21w5107 [day 1]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on November 30, 2021 by xi'an

The 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.

de la Sierra Norte de Oaxaca [jatp]

Posted in Mountains, pictures, Travel with tags , , , , , , , , on November 29, 2021 by xi'an

ordered allocation sampler

Posted in Books, Statistics with tags , , , , , , , , , , , on November 29, 2021 by xi'an

Recently, Pierpaolo De Blasi and María Gil-Leyva arXived a proposal for a novel Gibbs sampler for mixture models. In both finite and infinite mixture models. In connection with Pitman (1996) theory of species sampling and with interesting features in terms of removing the vexing label switching features.

The key idea is to work with the mixture components in the random order of appearance in an exchangeable sequence from the mixing distribution (…) In accordance with the order of appearance, we derive a new Gibbs sampling algorithm that we name the ordered allocation sampler. “

This central idea is thus a reinterpretation of the mixture model as the marginal of the component model when its parameter is distributed as a species sampling variate. An ensuing marginal algorithm is to integrate out the weights and the allocation variables to only consider the non-empty component parameters and the partition function, which are label invariant. Which reminded me of the proposal we made in our 2000 JASA paper with Gilles Celeux and Merrilee Hurn (one of my favourite papers!). And of the [first paper in Statistical Methodology] 2004 partitioned importance sampling version with George Casella and Marty Wells. As in the later, the solution seems to require the prior on the component parameters to be conjugate (as I do not see a way to produce an unbiased estimator of the partition allocation probabilities).

The ordered allocation sample considers the posterior distribution of the different object made of the parameters and of the sequence of allocations to the components for the sample written in a given order, ie y¹,y², &tc. Hence y¹ always gets associated with component 1, y² with either component 1 or component 2, and so on. For this distribution, the full conditionals are available, incl. the full posterior on the number m of components, only depending on the data through the partition sizes and the number m⁺ of non-empty components. (Which relates to the debate as to whether or not m is estimable…) This sequential allocation reminded me as well of an earlier 2007 JRSS paper by Nicolas Chopin. Albeit using particles rather than Gibbs and applied to a hidden Markov model. Funny enough, their synthetic dataset univ4 almost resembles the Galaxy dataset (as in the above picture of mine)!

San Jeronimo Tlacochahuaya [jatp]

Posted in pictures, Travel with tags , , , , , , on November 28, 2021 by xi'an

snapshot from Mitla, Oaxacan

Posted in Mountains, pictures, Travel with tags , , , , , , , , , on November 28, 2021 by xi'an

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