Introduction à Monte Carlo en R

Following a proposal by Springer-Verlag Paris, I have decided to translate Introducing Monte Carlo Methods with R with George Casella into French, since a new collection of R books (in French) is planed for the Spring of 2010. The translation will a priori be done by Joachim Robert and Robin Ryder, under my supervision and with the support of Springer-Verlag Paris. I have already translated the first chapter as I needed to cut most of the R coverage, since this collection assumes a prior knowledge of R and aims at a smaller number of pages (around 200) to keep the price as low as possible.

Monte Carlo Statistical Methods

Yesterday, I started my annual course on Monte Carlo Statistical Method, open to the last year Master students in Paris Dauphine. This is a seven week course covering the first half and then more of the book Monte Carlo Statistical Method, with George Casella. Here are the (yes, 584) slides

These slides have not changed from last year (no time and no need to!) but this year I have distributed a preliminary copy of Introducing Monte Carlo Methods with R to the students so that they can practice Monte Carlo methods, spot typos in the book (only 10 cents per typo because I have no prior about the number of typos!), and write the(ir) solutions to the exercises as homework.

Postdoc in Denmark

I just received the following email for a two year postodc offer in Lyngby, Denmark:

The Technical University of Denmark (DTU) has a dynamic and active group in Statistics, with a number of researchers concentrating on probabilistic forecasting and renewable energy applications. Focus is given to applied research, but also to new methodological developments. Owing to interesting recent results on spatio-temporal modeling of forecast error fields, we have decided to open a post-doc position for a duration of 2 years, which will mainly relate to that area of  research.

ABC in 1984

“Bayesian statistics and Monte Carlo methods are ideally suited to the task of passing many models over one dataset” D. Rubin, Annals of Statistics, 1984

Jean-Louis Foulley sent me a 1984 paper by Don Rubin that details in no uncertain terms the accept-reject algorithm at the core of the ABC algorithm! Namely,

Generate ;
Generate ;
Accept if

Obviously, ABC goes further by replacing the acceptance step with the tolerance condition

but this early occurence is worth noticing nonetheless. It is also interesting to see that Don Rubin does not promote this simulation method in situations where the likelihood is not available but rather as an intuitive way to understanding posterior distributions from a frequentist perspective, because ’s from the posterior are those that could have generated the observed data. (The issue of the zero probability of the exact equality between simulated and observed data is not dealt with in the paper, maybe because the notion of a “match” between simulated and observed data is not clearly defined.) Apart from this historical connection, I recommend the entire paper as providing a very compelling argument for practical Bayesianism!

Adaptive Metropolis

There have been several arXived entries on adaptive MCM on the past days. One is an adaptive extension to the recent Read Paper by Christophe Andrieu, Arnaud Doucet and Roman Holenstein, Particle Markov chain Monte Carlo where Silva, Giordani, Kohn and Pitt manage to use an adapted mixture of normals as their proposal within non-linear state-space models. They also obtain unbiased estimators of the likelihood, which may have an appeal in ABC settings! To see this extension appearing a few weeks after the original paper is amazing as well. A second paper by Matti Vihola considers the impact of removing the stabilising term in the Haario-Saaksman-Tamminen original paper

on the convergence of the corresponding adaptative Metropolis algorithm. The change is in using instead a stochastic approximation update

where decreases to zero at a proper speed and is the empirical mean updated the same way. The paper is highly technical but shows the almost sure explosion of the resulting sequence under a flat target, an ergodic for a double Laplace target and a unimodal proposal, and a more general version under assumptions on the target and for a proposal suggested by Gareth Roberts and Jeff Rosenthal (2009)

which is akin to a renewal process in that the static part is not adaptative and thus regulates the behaviour of the whole chain. At last, Yves Atachadé and Gersende Fort posted the second half of their paper on limit theorems for some adaptive MCMC algorithms with subgeometric kernels, yet another fairly technical work that relates to Andrieu and Moulines (2006) and Saaksman and Vihola (2008). The adaptivity is controlled by retroprojections and contains as a special case stochastic approximation schemes, the main assumptions being a drift condition on the core kernel

and a diminishing adaptation condition common to all adaptive MCMC papers.