I remember for instance the Valencia 7 meeting in Teneriffe where Larry Wasserman discussed about the Bayesian-frequentist agreement in multiple testing.)

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<j} |z_i-z_j|^2

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…

MCMSki IV (call for proposals)

Posted in Mountains, R, Statistics, University life with tags , , , , on October 15, 2012 by xi'an

The next MCMSki IV conference will for the first time host contributed sessions as well as invited sessions. The scientific committee thus welcomes proposals for contributed talks and even more for contributed sessions. Contributed talks are scheduled to last 20 minutes, plus questions, and contributed sessions one hour and a half, including questions, which corresponds to 4 talks or 3 talks and a discussant.

Proposals should be sent to me, Christian Robert, before March 20, 2013, and includes the name of the speaker(s), the title of the talk(s), and a short 5-15 lines abstract(s). All speakers in a contributed session must be contacted and give their agreement prior to the submission of a session, obviously. The scientific committee will then evaluate the proposals and notify the session organiser/the speaker before April 20, 2013. We remind everyone that MCMSki IV will also schedule two evening poster sessions in the best tradition of the Valencia and MCMSki meetings, sessions in which everyone is welcome to present.

Topics for the proposals include “Big Data issues”, “computationally intensive Bayesian applications”, “probabilistic advances for MC methods”, “variance reduction techniques and Rao-Blackwellisation”, “MC for non-parametric Bayes inference “, “adaptive MC”, “interacting MC”, “INLA”, and “ABC”.

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