Archive for Université Paris Dauphine

in the street for a year

Posted in Mountains, pictures, Travel, University life with tags , , , , , , , , , , on April 13, 2018 by xi'an

Just like about every year, I sent two of my pictures to the photography competition of Paris Dauphine, with not much consideration for the theme “green the future”, and was hence quite surprised to get selected this time! (Almost as much surprised as last year when an almost perfect copy of my picture of the Alcazar Baths of Lady María de Padilla got selected!) As I could travel back from Oxford to attend the opening ceremony, I went there last night, wondering at which of my pictures had been selected (Lac Pavin, Auvergne versus the Quinrang, Skye)…


And so this picture will remain exposed in the street, boulevard Lannes, for the incoming year, meaning I will cross it each time I bike to the university! The 22 other pictures were more in tune with the theme of a green future, like the winning one of a fast moving métro carriage at the station Chemin Vert. Or this simple blade of grass growing from ashes…

 
And thus the winner is… Continue reading

accelerating MCMC

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , on April 11, 2018 by xi'an

As forecasted a rather long while ago (!), I wrote a short and incomplete survey on some approaches to accelerating MCMC. With the massive help of Victor Elvira (Lille), Nick Tawn (Warwick) and Changye Wu (Dauphine). Survey which current version just got arXived and which has now been accepted by WIREs Computational Statistics. The typology (and even the range of methods) adopted here is certainly mostly arbitrary, with suggestions for different divisions made by a very involved and helpful reviewer. While we achieved a quick conclusion to the review process, suggestions and comments are most welcome! Even if we cannot include every possible suggestion, just like those already made on X validated. (WIREs stands for Wiley Interdisciplinary Reviews and its dozen topics cover several fields, from computational stats to biology, to medicine, to engineering.)

gender gaps

Posted in Statistics, University life with tags , , , , , , , , , , on March 31, 2018 by xi'an

Two of my colleagues [and co-authors] at Dauphine, Elyès Jouini and Clotilde Napp, published a paper in Science last week (and an associated tribune in Le Monde which I spotted first) about explaining differences in national gender inequalities in maths (as measured by PISA) in terms of the degree of overall inequality in the respective countries. Gaps in the highest maths performer sex ratio. While I have no qualm about the dependency or the overall statistical cum machine learning analysis (supported by our common co-author Jean-Michel Marin), and while I obviously know nothing about the topic!, I leisurely wonder at the cultural factor (which may also partly explain for the degree of inequality) when considering that the countries at the bottom of the above graphs are rather religious (and mostly catholic). I also find it most intriguing that the gender gap is consistently reversed when considering higher performer sex ratio for reading, because mastering the language should be a strong factor in power structures and hence differences therein should also lead to inequalities…

ABCDE for approximate Bayesian conditional density estimation

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on February 26, 2018 by xi'an

Another arXived paper I surprisingly (?) missed, by George Papamakarios and Iain Murray, on an ABCDE (my acronym!) substitute to ABC for generative models. The paper was reviewed [with reviews made available!] and accepted by NIPS 2016. (Most obviously, I was not one of the reviewers!)

“Conventional ABC algorithms such as the above suffer from three drawbacks. First, they only represent the parameter posterior as a set of (possibly weighted or correlated) samples [for which] it is not obvious how to perform some other computations using samples, such as combining posteriors from two separate analyses. Second, the parameter samples do not come from the correct Bayesian posterior (…) Third, as the ε-tolerance is reduced, it can become impractical to simulate the model enough times to match the observed data even once [when] simulations are expensive to perform”

The above criticisms are a wee bit overly harsh as, well…, Monte Carlo approximations remain a solution worth considering for all Bayesian purposes!, while the approximation [replacing the data with a ball] in ABC is replaced with an approximation of the true posterior as a mixture. Both requiring repeated [and likely expensive] simulations. The alternative is in iteratively simulating from pseudo-predictives towards learning better pseudo-posteriors, then used as new proposals at the next iteration modulo an importance sampling correction.  The approximation to the posterior chosen therein is a mixture density network, namely a mixture distribution with parameters obtained as neural networks based on the simulated pseudo-observations. Which the authors claim [p.4] requires no tuning. (Still, there are several aspects to tune, from the number of components to the hyper-parameter λ [p.11, eqn (35)], to the structure of the neural network [20 tanh? 50 tanh?], to the number of iterations, to the amount of X checking. As usual in NIPS papers, it is difficult to assess how arbitrary the choices made in the experiments are. Unless one starts experimenting with the codes provided.) All in all, I find the paper nonetheless exciting enough (!) to now start a summer student project on it in Dauphine and hope to check the performances of ABCDE on different models, as well as comparing this ABC implementation with a synthetic likelihood version.

 As an addendum, let me point out the very pertinent analysis of this paper by Dennis Prangle, 18 months ago!

complex Cauchys

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on February 8, 2018 by xi'an

During a visit of Don Fraser and Nancy Reid to Paris-Dauphine where Nancy gave a nice introduction to confidence distributions, Don pointed out to me a 1992 paper by Peter McCullagh on the Cauchy distribution. Following my recent foray into the estimation of the Cauchy location parameter. Among several most interesting aspects of the Cauchy, Peter re-expressed the density of a Cauchy C(θ¹,θ²) as

f(x;θ¹,θ²) = |θ²| / |x-θ|²

when θ=θ¹+ιθ² [a complex number on the half-plane]. Denoting the Cauchy C(θ¹,θ²) as Cauchy C(θ), the property that the ratio aX+b/cX+d follows a Cauchy for all real numbers a,b,c,d,

C(aθ+b/cθ+d)

[when X is C(θ)] follows rather readily. But then comes the remark that

“those properties follow immediately from the definition of the Cauchy as the ratio of two correlated normals with zero mean.”

which seems to relate to the conjecture solved by Natesh Pillai and Xiao-Li Meng a few years ago. But the fact that  a ratio of two correlated centred Normals is Cauchy is actually known at least from the1930’s, as shown by Feller (1930, Biometrika) and Geary (1930, JRSS B).

exams

Posted in Kids, Statistics, University life with tags , , , , , , , on February 7, 2018 by xi'an
As in every term, here comes the painful week of grading hundreds of exams! My mathematical statistics exam was highly traditional and did not even involve Bayesian material, as the few students who attended the lectures were so eager to discuss sufficiency and ancilarity, that I decided to spend an extra lecture on these notions rather than rushing though conjugate priors. Highly traditional indeed with an inverse Gaussian model and a few basic consequences of Basu’s theorem. actually exposed during this lecture. Plus mostly standard multiple choices about maximum likelihood estimation and R programming… Among the major trends this year, I spotted out the widespread use of strange derivatives of negative powers, the simultaneous derivation of two incompatible convergent estimates, the common mixup between the inverse of a sum and the sum of the inverses, the inability to produce the MLE of a constant transform of the parameter, the choice of estimators depending on the parameter, and a lack of concern for Fisher informations equal to zero.

distributions for parameters [seminar]

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , on January 22, 2018 by xi'an
Next Thursday, January 25, Nancy Reid will give a seminar in Paris-Dauphine on distributions for parameters that covers different statistical paradigms and bring a new light on the foundations of statistics. (Coffee is at 10am in the Maths department common room and the talk is at 10:15 in room A, second floor.)

Nancy Reid is University Professor of Statistical Sciences and the Canada Research Chair in Statistical Theory and Applications at the University of Toronto and internationally acclaimed statistician, as well as a 2014 Fellow of the Royal Society of Canada. In 2015, she received the Order of Canada, was elected a foreign associate of the National Academy of Sciences in 2016 and has been awarded many other prestigious statistical and science honours, including the Committee of Presidents of Statistical Societies (COPSS) Award in 1992.

Nancy Reid’s research focuses on finding more accurate and efficient methods to deduce and conclude facts from complex data sets to ultimately help scientists find specific solutions to specific problems.

There is currently some renewed interest in developing distributions for parameters, often without relying on prior probability measures. Several approaches have been proposed and discussed in the literature and in a series of “Bayes, fiducial, and frequentist” workshops and meeting sessions. Confidence distributions, generalized fiducial inference, inferential models, belief functions, are some of the terms associated with these approaches.  I will survey some of this work, with particular emphasis on common elements and calibration properties. I will try to situate the discussion in the context of the current explosion of interest in big data and data science.