**T**he workshop started by the bad news of our friend Michele Guindani being hit and mugged upon arrival in Oaxaca, Saturday night. Fortunately, he was not hurt, but lost both phone and wallet, always a major bummer when abroad… Still this did not cast a lasting pall on the gathering of long-time no-see friends, whom I had indeed not seen for at least two years. Except for those who came to the CIRMirror!

A few hours later, we got woken up by fairly loud firecrackers (palomas? cohetes?) at 5am, for no reason I can fathom (the Mexican Revolution day was a week ago) although it seemed correlated with the nearby church bells going on at full blast (for Lauds? Hanukkah? Cyber Monday? Chirac’s birthdate?). The above picture was taken the Santa María del Tule town with its super-massive Montezuma cypress tree, with remaining decorations from the Día de los Muertos.

Without launching (much) the debate on whether or not Bayesian non-parametrics qualified as “objective Bayesian” methods, Igor Prünster started the day with a non-parametric presentation of dependent random probability measures. With the always fascinating notion that a random discrete non-parametric prior is inducing a distribution on the partitions (EPPF). And applicability in mixtures and their generalisations. Realising that the highly discrete nature of such measures is not such an issue for a given sample size n, since there are at most n elements in the partition. Beatrice Franzolini discussed of specific ways to create dependent distributions based on independent samples, although her practical example based on one N(-10,1) sample and another (independently) N(10,1) sample seemed to fit in several of the dependent random measures she compared. And Marta Catalano (Warwick) presented her work on partial exchangeability and optimal transportation (which I had also heard in CIRM last June and in Warwick last week). One thing I had not realised earlier was the dependence of the Wasserstein distance on the parameterisation, although it now makes perfect sense. If only for the coupling. I had alas to miss Isadora Antoniano-Villalobos’ talk as I had to teach my undergrad class in Paris Dauphine at the same time… This non-parametric session was quite homogeneous and rich in perspectives.

In an all-MCMC afternoon, Julyan Arbel talked about reference priors for extreme value distributions, with the “shocking” case of a restriction on the support of one parameter, ξ. Which means in fact that the Jeffreys prior is then undefined. This reminded me somewhat of the work of Clara Grazian on Jeffreys priors for mixtures, where some models were not allowing for Fisher information to exist. The second part of this talk was about modified local versions of Gelman & Rubin (1992) R hats. And the recent modification proposed by Aki and co-authors. Where I thought that a simplification of the multivariate challenge of defining ranks could be alleviated by considering directly the likelihood values of the chains. And Trevor Campbell gradually built an involved parallel tempering method where the powers of a geometric mixture are optimised as spline functions of the temperature. Next, María Gil-Leyva presented her original and ordered approach to mixture estimation, which I discussed in a blog published two days ago (!). She corrected my impressions that (i) the methods were all impervious to label switching and (ii) required some conjugacy to operate. The final talk of the day was by Anirban Bhattacharya on high-D Bayesian regression and coupling techniques for checking convergence, a paper that had been on my reading list for a long while. A very elaborate construct of coupling strategies within a Gibbs sampler, with some steps relying on optimal coupling and others on the use of common random generators.