Next week, Rémi Bardenet is giving a seminar in Paris, Thursday April 14, 2pm, in ENSAE [room 15] on MCMC methods for tall data. Unfortunately, I will miss this opportunity to discuss with Rémi as I will be heading to La Sapienza, Roma, for Clara Grazian‘s PhD defence the next day. And on Monday afternoon, April 11, Nicolas Chopin will give a talk on quasi-Monte Carlo for sequential problems at Institut Henri Poincaré.
Archive for seminar
Next week, I will be in Harvard Monday and Tuesday, visiting friends in the Department of Statistics and giving a seminar. The slides for the talk will be quite similar to those of my talk in Bristol, a few weeks ago. Hopefully, there will not be too much overlap between both audiences! And hopefully I’ll manage to get to my conclusion before all hell breaks loose (which is why I strategically set my conclusion in the early slides!)
Yoav Benjamini will give a seminar talk in Paris next Monday on the above (full title: “The replicability crisis in science: It’s the selection’s fault not the p-values’“). (That I will miss for being in Warwick at the time.) With a fairly terse abstract:
I shall discuss the problem of lack of replicability of results in science, and point at selective inference as a statistical root cause. I shall then present a few strategies for addressing selective inference, and their application in genomics, brain research and earlier phases of clinical trials where both primary and secondary endpoints are being used.
Details: February 8, 2016, 16h, Université Pierre & Marie Curie, campus Jussieu, salle 15-16-101.
I went to give a seminar in Bristol last Friday and I chose to present the testing with mixture paper. As we are busy working on the revision, I was eagerly looking for comments and criticisms that could strengthen this new version. As it happened, the (Bristol) Bayesian Cake (Reading) Club had chosen our paper for discussion, two weeks in a row!, hence the title!, and I got invited to join the group the morning prior to the seminar! This was, of course, most enjoyable and relaxed, including an home-made cake!, but also quite helpful in assessing our arguments in the paper. One point of contention or at least of discussion was the common parametrisation between the components of the mixture. Although all parametrisations are equivalent from a single component point of view, I can [almost] see why using a mixture with the same parameter value on all components may impose some unsuspected constraint on that parameter. Even when the parameter is the same moment for both components. This still sounds like a minor counterpoint in that the weight should converge to either zero or one and hence eventually favour the posterior on the parameter corresponding to the “true” model.
Another point that was raised during the discussion is the behaviour of the method under misspecification or for an M-open framework: when neither model is correct does the weight still converge to the boundary associated with the closest model (as I believe) or does a convexity argument produce a non-zero weight as it limit (as hinted by one example in the paper)? I had thought very little about this and hence had just as little to argue though as this does not sound to me like the primary reason for conducting tests. Especially in a Bayesian framework. If one is uncertain about both models to be compared, one should have an alternative at the ready! Or use a non-parametric version, which is a direction we need to explore deeper before deciding it is coherent and convergent!
A third point of discussion was my argument that mixtures allow us to rely on the same parameter and hence the same prior, whether proper or not, while Bayes factors are less clearly open to this interpretation. This was not uniformly accepted!
Thinking afresh about this approach also led me to broaden my perspective on the use of the posterior distribution of the weight(s) α: while previously I had taken those weights mostly as a proxy to the posterior probabilities, to be calibrated by pseudo-data experiments, as for instance in Figure 9, I now perceive them primarily as the portion of the data in agreement with the corresponding model [or hypothesis] and more importantly as a solution for staying away from a Neyman-Pearson-like decision. Or error evaluation. Usually, when asked about the interpretation of the output, my answer is to compare the behaviour of the posterior on the weight(s) with a posterior associated with a sample from each model. Which does sound somewhat similar to posterior predictives if the samples are simulated from the associated predictives. But the issue was not raised during the visit to Bristol, which possibly reflects on how unfrequentist the audience was [the Statistics group is], as it apparently accepted with no further ado the use of a posterior distribution as a soft assessment of the comparative fits of the different models. If not necessarily agreeing the need of conducting hypothesis testing (especially in the case of the Pima Indian dataset!).
On Friday, I give a talk in München on ABC model choice. At the Max-Planck Institute for Astrophysics. As coincidence go, I happen to talk the week after John Skilling gave a seminar there. On Bayesian tomography, not on nested sampling. And the conference organisers put the cover of the book Think Bayes: Bayesian Statistics Made Simple, written by Allen Downey, a book I reviewed yesterday night for CHANCE (soon to appear on the ‘Og!) [not that I understand the connection with the Max-Planck Institute or with my talk!, warum nicht?!] The slides are the same as in Oxford for SPA 2015:
Today was the final session of our Reading Classics Seminar for the academic year 2014-2015. I have not reported on this seminar much so far because it has had starting problems, namely hardly any student present on the first classes and therefore several re-starts until we reached a small group of interested students. And this is truly The End for this enjoyable experiment as this is the final year for my TSI Master at Paris-Dauphine, as it will become integrated within the new MASH Master next year.
As a last presentation for the entire series, my student picked John Skilling’s Nested Sampling, not that it was in my list of “classics”, but he had worked on the paper in a summer project and was thus reasonably fluent with the topic. As he did a good enough job (!), here are his slides.
Some of the questions that came to me during the talk were on how to run nested sampling sequentially, both in the data and in the number of simulated points, and on incorporating more deterministic moves in order to remove some of the Monte Carlo variability. I was about to ask about (!) the Hamiltonian version of nested sampling but then he mentioned his last summer internship on this very topic! I also realised during that talk that the formula (for positive random variables)
does not require absolute continuity of the distribution F.
Today was the second session of our Reading Classics Seminar for the academic year 2014-2015. I have not reported on this seminar so far because it has had starting problems, namely hardly any student present on the first classes and therefore several re-starts until we reach a small group of interested students. Actually, this is the final year for my TSI Master at Paris-Dauphine, as it will become integrated within the new MASH Master next year. The latter started this year and drew away half of our potential applicants, presumably because of the wider spectrum between machine-learning, optimisation, programming and a tiny bit of statistics… If we manage to salvage [within the new Master] our speciality of offering the only Bayesian Statistics training in France, this will not be a complete disaster!
Anyway, the first seminar was about the great 1939 Biometrika paper by Pitman about the best invariant estimator appearing magically as a Bayes estimator! Alas, the student did not grasp the invariance part and hence focussed on less relevant technical parts, which was not a great experience (and therefore led me to abstain from posting the slides here). The second paper was not on my list but was proposed by another student as of yesterday when he realised he was to present today! This paper, entitled “The Counter-intuitive Non-informative Prior for the Bernoulli Family”, was published in the Journal of Statistics Education in 2004 by Zu and Liu, I had not heard of the paper (or of the journal) previously and I do not think it is worth advertising any further as it gives a very poor entry to non-informative priors in the simplest of settings, namely for Bernoulli B(p) observations. Indeed, the stance of the paper is to define a non-informative prior as one returning the MLE of p as its posterior expectation (missing altogether the facts that such a definition is parameterisation-invariant and that, given the modal nature of the MLE, a posterior mode would be much more appropriate, leading to the uniform prior of p as a solution) and that the corresponding prior was made of two Dirac masses at 0 and 1! Which again misses several key points like defining properly convergence in a space of probability distributions and using an improper prior differently from a proper prior. Esp. since in the next section, the authors switch to Haldane’s prior being the Be(0,0) distribution..! A prior that cannot be used since the posterior is not defined when all the observations are identical. Certainly not a paper to make it to the list! (My student simply pasted pages from this paper as his slides and so I see again no point in reposting them here. )