**N**ext month, I am taking part in a workshop on sampling & clustering at the Max-Planck-Institut für Physik in Garching, Germany (near München). By giving a three hour introduction to ABC, as I did three years ago in Autrans. Being there and talking with local researchers if the sanitary conditions allow. From my office otherwise. Other speakers include Michael Betancourt on HMC and Johannes Buchner on nested sampling. The remote participation to this MPI workshop is both open and free, **but participants must register before 18 September, namely tomorrow.**

## Archive for clustering

## state of the art in sampling & clustering [workshop]

Posted in Books, pictures, Statistics, Travel, University life with tags Autrans, clustering, Garching, Germany, HMC, Max Planck Institute, Max-Planck-Institut für Physik, München, nested sampling, sampling, workshop on September 17, 2020 by xi'an## ravencry [book review]

Posted in Books, Kids, Travel with tags Blackwing, book review, clustering, fantasy, grimdark, John Snow, Ravencry, religious cult, the raven's mark trilogy on November 2, 2019 by xi'an**A**fter enjoying Ed McDonald’s Blackwing this summer, I ordered the second volume, Ravencry, which I read in a couple of days between Warwick and Edinburgh.

“Valya had marked all of the impact sites, then numbered them according to the night they had struck. The first night was more widely distributed, the second slightly more clustered. As the nights passed, the clusters drew together with fewer and fewer outliers.”

Since this is a sequel, the fantasy universe in which the story takes place has not changed much, but gains in consistence and depth. Especially the wastelands created by the wizard controlling the central character. The characters are mostly the same, with the same limited ethics for the surviving ones!, albeit with unexpected twists (no spoiler!), with the perils of a second volume, namely the sudden occurrence of a completely new and obviously deadly threat to the entire world, mostly avoided by connecting quite closely with the first volume. Even the arch-exploited theme of a new religious cult fits rather nicely the new plot. Despite of the urgency of the menace (as usual) to their world, the core characters do not do much in the first part of the book, engaged in a kind of detective work that is rather unusual for fantasy books, but the second part sees a lot of both action and explanation, which is why it became a page-turner for me. And while there are much less allusions to magical mathematics in this volume, a John Snow moment occurs near the above quote.

## MHC2020

Posted in pictures, Statistics, Travel, University life with tags clustering, conference, France, French Alps, hidden Markov models, Institut de Mathématique d'Orsay, mixtures of distributions, Orsay, Paris suburbs, Savoie, Yvette on October 15, 2019 by xi'an**T**here is a conference on mixtures (M) and hidden Markov models (H) and clustering (C) taking place in Orsay on June 17-19, next year. Registration is free if compulsory. With about twenty confirmed speakers. (Irrelevant as the following remark is, this is the opportunity to recall the conference on mixtures I organised in Aussois 25 years before! Which website is amazingly still alive at Duke, thanks to Mike West, my co-organiser along with Kathryn Roeder and Gilles Celeux. When checking the abstracts, I found only two presenters common to both conferences, Christophe Biernaki and Jiahua Chen. And alas several names of departed friends.)

## from here to infinity

Posted in Books, Statistics, Travel with tags Bayesian inference, classification, Clermont-Ferrand, clustering, Dirichlet process mixture, From Here to Infinity, hyperparameter, Ian Stewart, label switching, mixtures of distributions, prior distributions, sparse finite mixtures, University of Warwick, Vienna on September 30, 2019 by xi'an

“Introducing a sparsity prior avoids overfitting the number of clusters not only for finite mixtures, but also (somewhat unexpectedly) for Dirichlet process mixtures which are known to overfit the number of clusters.”

**O**n my way back from Clermont-Ferrand, in an old train that reminded me of my previous ride on that line that took place in… 1975!, I read a fairly interesting paper published in Advances in Data Analysis and Classification by [my Viennese friends] Sylvia Früwirth-Schnatter and Gertrud Malsiner-Walli, where they describe how sparse finite mixtures and Dirichlet process mixtures can achieve similar results when clustering a given dataset. Provided the hyperparameters in both approaches are calibrated accordingly. In both cases these hyperparameters (scale of the Dirichlet process mixture versus scale of the Dirichlet prior on the weights) are endowed with Gamma priors, both depending on the number of components in the finite mixture. Another interesting feature of the paper is to witness how close the related MCMC algorithms are when exploiting the stick-breaking representation of the Dirichlet process mixture. With a resolution of the label switching difficulties via a point process representation and k-mean clustering in the parameter space. *[The title of the paper is inspired from Ian Stewart’s book.]*

## latent nested nonparametric priors

Posted in Books, Statistics with tags Bayesian Analysis, Bayesian non-parametrics, clustering, completely random measures, Dirichlet mixture priors, discussion paper, hierarchical Bayesian modelling, iris data on September 23, 2019 by xi'an**A** paper on an extended type of non-parametric priors by Camerlenghi et al. [all good friends!] is about to appear in Bayesian Analysis, with a discussion open for contributions (**until October 15**). While a fairly theoretical piece of work, it validates a Bayesian approach for non-parametric clustering of separate populations with, broadly speaking, common clusters. More formally, it constructs a new family of models that allows for a partial or complete equality between two probability measures, but does not force full identity when the associated samples do share some common observations. Indeed, the more traditional structures prohibit one or the other, from the Dirichlet process (DP) prohibiting two probability measure realisations from being equal or partly equal to some hierarchical DP (HDP) already allowing for common atoms across measure realisations, but prohibiting complete identity between two realised distributions, to nested DP offering one extra level of randomness, but with an infinity of DP realisations that prohibits common atomic support besides completely identical support (and hence distribution).

The current paper imagines *two* realisations of random measures written as a sum of a common random measure and of one of two separate almost independent random measures: (14) is the core formula of the paper that allows for partial or total equality. An extension to a setting larger than facing *two* samples seems complicated if only because of the number of common measures one has to introduce, from the totally common measure to measures that are only shared by a subset of the samples. Except in the simplified framework when a single and universally common measure is adopted (with enough justification). The randomness of the model is handled via different completely random measures that involved something like four degrees of hierarchy in the Bayesian model.

Since the example is somewhat central to the paper, the case of one or rather two two-component Normal mixtures with a common component (but with different mixture weights) is handled by the approach, although it seems that it was already covered by HDP. Having exactly the same term (i.e., with the very same weight) is not, but this may be less interesting in real life applications. Note that alternative & easily constructed & parametric constructs are already available in this specific case, involving a limited prior input and a lighter computational burden, although the Gibbs sampler behind the model proves extremely simple on the paper. (One may wonder at the robustness of the sampler once the case of identical distributions is visited.)

Due to the combinatoric explosion associated with a higher number of observed samples, despite obvious practical situations, one may wonder at any feasible (and possibly sequential) extension, that would further keep a coherence under marginalisation (in the number of samples). And also whether or not multiple testing could be coherently envisioned in this setting, for instance when handling all hospitals in the UK. Another consistency question covers the Bayes factor used to assess whether the two distributions behind the samples are or not identical. (One may wonder at the importance of the question, hopefully applied to more relevant dataset than the Iris data!)