evidence estimation in finite and infinite mixture models

Adrien Hairault (PhD student at Dauphine), Judith and I just arXived a new paper on evidence estimation for mixtures. This may sound like a well-trodden path that I have repeatedly explored in the past, but methinks that estimating the model evidence doth remain a notoriously difficult task for large sample or many component finite mixtures and even more for “infinite” mixture models corresponding to a Dirichlet process. When considering different Monte Carlo techniques advocated in the past, like Chib’s (1995) method, SMC, or bridge sampling, they exhibit a range of performances, in terms of computing time… One novel (?) approach in the paper is to write Chib’s (1995) identity for partitions rather than parameters as (a) it bypasses the label switching issue (as we already noted in Hurn et al., 2000), another one is to exploit  Geyer (1991-1994) reverse logistic regression technique in the more challenging Dirichlet mixture setting, and yet another one a sequential importance sampling solution à la  Kong et al. (1994), as also noticed by Carvalho et al. (2010). [We did not cover nested sampling as it quickly becomes onerous.]

Applications are numerous. In particular, testing for the number of components in a finite mixture model or against the fit of a finite mixture model for a given dataset has long been and still is an issue of much interest and diverging opinions, albeit yet missing a fully satisfactory resolution. Using a Bayes factor to find the right number of components K in a finite mixture model is known to provide a consistent procedure. We furthermore establish there the consistence of the Bayes factor when comparing a parametric family of finite mixtures against the nonparametric ‘strongly identifiable’ Dirichlet Process Mixture (DPM) model.

Conferenza a Padova [2]

Padova being a reasonably compact (and thoroughly pedestrian/bicycle friendly!) city, it is not hard to find one’s bearing, especially given my visit there last Spring. (The fact that the SIS conference is mostly on the outskirt helps too!) After a wet trek from the station to the hotel, I went to register and attended the “French statistics” invited session, where Jean-Michel Marin talked about our ABC papers. After that, I went to my 7pm appointed visit of the Cappella degli Scrovegni where I admired the superb Giotto frescoes (for my alloted time) and wished I had more time and binoculars!

I finished the day in an osteria with George Casella, who is currently teaching an 8 hour class out of our book Introducing Monte Carlo Methods with R. We managed to eat a failry decent dinner from half-guesses at the menu and, thanks to the Lambrusco, decided to write a third edition of Monte Carlo Statistical Methods ! For one thing, it needs incorporation of latest particle, renewal, and adaptive MCMC developments, as well as a reduction of the chapters on convergence assessment, perfect sampling and reversible jump. (For another, this will make the cheap Chinese printing of the second edition less appealing!)

http://www.osterianfora.it/website/cosa/vini01-07.jpg

Conferenza a Padova

Today and tomorrow, I am attending the annual Italian statistical society meeting. While I appreciate very much the invitation, as well as the opportunity to walk through  Padova and Venezia for a short (and alas rainy!) hour on the way there (leaving home at 8am, walking in Venezia at noon!), I am rather skeptical of the impact of my talk on Bayes factor approximations there, given that the audience will mostly be made of people who had already heard me talk on that topic or seen my poster in Benidorm. Here are the slides anyway.