Following an earlier submission to Statistical Science, we have now resubmitted and arXived the new version of our paper “Improving the convergence properties of the Data Augmentation algorithm with an application to Bayesian mixture modelling”, written with Jim Hobert (University of Florida), and Vivek Roy (Iowa State University). Given that both referees were quite positive about the earlier version, the changes are truly minor and overwhelmingly stylistic. Again, I am I am very glad to be part of this paper because of the results but also because it relates to a problem I discussed at length with Richard Tweedie when I visited him in Colorado in 1993… (The above picture of Richard, along with Gareth Roberts and Anto Mira, was taken during the TMR Workshop on Computational and Spatial Statistics I organised in Aussois in 1998, with unfortunately no remaining webpage! A pre-MCMC’ski of sorts, when I had not yet started skiing!)
Archive for Statistical Science
Improving convergence of Data Augmentation algorithms
Posted in Mountains, Statistics, University life with tags Aussois, convergence, Data augmentation, mixture estimation, Statistical Science on June 7, 2011 by xi'anStochastic approximation in mixtures
Posted in R, Statistics with tags J.K. Ghosh, mixtures, Newton-Raphson, Robbins-Monro, Statistical Science, stochastic approximation on February 23, 2011 by xi'an
On Friday, a 2008 paper on Stochastic Approximation and Newton’s Estimate of a Mixing Distribution by Ryan Martin and J.K. Ghosh was posted on arXiv. (I do not really see why it took so long to post on arXiv a 2008 Statistical Science paper but given that it is not available on project Euclid, it may be that not all papers in Statistical Science are published immediately. Anyway, this is irrelevant to my point here!).
The paper provides a very nice introduction to stochastic approximation methods, making the link to recent works by Christophe Andrieu, Heikki Haario, Faming Liang, Eric Moulines, Enro Saksman, and co-authors. Martin and Ghosh also reinterpret Newton-Raphson as a special case of stochastic approximation. The whole paper is very pleasant to read, quite in tune with Statistical Science. I will most certainly use this material in my graduate courses and also include part of it in the revision of Monte Carlo Statistical Methods.
History makes Stat. Science!
Posted in Books, R, Statistics with tags handbook of Markov chain Monte Carlo, Markov chains, MCMC, Monte Carlo Statistical Methods, simulation, Statistical Science on January 1, 2011 by xi'an
While the above heading sounds like a title in reverse, its words are in the “correct” order in that our paper with George Casella, A Short History of Markov Chain Monte Carlo, has been accepted for publication by Statistical Science. This publication may sound weird when considering that the paper is also scheduled to appear in the Handbook of Markov Chain Monte Carlo: Methods and Applications, edited by Steve Brooks, Andrew Gelman, Galin Jones, and Xiao-Li Meng… However, George noticed we were allowed to keep our copyright ownership when publishing a chapter of this handbook, hence the possibility to submit the chapter to a journal as well. After a smooth editorial process, the paper has thus been accepted, which makes it my last acceptance for 2010, a rather productive year. I wish (myself!) that the extra-time brought by my appointment at Institut Universitaire de France will see an even more productive 2011 year! And very best wishes to all readers of the ‘Og, in terms of personal and professional accomplishments!!!
Particle learning [rejoinder]
Posted in R, Statistics, University life with tags Bayesian Analysis, convergence diagnostics, degeneracy, discussions, MCMC, mixtures, Monte Carlo Statistical Methods, particle learning, sequential Monte Carlo, Statistical Science, Valencia 9 on November 10, 2010 by xi'anFollowing the posting on arXiv of the Statistical Science paper of Carvalho et al., and the publication by the same authors in Bayesian Analysis of Particle Learning for general mixtures I noticed on Hedibert Lopes’ website his rejoinder to the discussion of his Valencia 9 paper has been posted. Since the discussion involved several points made by members of the CREST statistics lab (and covered the mixture paper as much as the Valencia 9 paper), I was quite eager to read Hedie’s reply. Unsurprisingly, this rejoinder is however unlikely to modify my reservations about particle learning. The following is a detailed examination of the arguments found in the rejoinder but requires a preliminary reading of the above papers as well as our discussion..
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Re-reading Jeffreys’ Theory of Probability
Posted in Books, Statistics with tags Harold Jeffreys, Keynes, Statistical Science, Theory of Probability on January 20, 2010 by xi'an
Our paper with Nicolas Chopin and Judith Rousseau, Harold Jeffreys’s Theory of Probability Revisited, has now appeared in Statistical Science, 2009, Vol. 24, No. 2, 141-172, along with six discussions and our reply. It is very nice that the paper appeared in the 2009 volume of Statistical Science, as it made it as a 70th anniversary celebration for this important book. (In a similar spirit, I will start a reading class in March at CREST on Keynes’ A Treatise On Probability. With the hope that this can lead to another reassessment.)
