mini Bayesian nonparametrics in Paris

Today, I attended a “miniworkshop” on Bayesian nonparametrics in Paris (Université René Descartes, now located in an intensely renovated area near the Grands Moulins de Paris), in connection with one of the ANR research grants that support my research, BANHDITS in the present case. Reflecting incidentally that it was the third Monday in a row that I was at a meeting listening to talks (after Hong Kong and Newcastle)… The talks were as follows

9h30 – 10h15 : Dominique Bontemps/Sébastien Gadat
Bayesian point of view on the Shape Invariant Model
10h15 – 11h : Pierpaolo De Blasi
Posterior consistency of nonparametric location-scale mixtures for multivariate density estimation
11h30 – 12h15 : Jean-Bernard Salomond
General posterior contraction rate Theorem in inverse problems.
12h15 – 13h : Eduard Belitser
On lower bounds for posterior consistency (I)
14h30 – 15h15 : Eduard Belitser
On lower bounds for posterior consistency (II)
15h15 – 16h : Judith Rousseau
Posterior concentration rates for empirical Bayes approaches
16h – 16h45 : Elisabeth Gassiat
Nonparametric HMM models

While most talks were focussing on contraction and consistency rates, hence far from my current interests, both talk by Judith and Elisabeth held more appeal to me. Judith gave conditions for an empirical Bayes nonparametric modelling to be consistent, with examples taken from Peter Green’s mixtures of Dirichlet, and Elisabeth concluded with a very generic result on the consistent estimation of a finite hidden Markov model. (Incidentally, the same BANHDITS grant will also support the satellite meeting on Bayesian non-parametric at MCMSki IV on Jan. 09.)

Seminar of philosophy of mathematics

Following in the steps of Andrew last year, I will make a presentation in the seminar of philosophy of mathematics (and statistics!) of Université Paris Diderot, in about two weeks (November 30, 9am/6pm, Université Paris Diderot – Site Rive Gauche, Bâtiment Condorcet 4, rue Elsa Morante, 75013, Paris.). Here is my abstract, the slides will come later:

Classical Bayesian model selection, alternatives and criticisms Christian P. Robert (Université Paris-Dauphine, Institut Universitaire de France and CREST)

I will cover the most orthodox approach to Bayesian model selection, followed by alternatives that have been recently proposed in the literature and by a description of an on-going controversy with phylogeneticists about the nature of testing.

Meaning that I will draw from my recent reading of Aitkin’s book, as well as from the controversy with Templeton.

To philosophy…and back

Today, I went to listen to Andrew Gelman’s views on the philosophy of Bayesian statistics and this gave me a good opportunity for a 22k bike ride!, as the talk took place in the south-eastern part of the city. (I had not been yet to the new campus of Université Paris Diderot called Paris Rive Gauche. It is brand new, in a renovated district around the Grands Moulins de Paris. The place is buzzing with construction work and the Rue Watt I wanted to visit for its association with Léo Mallet is surrounded by cranes and engines.)

Back to philosophy: Andrew unsurprisingly stated he was not one for conventional philosophical perspectives! He thus went on to demonstrate that Bayesian statistics was not an inductive method but truly an hypothetico-deductive meccanism in the right line of Popper and Lakatos. The main criticism about conventional Bayesian thinking was that Bayesian model choice, by using a discrete collection ot models is inappropriate: on the one hand, models (including priors) can be criticised from the inside. On the other hand, a continuous collective is preferable to the standard model averaging found in Bayesian statistics. Obviously, I do not agree with the ideas that you can test your prior based on the data nor with the fact that the requirement of Bayesian testing on alternatives is a drawback [as we also argued in the Molecular Ecology disputing paper]. But, thanks to all its provocative aspects, this was an enjoyable talk and I think that thru it I understood a bit better Popper’s opposition to induction…