**T**oday I made a “quick” (10h door to door!) round trip visit to Marseille (by train) to take part in the PhD thesis defense (committee) of Edwin Fourrier-Nicolaï, which title was *Poverty, inequality and redistribution: an econometric approach*. While this was mainly a thesis in economics, meaning defending some theory on inequalities based on East German data, there were Bayesian components in the thesis that justified (to some extent!) my presence in the jury. Especially around mixture estimation by Gibbs sampling. (On which I started working almost exactly 30 years ago, when I joined Paris 6 and met Gilles Celeux and Jean Diebolt.) One intriguing [for me] question stemmed from this defense, namely the notion of a Bayesian estimation of a *three i’s of poverty* (TIP) curve. The three i’s stand for incidence, intensity, and inequality, as, introduced in Jenkins and Lambert (1997), this curve measure the average income loss from the poverty level for the *100p*% lower incomes, when p varies between 0 and 1. It thus depends on the distribution F of the incomes and when using a mixture distribution its computation requires a numerical cdf inversion to determine the income *p*-th quantile. A related question is thus on how to define a Bayesian estimate of the TIP curve. Using an average over the values of an MCMC sample does not sound absolutely satisfactory since the upper bound in the integral varies for each realisation of the parameter. The use of another estimate would however require a specific loss function, an issue not discussed in the thesis.

## Archive for thesis defence

## the three i’s of poverty

Posted in Books, pictures, Statistics, Travel, University life with tags Gibbs sampling, loss function, Marseille, mixture of distributions, thesis defence, three i's of poverty on September 15, 2019 by xi'an## noise contrastive estimation

Posted in Statistics with tags Bayesian GANs, CREST, doubly intractable problems, Electronic Journal of Statistics, ENSAE, Langevin MCMC algorithm, noise-contrastive estimation, Paris-Saclay campus, PhD thesis, thesis defence on July 15, 2019 by xi'an**A**s I was attending Lionel Riou-Durand’s PhD thesis defence in ENSAE-CREST last week, I had a look at his papers (!). The 2018 noise contrastive paper is written with Nicolas Chopin (both authors share the CREST affiliation with me). Which compares Charlie Geyer’s 1994 bypassing the intractable normalising constant problem by virtue of an artificial logit model with additional simulated data from another distribution *ψ*.

“Geyer (1994) established the asymptotic properties of the MC-MLE estimates under general conditions; in particular that the x’s are realisations of an ergodic process. This is remarkable, given that most of the theory on M-estimation (i.e.estimation obtained by maximising functions) is restricted to iid data.”

Michael Guttman and Aapo Hyvärinen also use additional simulated data in another likelihood of a logistic classifier, called noise contrastive estimation. Both methods replace the unknown ratio of normalising constants with an unbiased estimate based on the additional simulated data. The major and impressive result in this paper [now published in the Electronic Journal of Statistics] is that the noise contrastive estimation approach always enjoys a smaller variance than Geyer’s solution, at an equivalent computational cost when the actual data observations are iid. And the artificial data simulations ergodic. The difference between both estimators is however negligible against the Monte Carlo error (Theorem 2).

This may be a rather naïve question, but I wonder at the choice of the alternative distribution *ψ*. With a vague notion that it could be optimised in a GANs perspective. A side result of interest in the paper is to provide a minimal (re)parameterisation of the truncated multivariate Gaussian distribution, if only as an exercise for future exams. Truncated multivariate Gaussian for which the normalising constant is of course unknown.

## congratulations, Dr. Wu!

Posted in pictures, Statistics, University life with tags academic position, HMC, PDMP, PhD thesis, thesis defence, Université Paris Dauphine on October 4, 2018 by xi'an**T**his afternoon, my (now former) PhD student Changye Wu defended his thesis on Accelerated methods for MCMC, for which the jury awarded him the title of Docteur de l’Université Paris Dauphine. Congratulations to him and best wishes for his job hunting!

## advances in Bayesian modelling a Venezia

Posted in Statistics with tags Bayesian graphical model, Bayesian modelling, Ca' Foscari University, day trip, Italy, PhD thesis, thesis defence, Venezia, Venice, workshop on July 4, 2018 by xi'an## le soleil de Massilia [jatp]

Posted in pictures, Statistics, Travel, University life with tags Bayesian econometrics, bread, Lorraine, Marseille, Méditerranée, Notre-Dame-de-la-Garde, PhD thesis, Saint-Charles, thesis defence, Université Aix Marseille on December 10, 2017 by xi'an## Bayesian astrostats under Laplace’s gaze

Posted in Books, Kids, pictures, Statistics, Travel, University life, Wines with tags Arago, astrostatistics, Greenwich Meridian, jazz, Le Verrier, Louis XIV, Observatoire de Paris, Paris, Paris Meridian, Perrault, Pierre Simon de Laplace, thesis defence on October 11, 2016 by xi'an**T**his afternoon, I was part of a jury of an astrostatistics thesis, where the astronomy part was about binary objects in the Solar System, and the statistics part about detecting patterns in those objects, unsurprisingly. The first part was highly classical using several non-parametric tests like Kolmogorov-Smirnov to test whether those binary objects were different from single objects. While the p-values were very tiny, I felt these values were over-interpreted in the thesis, because the sample size of N=30 leads to some scepticism about numerical quantities like 0.0008. While I do not want to sound pushing for Bayesian solutions in every setting, this case is a good illustration of the nefarious power of p-values, which are almost always taken at face value, i.e., where 0.008 is understood in terms of the null hypothesis and not in terms of the observed realisation of the p-value. Even within a frequentist framework, the distribution of this p-value should be evaluated or estimated one way or another, as there is no reason to believe it is anywhere near a Uniform(0,1) distribution.The second part of the thesis was about the estimation of some parameters of the laws of the orbits of those dual objects and the point of interest for me was the purely mechanical construction of a likelihood function that was an exponential transform of a sum of residuals, made of squared differences between the observations and their expectations. Or a power of such differences. This was called the “statistical model” in the thesis and I presume in part of the astrostats literature. This reminded me of the first meeting I had with my colleagues from Besançon, where they could not use such mechanical versions because of intractable expectations and used instead simulations from their physical model, literally reinventing ABC. This resolution had the same feeling, closer to indirect inference than regular inference, although it took me half the defence to realise it.

The defence actually took part in the beautiful historical Perrault’s building of Observatoire de Paris, in downtown Paris, where Cassini, Arago and Le Verrier once ruled! In the council room under paintings of major French astronomers, including Laplace himself, looking quite smug in his academician costume. The building is built around the Paris Zero Meridian (which got dethroned in 1911 by the Greenwich Zero Meridian, which I contemplated as a kid since my childhood church had the Greenwich drawn on the nave stones). The customary “pot” after the thesis and its validation by the jury was in the less historical cafeteria of the Observatoire, but it included a jazz big band, which made this thesis defence quite unique in many ways!