21w5107 [day 2]

After a rich and local (if freezing) dinner on a rooftop facing the baroque Oaxaca cathedral, and an early invigorating outdoor swim in my case!, the morning session was mostly on mixtures, with Helen Ogden exploring X validation for (estimating the number k of components for) finite mixtures, when using the likelihood as an objective function. I was unclear of the goal however when considering that the data supporting the study was Uniform (0,1), nothing like a mixture of Normal distributions. And about the consistency attached to the objective function. The session ended with Diana Cai presenting a counter-argument in the sense that she proved, along with Trevor Campbell and Tamara Broderick, that the posterior on k diverges to infinity with the number n of observations if a mixture model is misspecified for said data. Which does not come as a major surprise since there is no properly defined value of k when the data is not generated from the adopted mixture. I would love to see an extension to the case when the k component mixture contains a non-parametric component! In-between, Alexander Ly discussed Bayes factors for multiple datasets, with some asymptotics showing consistency for some (improper!) priors if one sample size grows to infinity. With actually attaining the same rate under both hypotheses. Luis Nieto-Barajas presented an approach on uncertainty assessment through KL divergence for random probability measures, which requires a calibration of the KL in this setting, as KL does not enjoy a uniform scale, and a prior on a Pólya tree. And Chris Holmes presented a recent work with Edwin Fong and Steven Walker on a prediction approach to Bayesian inference. Which I had had on my reading list for a while. It is a very original proposal where likelihoods and priors are replaced by the sequence of posterior predictives and only parameters of interest get simulated. The Bayesian flavour of the approach is delicate to assess though, albeit a form of non-parametric Bayesian perspective… (I still need to read the paper carefully.)

In the afternoon session, Judith Rousseau presented her recent foray in cut posteriors for semi-parametric HMMs. With interesting outcomes for efficiently estimating the transition matrix, the component distributions, and the smoothing distribution. I wonder at the connection with safe Bayes in that cut posteriors induce a loss of information. Sinead Williamson spoke on distributed MCMC for BNP. Going back at the “theme of the day”, namely clustering and finding the correct (?) number of clusters. With a collapsed versus uncollapsed division that reminded me of the marginal vs. conditional María Gil-Leyva discussed yesterday. Plus a decomposition of a random measure into a finite mixture and an infinite one that also reminded me of the morning talk of Diana Cai. (And making me wonder at the choice of the number K of terms in the finite part.) Michele Guindani spoke about clustering distributions (with firecrackers as a background!). Using the nDP mixture model, which was show to suffer from degeneracy (as discussed by Frederico Camerlenghi et al. in BA). The subtle difference stands in using the same (common) atoms in all random distributions at the top of the hierarchy, with independent weights. Making the partitions partially exchangeable. The approach relies on Sylvia’s generalised mixtures of finite mixtures. With interesting applications to microbiome and calcium imaging (including a mice brain in action!). And Giovanni Rebaudo presented a generalised notion of clustering aligned on a graph, with some observations located between the nodes corresponding to clusters. Represented as a random measure with common parameters for the clusters and separated parameters outside. Interestingly playing on random partitions, Pólya urns, and species sampling.

the mysterious disappearance of the Leiden statistics group

I was forwarded an article from Mare, the journal of the University of Leiden (Universiteit Leiden), a weekly newspaper written by an independent team of professional journalists. Entitled “Fraude, verdwenen evaluaties en een verziekt klimaat: hoe de beste statistiekgroep van Nederland uiteenviel” (Fraud, lost evaluations and a sickening climate: how the best statistics group in the Netherlands fell apart), it tells (through Google translate) the appalling story of how an investigation on mishandled student course evaluations led to the disintegration of the World-renowned Leiden statistics group,  with the departure of a large fraction of its members, including its head, Aad van der Vaart, a giant in mathematical statistics, author of deep, reference, books like Asymptotic Statistics and  Fundamentals of Nonparametric Bayesian Inference, an ERC advanced grant recipient, and now professor at TU Delft… While I am not at all acquainted with the specifics, reading the article makes the chain of events sound like chaos propagation, when the suspicious disappearance of student evaluation forms about a statistics course leads to a re-evaluation round, itself put under scrutiny by the University, then to a recruitment freeze of prospective statistician appointments by the (pure math) successor of Aad, as well as increasing harassment of the statisticians in the  Mathematisch Instituut, and eventually to the exile of most of them. Wat een verspilling!

ABC webinar, first!

The première of the ABC World Seminar last Thursday was most successful! It took place at the scheduled time, with no technical interruption and allowed 130⁺ participants from most of the World [sorry, West Coast friends!] to listen to the first speaker, Dennis Prangle,  presenting normalising flows and distilled importance sampling. And to answer questions. As I had already commented on the earlier version of his paper, I will not reproduce them here. In short, I remain uncertain, albeit not skeptical, about the notions of normalising flows and variational encoders for estimating densities, when perceived as a non-parametric estimator due to the large number of parameters it involves and wonder at the availability of convergence rates. Incidentally, I had forgotten at the remarkable link between KL distance & importance sampling variability. Adding to the to-read list Müller et al. (2018) on neural importance sampling.

Judith’s colloquium at Warwick

the most important statistical ideas of the past 50 years

Aki and Andrew are celebrating the New Year in advance by composing a list of the most important statistics ideas occurring (roughly) since they were born (or since Fisher died)! Like

• substitution of computing for mathematical analysis (incl. bootstrap)
• fitting a model with a large number of parameters, using some regularization procedure to get stable estimates and good predictions (e.g., Gaussian processes, neural networks, generative adversarial networks, variational autoencoders)
• multilevel or hierarchical modelling (incl. Bayesian inference)
• advances in statistical algorithms for efficient computing (with a long list of innovations since 1970, including ABC!), pointing out that a large fraction was of the  divide & conquer flavour (in connection with large—if not necessarily Big—data)
• statistical decision analysis (e.g., Bayesian optimization and reinforcement learning, getting beyond classical experimental design )
• robustness (under partial specification, misspecification or in the M-open world)
• EDA à la Tukey and statistical graphics (and R!)
• causal inference (via counterfactuals)

Now, had I been painfully arm-bent into coming up with such a list, it would have certainly been shorter, for lack of opinion about some of these directions (even the Biometrika deputeditoship has certainly helped in reassessing the popularity of different branches!), and I would have have presumably been biased towards Bayes as well as more mathematical flavours. Hence objecting to the witty comment that “theoretical statistics is the theory of applied statistics”(p.10) and including Ghosal and van der Vaart (2017) as a major reference. Also bemoaning the lack of long-term structure and theoretical support of a branch of the machine-learning literature.

Maybe also more space and analysis could have been spent on “debates remain regarding appropriate use and interpretation of statistical methods” (p.11) in that a major difficulty with the latest in data science is not so much the method(s) as the data on which they are based, which in a large fraction of the cases, is not representative and is poorly if at all corrected for this bias. The “replication crisis” is thus only one (tiny) aspect of the challenge.