## Archive for the University life Category

## à la maison des mathématiciens [Jean Morlet chair, CIRM, Luminy]

Posted in pictures, Travel, University life with tags architecture, CIRM, CNRS, jatp, Jean Morlet Chair, Kerrie Mengersen, Lumi, Luminy campus, maison des chercheurs, Marseille, Total, trail running, triplex, woodpecker on December 6, 2018 by xi'an## noninformative Bayesian prior with a finite support

Posted in Statistics, University life with tags Bayesian nonparametrics, data dependent priors, minimal description length principle, minimaxity, noninformative priors, objective Bayes, PNAS on December 4, 2018 by xi'an**A** few days ago, Pierre Jacob pointed me to a PNAS paper published earlier this year on a form of noninformative Bayesian analysis by Henri Mattingly and coauthors. They consider a prior that “maximizes the mutual information between parameters and predictions”, which sounds very much like José Bernardo’s notion of reference priors. With the rather strange twist of having the prior depending on the data size m even they work under an iid assumption. Here information is defined as the difference between the entropy of the prior and the conditional entropy which is not precisely defined in the paper but looks like the expected [in the data x] Kullback-Leibler divergence between prior and posterior. (I have general issues with the paper in that I often find it hard to read for a lack of precision and of definition of the main notions.)

One highly specific (and puzzling to me) feature of the proposed priors is that they are supported by a finite number of atoms, which reminds me very much of the (minimax) least favourable priors over compact parameter spaces, as for instance in the iconic paper by Casella and Strawderman (1984). For the same mathematical reason that non-constant analytic functions must have separated maxima. This is conducted under the assumption and restriction of a compact parameter space, which must be chosen in most cases. somewhat arbitrarily and not without consequences. I can somehow relate to the notion that a finite support prior translates the limited precision in the estimation brought by a finite sample. In other words, given a sample size of m, there is a maximal precision one can hope for, producing further decimals being silly. Still, the fact that the support of the prior is fixed *a priori*, completely independently of the data, is both unavoidable (for the prior to be *prior*!) and very dependent on the choice of the compact set. I would certainly prefer to see a maximal degree of precision expressed *a posteriori*, meaning that the support would then depend on the data. And handling finite support posteriors is rather awkward in that many notions like confidence intervals do not make much sense in that setup. (Similarly, one could argue that Bayesian non-parametric procedures lead to estimates with a finite number of support points but these are determined based on the data, not *a priori*.)

Interestingly, the derivation of the “optimal” prior is operated by iterations where the next prior is the renormalised version of the current prior times the exponentiated Kullback-Leibler divergence, which is “guaranteed to converge to the global maximum” for a discretised parameter space. The authors acknowledge that the resolution is poorly suited to multidimensional settings and hence to complex models, and indeed the paper only covers a few toy examples of moderate and even humble dimensions.

Another difficulty with the paper is the absence of temporal consistency: since the prior depends on the sample size, the posterior for n i.i.d. observations is no longer the prior for the (n+1)th observation.

“Because it weights the irrelevant parameter volume, the Jeffreys prior has strong dependence on microscopic effects invisible to experiment”

I simply do not understand the above sentence that apparently counts as a criticism of Jeffreys (1939). And would appreciate anyone enlightening me! The paper goes into comparing priors through Bayes factors, which ignores the main difficulty of an automated solution such as Jeffreys priors in its inability to handle infinite parameter spaces by being almost invariably improper.

## graphe, graphons, graphez !

Posted in Books, pictures, Statistics, University life with tags graphs, Institut Henri Poincaré, mathematical statistics, Paris, phase transition, SFDS, variational Bayes methods on December 3, 2018 by xi'an## a la casa matemática de Oaxaca [reminiscence]

Posted in Mountains, Running, Travel, University life with tags Banff, Banff International Research Station, Casa Matemática Oaxaca, Highlands, Hotel los Laureles, Mexico, Oaxaca, Oaxaca gastronomia, San Sebastian de Tutla, stray dogs, Unesco World Heritage List on December 2, 2018 by xi'an **A**s this was my very first trip to the CMO part of CMO-BIRS, as opposed to many visits to BIRS, Banff, here are my impressions about this other mathematical haven, aka resort, aka retreat… First definitely a very loooong trip from Paris (especially when sitting next to three drunk women speaking loudly the whole trip, thankfully incomprehensibly in Russian!), with few connections between Mexico City [airport] and Oaxaca, adding [for me] a five and a half hour stay over in the airport, where I experimented for the first time a coffin-like “sleep pod” hostel and some welcome rest. But presumably an easier access compared with Calgary for mathematicians from the South and East of the USA. And obviously for those Central and from South Americas.Then, contrary to Banff, the place for the Casa Matemàtica Oaxaca is for the time being essentially a permanently booked hotel, rather than a dedicated conference centre. Facilities are thus less attuned to visiting mathematicians, like missing real desks in bedrooms or working rooms. Still a nice with a very peaceful inner yard (and too small a pool to consider swimming). Actually facilitating interactions when compared with Banff: blackboards in the patios, tables outside, general quiet atmosphere (except for the endlessly barking dogs in the neighbourhood). Of course the huge difference in the weathers between both places does matter. Paradoxically (given the size of Oaxaca City), CMO is more isolated than BIRS, where downtown is a mere five minute walks, even in the middle of winter. Except for the occasional blizzard. But Oaxaca offers a fabulous food scene worth the longer trip!As for outdoors, there is also a swimming pool (Cina). And back streets to run on, even though the presence of stray dogs in about every road making running broken and haphazard (never run by a dog!, which is my rule since a tiny but angry dog bit my ankle in Caracas!). Running splits up hill a few times every morning was great training! There is furthermore the possibility of sport climbing in nearby San Sebastian de Tutla, as I experienced with Aventours, a local guiding company. And bouldering in an even closer gym.

## French Econometrics [discussion]

Posted in Books, pictures, Statistics, University life with tags 10th French Econometrics Conference, architecture, econometrics, empirical likelihood, France, moments, Paris, Paris School of Economics on November 30, 2018 by xi'an**T**his Friday, I am briefly taking part in the 10th French Econometrics Conference as a discussant of Anna Simoni’s (CREST) talk, based on a paper co-written with Sid Chib and Minchul Shin. The conference is located at the Paris School of Economics (PSE), on Paris South End, in an impressive new building. The topic of the paper is a Bayesian empirical likelihood approach to the econometrics notion of moments model. Which I discussed here during ISBA last summer since Sid spoke (twice!) there.