ABC-SAEM

In connection with the recent PhD thesis defence of Juliette Chevallier, in which I took a somewhat virtual part for being physically in Warwick, I read a paper she wrote with Stéphanie Allassonnière on stochastic approximation versions of the EM algorithm. Computing the MAP estimator can be done via some adapted for simulated annealing versions of EM, possibly using MCMC as for instance in the Monolix software and its MCMC-SAEM algorithm. Where SA stands sometimes for stochastic approximation and sometimes for simulated annealing, originally developed by Gilles Celeux and Jean Diebolt, then reframed by Marc Lavielle and Eric Moulines [friends and coauthors]. With an MCMC step because the simulation of the latent variables involves an untractable normalising constant. (Contrary to this paper, Umberto Picchini and Adeline Samson proposed in 2015 a genuine ABC version of this approach, paper that I thought I missed—although I now remember discussing it with Adeline at JSM in Seattle—, ABC is used as a substitute for the conditional distribution of the latent variables given data and parameter. To be used as a substitute for the Q step of the (SA)EM algorithm. One more approximation step and one more simulation step and we would reach a form of ABC-Gibbs!) In this version, there are very few assumptions made on the approximation sequence, except that it converges with the iteration index to the true distribution (for a fixed observed sample) if convergence of ABC-SAEM is to happen. The paper takes as an illustrative sequence a collection of tempered versions of the true conditionals, but this is quite formal as I cannot fathom a feasible simulation from the tempered version and not from the untempered one. It is thus much more a version of tempered SAEM than truly connected with ABC (although a genuine ABC-EM version could be envisioned).

Bangalore workshop [ಬೆಂಗಳೂರು ಕಾರ್ಯಾಗಾರ] and new book

On the last day of the IFCAM workshop in Bangalore, Marc Lavielle from INRIA presented a talk on mixed effects where he illustrated his original computer language Monolix. And mentioned that his CRC Press book on Mixed Effects Models for the Population Approach was out! (Appropriately listed as out on a 14th of July on amazon!) He actually demonstrated the abilities of Monolix live and on diabets data provided by an earlier speaker from Kolkata, which was a perfect way to start initiating a collaboration! Nice cover (which is all I saw from the book at this stage!) that maybe will induce candidates to write a review for CHANCE. Estimation of those mixed effect models relies on stochastic EM algorithms developed by Marc Lavielle and Éric Moulines in the 90’s, as well as MCMC methods.

finite mixture models [book review]

Here is a review of Finite Mixture Models (2000) by Geoff McLachlan & David Peel that I wrote aeons ago (circa 1999), supposedly for JASA, which lost first the files and second the will to publish it. As I was working with my student today, I mentioned the book to her and decided to publish it here, if only because I think the book deserved a positive review, even after all those years! (Since then, Sylvia Frühwirth-Schnatter published Finite Mixture and Markov Switching Models (2004), which is closer to my perspective on the topic and that I would more naturally recommend.)

Mixture modeling, that is, the use of weighted sums of standard distributions as in

is a widespread and increasingly used technique to overcome the rigidity of standard parametric distributions such as f(y;θ), while retaining a parametric nature, as exposed in the introduction of my JASA review to Böhning’s (1998) book on non-parametric mixture estimation (Robert, 2000). This review pointed out that, while there are many books available on the topic of mixture estimation, the unsurpassed reference remained the book by Titterington, Smith and Makov (1985)  [hereafter TSM]. I also suggested that a new edition of TSM would be quite timely, given the methodological and computational advances that took place in the past 15 years: while it remains unclear whether or not this new edition will ever take place, the book by McLachlan and Peel gives an enjoyable and fairly exhaustive update on the topic, incorporating the most recent advances on mixtures and some related models.

Geoff McLachlan has been a major actor in the field for at least 25 years, through papers, software—the book concludes with a review of existing software—and books: McLachlan (1992), McLachlan and Basford (1988), and McLachlan and Krishnan (1997). I refer the reader to Lindsay (1989) for a review of the second book, which is a forerunner of, and has much in common with, the present book.