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Postdoc on adaptive MCMC in Paris

Posted in R, University life with tags , , , , on May 2, 2011 by xi'an

Although the official deadline is long past, I just became aware of this call for a postdoctoral position in Paris starting next Fall. Please feel free to apply:

Summary Adaptive Markov Chain Monte Carlo (MCMC) methods are currently a very active field of research. MCMC methods are sampling methods, based on Markov Chains which are ergodic with respect to the target probability measure. The principle of adaptive methods is to optimize on the fly some design parameters of the algorithm with respect to a given criterion reflecting the sampler’s performance (optimize the acceptance rate, optimize an importance sampling function, etc…). A postdoctoral position is opened to work on the numerical analysis of adaptive MCMC methods: convergence, numerical efficiency, development and analysis of new algorithms. A particular emphasis will be given to applications in statistics and molecular dynamics. (Detailed description) Position funded by the French National Research Agency (ANR) through the 2009-2012 project ANR-08-BLAN-0218. The position will benefit from an interdisciplinary environment involving numerical analysts, statisticians and probabilists, and of strong interactions between the partners of the project ANR-08-BLAN-021

Required diploma PhD thesis in statistics or probability, with a competitive track record.

Required skills experience in MCMC methods and their mathematical analysis.

Deadline for applications : September 2010. Applications must include : a detailed CV with a description of realized projects a motivation letter a summary of the thesis 2 or 3 recommendation letters preferred starting dates and duration and must be sent to Gersende FORT (gfort@tsi.enst.fr) in pdf format; or by standard mail to : Gersende FORT (LTCI, 46 rue Barrault, 75 634 Paris Cedex 13, Paris, France).

Duration : 11 months.

Location : Paris.

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“Bayesian model comparison in cosmology” on-line

Posted in Statistics, University life with tags , , , , , on June 27, 2010 by xi'an

I actually missed the piece of information that our our paper “Bayesian model comparison in cosmology with Population Monte Carlo” has been accepted by Monthly Notices of the Royal Astronomical Society on March 1! The abstract if not the whole paper is available on-line as early-view since mid-April… This is my last paper published in collaboration with the cosmologists of the Ecosstat 2005-2009 ANR program. Hopefully not the end of our collaboration as this was a very fruitful experience from my viewpoint, which happened to coincide with the golden years of population Monte Carlo, just as the Misgepop ANR program launched our foray into ABC methods. (In case you are unaware of the link, Scott Sisson has a twitter page posting news on ABC methods.)

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Physical Review D

Posted in Statistics, University life with tags , , , on June 12, 2009 by xi'an

Our “PMC for cosmology” paper has been accepted,

The manuscript “Estimation of cosmological parameters using adaptive importance sampling” (DC10621) by Darren Wraith et al. is being accepted for publication in Physical Review D. The formal notice of acceptance will be sent separately.

Sincerely,

Dennis Nordstrom
Editor
Physical Review D

which is a very good item of news, indeed! Thanks again to Darren Wraith—soon to move to INRIA Rhones-Alpes—and Martin Kilbinger for their involvement in this paper.

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Population Monte Carlo for cosmologists

Posted in Statistics with tags , , , on March 6, 2009 by xi'an

The population Monte Carlo (PMC) study that is the result of an ANR (ANR-05-BLAN-0283-04 “Ecosstat”) PMC Adaptationcollaboration between cosmologists at the Institut d’Astrophysique de Paris (IAP) and statisticians from Telecom Paritech and Dauphine is finally out on arXiv! The main bulk of the work was shared by two postdocs from the project, Darren Wraith and Martin Kilbinger, who thus deserve most of the praise.

The first part of the paper consists in an intensive comparison of PMC (as implemented in this arXived paper to appear in Statistics and Computing) with an adaptive state-of-the-art MCMC algorithm. The artificial target used for this comparison is of the banana-shape version in dimension 10 as in the figure on the left, inspired from Haario, Saksman and Tamminen (Bernoulli, 2001). The figure illustrates the adaptation of the importance function made of 9 Student’s t distributions with evolving parameters. The estimates of representative functions of interest in this setting are significantly improved when compared with an MCMC evaluation based on the same number of simulations. We also found that this banana target can be quite challenging when the correlation coefficient involved gets too high, as any simulation method then has difficulties reaching the tails. The evaluation of PMC also introduces convergence monitoring via the effective sample size and the less standard perplexity

p_N=\exp(H_N)/N \qquad H_N=-\sum_{i=1}^N \overline \omega_i \log(\overline \omega_i)

that corresponds to the exponential of the Shannon entropy. p_N is less than 1, with a proximity to 1 indicating a good fit between the target and the importance function. Compared with MCMC methods, using the perplexity in importance sampling settings allows for a simple convergence diagnostic.

The second part of the paper focus on a non-trivial implementation of the PMC scheme when the target is the posterior distribution on the cosmological parameters corresponding to three important datasets, CMB (associated with the WMAP5 code), SNIa and cosmic shear. The likelihood corresponding to some of those datasets can be quite demanding in terms of computing time and producing a good approximation of the posterior with a small number of points is crucial. Compared with MCMC approaches, the importance sampling nature of the algorithm allows for a speed improvement of 100, thanks to the parallel processing of the simulation! Besides this massive time gain (from several days to a few hours), the agreement between our PMC and the standard MCMC solutions is excellent.

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