Archive for thesis defence

Bayesian inference with no likelihood

Posted in Books, Statistics, University life with tags , , , , , , , , on January 28, 2020 by xi'an

This week I made a quick trip to Warwick for the defence (or viva) of the PhD thesis of Jack Jewson, containing novel perspectives on constructing Bayesian inference without likelihood or without complete trust in said likelihood. The thesis aimed at constructing minimum divergence posteriors in an M-open perspective and built a rather coherent framework from principles to implementation. There is a clear link with the earlier work of Bissiri et al. (2016), with further consistency constraints where the outcome must recover the true posterior in the M-closed scenario (if not always the case with the procedures proposed in the thesis).

Although I am partial to the use of empirical likelihoods in setting, I appreciated the position of the thesis and the discussion of the various divergences towards the posterior derivation (already discussed on this blog) , with interesting perspectives on the calibration of the pseudo-posterior à la Bissiri et al. (2016). Among other things, the thesis pointed out a departure from the likelihood principle and some of its most established consequences, like Bayesian additivity. In that regard, there were connections with generative adversarial networks (GANs) and their Bayesian versions that could have been explored. And an impression that the type of Bayesian robustness explored in the thesis has more to do with outliers than with misspecification. Epsilon-contamination amodels re quite specific as it happens, in terms of tails and other things.

The next chapter is somewhat “less” Bayesian in my view as it considers a generalised form of variational inference. I agree that the view of the posterior as a solution to an optimisation is tempting but changing the objective function makes the notion less precise.  Which makes reading it somewhat delicate as it seems to dilute the meaning of both prior and posterior to the point of becoming irrelevant.

The last chapter on change-point models is quite alluring in that it capitalises on the previous developments to analyse a fairly realistic if traditional problem, applied to traffic in London, prior and posterior to the congestion tax. However, there is always an issue with robustness and outliers in that the notion is somewhat vague or informal. Things start clarifying at the end but I find surprising that conjugates are robust optimal solutions since the usual folk theorem from the 80’s is that they are not robust.

the three i’s of poverty

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , on September 15, 2019 by xi'an

Today 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.

noise contrastive estimation

Posted in Statistics with tags , , , , , , , , , on July 15, 2019 by xi'an

As 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 , , , , , on October 4, 2018 by xi'an

This 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 , , , , , , , , , on July 4, 2018 by xi'an

Bayesian workers, unite!

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , on January 19, 2018 by xi'an

This afternoon, Alexander Ly is defending his PhD thesis at the University of Amsterdam. While I cannot attend the event, I want to celebrate the event and a remarkable thesis around the Bayes factor [even though we disagree on its role!] and the Jeffreys’s Amazing Statistics Program (!), otherwise known as JASP. Plus commend the coolest thesis cover I ever saw, made by the JASP graphical designer Viktor Beekman and representing Harold Jeffreys leading empirical science workers in the best tradition of socialist realism! Alexander wrote a post on the JASP blog to describe the thesis, the cover, and his plans for the future. Congratulations!

le soleil de Massilia [jatp]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on December 10, 2017 by xi'an