Archive for regeneration

Statistics, with interactions

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , on June 6, 2013 by xi'an

Ton Duc Thang University entrance hall, June 5, 2013Due to a tight June schedule (3rd conference in a week!), I only stayed one day at the SIOD 2013 conference in Saigon. (SIOD means Statistics and interaction with other disciplines.) The conference was housed by Ton Duc Thang University, on a very modern campus, and it sounded like the university had drafted a lot of his undergrads to catter to the SIOD participants: similar to the Bayesian conference in India a few months ago, those students would stand at the ready to guide us around the campus and to relay any problem to the organisers. This was very helpful and enjoyable, a plus being that most female students wore the traditional pink costume adopted by the university, but it also made me a wee bit uncomfortable as I do not know how much say those students had in this draft… In particular, most of the students I talked with were from other fields than Statistics. (And definitely not complaining, but being on the opposite very friendly the whole time!) A funny side story is that I got a wake-up call from the conference organisers in the morning as I had missed a welcome ceremony with the president due to oversleeping (itself due to an excess of iced coffee rather than minimal jetlag!). Among the few talks I attended, some French school statistics due to the presence of a large contingent from Toulouse, a talk about zero inflated normal distributions which sounded like missing-at-random normal observations (hence easy to process), and a talk about the point of using Bayes factors in hypothesis testing which essentially if independently provided a second version of my course from the previous day.

DSC_4983Yesterday, I also had a short discussion with Paul Minh who presented a talk on a general regenerative device for MCMC algorithms, using a bound on the target density rather than on the Markov transition in order to achieve easier regeneration. While a neat idea, this method requires the construction of a lower bound that can easily simulated. Furthermore, if the regeneration probability is low, the mixing speed may remain similar to the original MCMC sampler, as the method ressorts to a standard MCMC step on the remaining part of the target density.

advanced Markov chain Monte Carlo methods

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , on December 5, 2011 by xi'an

This book, Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples, by Faming Liang, Chuanhai Liu, and Raymond Carroll, appeared last year and has been sitting on my desk all this time, patiently (?) waiting for a review. When I received it, I took a brief look at it (further than the cool cover!) and then decided I needed more than that to write a useful review! Here are my impressions  on Advanced Markov Chain Monte Carlo Methods after a deeper read. (I have not read any other review in the main statistical journals so far.)

The title, Advanced Markov Chain Monte Carlo Methods, is a clear warning on the level of the book: “advanced”, it certainly is!!! By page 85, the general description of MCMC simulation methods is completed, including perfect sampling and reversible jump MCMC, and the authors engage into a detailed description of highly specialised topics of their choice: Auxiliary variables (Chap. 4), Population-based MCMC (Chap. 5), Dynamic weighting (Chap. 6), Stochastic approximation Monte Carlo (Chap. 7), and MCMC with adaptive proposals (Chap. 8).  The book is clearly inspired by the numerous papers the authors have written in those area, especially Faming Liang. (The uneven distribution of the number of citations per year with peaks in 2000 and 2009 reflects this strong connection.) While the book attempts at broadening the spectrum by including introductory sections, and discussing other papers, it remains nonetheless that this centred focus of the book reduces its potential readership to graduate students and researchers who could directly work on the original papers. I would thus hesitate in teaching my graduate students from this book, given that they only attend a single course on Monte Carlo methods. Continue reading

Adap’skiii [day 2]

Posted in R, Statistics, University life with tags , , , , , , , , , on January 5, 2011 by xi'an

Another exciting day at Adap’skiii!!!

Yves Atchadé presented a very recent work on the fundamental issue of estimating the asymptotic variance estimation for adaptive MCMC algorithms, with an intriguing experimental observation that a non-converging bandwidth with rate 1/n was providing better coverage than the converging rate. (I always found the issue of estimating the asymptotic variance both a tough problem and an important item in convergence assessment.) Galin Jones showed new regeneration results for componentwise MCMC samplers, with applications to quantile estimation. The iid structure produced by the regeneration mechanism allows rather naturally to introduce an adaptive improvement in those algorithms, if regeneration occurs often enough. (From the days of my Stat’Sci’ paper on convergence assessment, I  love regeneration techniques for both theoretical and methodological reasons, even though they are often difficult to efficiently implement in practice.) Matti Vihola summarised several of his recent papers on the stability and convergence of adaptive MCMC algorithms, pursuing the Finnish tradition of leadership in adaptive algorithms! One point I found particularly interesting was the possibility of separating ergodicity from the Law of Large Numbers, thus reducing the constraints imposed by the containment condition. In the afternoon, Dawn Woodard discussed the convergence rate of the Gibbs sampler used for genomic motif discovery by Liu, Lawrence and Neuwald (1995). Scott Schmidler concluded the workshop by a far-ranging talk distinguishing between exploration and exploitation in adaptive MCMC algorithms, ie mixing vs burning, with illustrations using the Wang-Landau algorithm.

Thus, as in the previous editions of Adap’ski, we have had a uniformly high quality of talks about the current research in the area of adaptive algorithms (and a wee further). This shows the field is very well active and expanding, aiming at reaching a wider audience by providing verifiable convergence conditions and semi-automated softwares (like Jeff Rosenthal’s amcmc R code we used in Introducing Monte Carlo Methods with R). Looking forward Adap’ski 4 (Adap’skiV?!), hopefully in Europe and why not in Chamonix?! Which could then lead us to call the next meeting Adap’skiX…

Monte Carlo Statistical Methods third edition

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , on September 23, 2010 by xi'an

Last week, George Casella and I worked around the clock on starting the third edition of Monte Carlo Statistical Methods by detailing the changes to make and designing the new table of contents. The new edition will not see a revolution in the presentation of the material but rather a more mature perspective on what matters most in statistical simulation:

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