## MCMC with mutually singular distributions (2)

Posted in Statistics with tags , , on March 31, 2009 by xi'an

In connection with questions I had posted earlier about the interesting paper of Raphael Gottardo and Adrian Raftery, I got several emails from Raphael that helped with my understanding of the paper, the main point being that having the target being defined against the same measure as the proposal does not prevent from having zero components in this target, thus incorporates within-Gibbs moves quite naturally. Arnaud Doucet also pointed out to me that using kernels with Dirac masses is possible when looking at them from an empirical measure point of view, as explained in this short note. As a coincidence, Raphael also added some comments and explanations on the first post.

## Incredibly ugly squalid pictures…

Posted in Statistics with tags , , , on March 30, 2009 by xi'an

Well, this is not a common teaser to attract readers, but a comment on one of my graphs in the second revision of our paper Adaptivity for approximate Bayesian computation algorithms: a population Monte Carlo approach, written with Marc Beaumont, Jean-Marie Cornuet, and Jean-Michel Marin, and (re-re-)submitted to Biometrika… Not something I’d like to hear about my graphs, thank you!, as the pdf version of the graph on the right actually looks better than that one…. Anyway, we revised the paper towards less squalidness, replacing histogram with density using the “h” type in R. The major request on the revision was to get under eight pages in order to fit inside the Miscelanea section of Biometrika. Changes are thus mostly cosmetic compared with the earlier version, as you can check on the arXiv list of versions. The background for the paper and the earlier paper of Sisson, Fan, and Tanaka (2007, PNAS) it analyses, are described in this earlier post.

Posted in University life on March 29, 2009 by xi'an

As actions against the new status of university lecturers and professors continue in French universities, with some places being on strike for the 8th consecutive week and La Sorbonne being briefly “occupied” by part of its faculty earlier this week, some of my colleagues in the Math department drafted a motion in support of the protests that called for (a) advertising this motion on the webpage of the department, (b) cancelling all seminars, and (c) not returning students’ grades.

As posted earlier, I thought a reform on the status of lecturers and professors that would account for the research activities in setting the teaching duties was a step in the right direction, but, when faced with strong protests from faculty members, the government backed up so much on this that it is hardly worth mentioning any longer and definitely not worth going on industrial action at this (late) stage… Further, I find those calls for closing seminars both ridiculous and disturbing: ridiculous because no one in the administration cares a fig about whether or not a seminar in differential geometry stopped meeting, disturbing because it constitutes a first degree of picketing and, as such, that it is an attack (of a very mild sort) against my freedom of thought, work, and action, in that the motion does not recognise me a right to think differently! Each time I am faced with this kind of situation, as during the harsh strikes of the 1990′s, I tend to react by taking systematically the opposite stand: then to keep teaching despite disruptions by strikers and now to start a stat seminar as a defiance to orders… This is obviously quite a childish reaction, as I do not think my colleagues would do anything to prevent the putative seminar from going on! Similarly, nobody barred me from handling my (ok, by the way!) R grades back to the administration. But I also think this motion and more generally a lot of actions reported on that site have been equally childish and that the goals of the protests have gone so wide that they are now completely inaudible.

A radicalisation of the university protests is very unlikely to gain more sympathy from a general public who is currently facing layoffs and mortgage issues: discussions about the number of teaching hours or the role of the local administration for allocating promotions are not bound to appeal to outsiders enough to justify violent occupations or fights with the police.

## Shorter, clearer, with no swan in the pond

Posted in Books, Statistics with tags , , , , on March 28, 2009 by xi'an

In the current issue of Significance, there is a four page discussion by Bill Janeway on the current financial crisis and the role of statistical models. If you remove the pictures and the quotes from Alice, it is more like three pages and they tell you much more than the three-hundred-somes of The Black Swan. For instance, the paper relates to references that appeared much earlier than the book to point out the distinction between uncertainty and randomness, a point on which The Black Swan is always vague, it also spells out that there are not always true models and that time-series are not always stationary, two points that The Black Swan misses, and that ergodicity does not apply and that markets are not rational. As in The Black Swan, there are mentions there of black swans as events that “happen once in five hundred years”, too, as well as of the inadequacy of models like Value at Risk (which provides a quantile estimate on the risk but no loss evaluation) and of Gaussian assumptions, but the paper also blames the crisis on the abandonment of the essential balance-sheet by banks. In its conclusion about the rise of behavioural finance, Janeway relates to Taleb by quoting from his hero, John Maynard Keynes, but for reasons different from Fooled by Randomness. Ending on “bad models are bad” by calling for models that explore inefficiencies in the markets is not going to solve the crisis, but, again, the paper gives a much clearer and more informative message than The Black Swan did.

Matti Vihola from the University of Jyväskylä posted a paper on arXiv yesterday on a convergence result for an adaptive scheme related with the basic random walk Metropolis-Hastings algorithm. The scale$\theta$used in the random walk is adapted using the Robbins-Monro stochastic approximation schedule
$\log \theta_{t+1} = \log\theta_t + Ct^{-\gamma}(\alpha_t-\alpha^\star)$
where$\alpha^\star$is the gold standard for acceptance, and$\alpha_t$is the empirical acceptance rate. (This was one of the examples in our 2001 paper with Christophe Andrieu, Controlled MCMC for Optimal Sampling, that never got published but can nonetheless boasts about its 43 citations!) The constraints imposed upon the target density$\pi$and on the integrand$f$are fairly harsh, including$f$being bounded (those constraints seem to be more restrictive than in Roberts and Rosenthal, 2007, J.A.P., although of course I did not check the correspondance) and there is a surprising restriction on$\alpha^\star$, namely$\alpha^\star<1/2$. I do not have any intuitive explanation for this hard boundary on the acceptance rate: staying away from 0 and from 1 makes sense, obviously, but 1/2? Looking at the reason, this seems to be related to a lower bound on the average acceptance rate found in the proof of Proposition 12, which is itself related with the convergence of the Robbins-Monro sequence.
Ps-When checking for the role of$\alpha$, I came across the possibility to search for$\alpha$in a pdf file with Acrobat Reader by simply typing$\alpha$in the Find box. Neat!