Archive for Bayesian statistics

Statistics month in Marseilles (CIRM)

Posted in Books, Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , on June 24, 2015 by xi'an

Calanque de Morgiou, Marseille, July 7, 2010Next February, the fabulous Centre International de Recherche en Mathématiques (CIRM) in Marseilles, France, will hold a Statistics month, with the following programme over five weeks

Each week will see minicourses of a few hours (2-3) and advanced talks, leaving time for interactions and collaborations. (I will give one of those minicourses on Bayesian foundations.) The scientific organisers of the B’ week are Gilles Celeux and Nicolas Chopin.

The CIRM is a wonderful meeting place, in the mountains between Marseilles and Cassis, with many trails to walk and run, and hundreds of fantastic climbing routes in the Calanques at all levels. (In February, the sea is too cold to contemplate swimming. The good side is that it is not too warm to climb and the risk of bush fire is very low!) We stayed there with Jean-Michel Marin a few years ago when preparing Bayesian Essentials. The maths and stats library is well-provided, with permanent access for quiet working sessions. This is the French version of the equally fantastic German Mathematik Forschungsinstitut Oberwolfach. There will be financial support available from the supporting societies and research bodies, at least for young participants and the costs if any are low, for excellent food and excellent lodging. Definitely not a scam conference!

arXiv frenzy

Posted in R, Statistics, University life with tags , , , , , , on June 23, 2015 by xi'an

In the few past days, there has been so many arXiv postings of interest—presumably the NIPS submission effect!—that I cannot hope to cover them in the coming weeks! Hopefully, some will still come out on the ‘Og in a near future:

  • arXiv:1506.06629: Scalable Approximations of Marginal Posteriors in Variable Selection by Willem van den Boom, Galen Reeves, David B. Dunson
  • arXiv:1506.06285: The MCMC split sampler: A block Gibbs sampling scheme for latent Gaussian models by Óli Páll Geirsson, Birgir Hrafnkelsson, Daniel Simpson, Helgi Sigurðarson [also deserves a special mention for gathering only ***son authors!]
  • arXiv:1506.06268: Bayesian Nonparametric Modeling of Higher Order Markov Chains by Abhra Sarkar, David B. Dunson
  • arXiv:1506.06117: Convergence of Sequential Quasi-Monte Carlo Smoothing Algorithms by Mathieu Gerber, Nicolas Chopin
  • arXiv:1506.06101: Robust Bayesian inference via coarsening by Jeffrey W. Miller, David B. Dunson
  • arXiv:1506.05934: Expectation Particle Belief Propagation by Thibaut Lienart, Yee Whye Teh, Arnaud Doucet
  • arXiv:1506.05860: Variational Gaussian Copula Inference by Shaobo Han, Xuejun Liao, David B. Dunson, Lawrence Carin
  • arXiv:1506.05855: The Frequentist Information Criterion (FIC): The unification of information-based and frequentist inference by Colin H. LaMont, Paul A. Wiggins
  • arXiv:1506.05757: Bayesian Inference for the Multivariate Extended-Skew Normal Distribution by Mathieu Gerber, Florian Pelgrin
  • arXiv:1506.05741: Accelerated dimension-independent adaptive Metropolis by Yuxin Chen, David Keyes, Kody J.H. Law, Hatem Ltaief
  • arXiv:1506.05269: Bayesian Survival Model based on Moment Characterization by Julyan Arbel, Antonio Lijoi, Bernardo Nipoti
  • arXiv:1506.04778: Fast sampling with Gaussian scale-mixture priors in high-dimensional regression by Anirban Bhattacharya, Antik Chakraborty, Bani K. Mallick
  • arXiv:1506.04416: Bayesian Dark Knowledge by Anoop Korattikara, Vivek Rathod, Kevin Murphy, Max Welling [a special mention for this title!]
  • arXiv:1506.03693: Optimization Monte Carlo: Efficient and Embarrassingly Parallel Likelihood-Free Inference by Edward Meeds, Max Welling
  • arXiv:1506.03074: Variational consensus Monte Carlo by Maxim Rabinovich, Elaine Angelino, Michael I. Jordan
  • arXiv:1506.02564: Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families by Heiko Strathmann, Dino Sejdinovic, Samuel Livingstone, Zoltan Szabo, Arthur Gretton [comments coming soon!]

Current trends in Bayesian methodology with applications

Posted in Books, Statistics, Travel, University life with tags , , , , , on June 20, 2015 by xi'an

When putting this volume together with Umesh Singh, Dipak Dey, and Appaia Loganathan, my friend Satyanshu Upadhyay from Varanasi, India, asked me for a foreword. The book is now out, with chapters written by a wide variety of Bayesians. And here is my foreword, for what it’s worth:

It is a great pleasure to see a new book published on current aspects of Bayesian Analysis and coming out of India. This wide scope volume reflects very accurately on the present role of Bayesian Analysis in scientific inference, be it by statisticians, computer scientists or data analysts. Indeed, we have witnessed in the past decade a massive adoption of Bayesian techniques by users in need of statistical analyses, partly because it became easier to implement such techniques, partly because both the inclusion of prior beliefs and the production of a posterior distribution that provides a single filter for all inferential questions is a natural and intuitive way to process the latter. As reflected so nicely by the subtitle of Sharon McGrayne’s The Theory that Would not Die, the Bayesian approach to inference “cracked the Enigma code, hunted down Russian submarines” and more generally contributed to solve many real life or cognitive problems that did not seem to fit within the traditional patterns of a statistical model.
Two hundred and fifty years after Bayes published his note, the field is more diverse than ever, as reflected by the range of topics covered by this new book, from the foundations (with objective Bayes developments) to the implementation by filters and simulation devices, to the new Bayesian methodology (regression and small areas, non-ignorable response and factor analysis), to a fantastic array of applications. This display reflects very very well on the vitality and appeal of Bayesian Analysis. Furthermore, I note with great pleasure that the new book is edited by distinguished Indian Bayesians, India having always been a provider of fine and dedicated Bayesians. I thus warmly congratulate the editors for putting this exciting volume together and I offer my best wishes to readers about to appreciate the appeal and diversity of Bayesian Analysis.

the most patronizing start to an answer I have ever received

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , on April 30, 2015 by xi'an

Another occurrence [out of many!] of a question on X validated where the originator (primitivus petitor) was trying to get an explanation without the proper background. On either Bayesian statistics or simulation. The introductory sentence to the question was about “trying to understand how the choice of priors affects a Bayesian model estimated using MCMC” but the bulk of the question was in fact failing to understand an R code for a random-walk Metropolis-Hastings algorithm for a simple regression model provided in a introductory blog by Florian Hartig. And even more precisely about confusing the R code dnorm(b, sd = 5, log = T) in the prior with rnorm(1,mean=b, sd = 5, log = T) in the proposal…

“You should definitely invest some time in learning the bases of Bayesian statistics and MCMC methods from textbooks or on-line courses.” X

So I started my answer with the above warning. Which sums up my feelings about many of those X validated questions, namely that primitivi petitores lack the most basic background to consider such questions. Obviously, I should not have bothered with an answer, but it was late at night after a long day, a good meal at the pub in Kenilworth, and a broken toe still bothering me. So I got this reply from the primitivus petitor that it was a patronizing piece of advice and he prefers to learn from R code than from textbooks and on-line courses, having “looked through a number of textbooks”. Good luck with this endeavour then!

probabilistic numerics

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , on April 27, 2015 by xi'an

sunwar2I attended an highly unusual workshop while in Warwick last week. Unusual for me, obviously. It was about probabilistic numerics, i.e., the use of probabilistic or stochastic arguments in the numerical resolution of (possibly) deterministic problems. The notion in this approach is fairly Bayesian in that it makes use to prior information or belief about the quantity of interest, e.g., a function, to construct an usually Gaussian process prior and derive both an estimator that is identical to a numerical method (e.g., Runge-Kutta or trapezoidal integration) and uncertainty or variability around this estimator. While I did not grasp much more than the classy introduction talk by Philipp Hennig, this concept sounds fairly interesting, if only because of the Bayesian connection, and I wonder if we will soon see a probability numerics section at ISBA! More seriously, placing priors on functions or functionals is a highly formal perspective (as in Bayesian non-parametrics) and it makes me wonder how much of the data (evaluation of a function at a given set of points) and how much of the prior is reflected in the output [variability]. (Obviously, one could also ask a similar question for statistical analyses!)  For instance, issues of singularity arise among those stochastic process priors.

Another question that stemmed from this talk is whether or not more efficient numerical methods can derived that way, in addition to recovering the most classical ones. Somewhat, somehow, given the idealised nature of the prior, it feels like priors could be more easily compared or ranked than in classical statistical problems. Since the aim is to figure out the value of an integral or the solution to an ODE. (Or maybe not, since again almost the same could be said about estimating a normal mean.)

reis naar Amsterdam

Posted in Books, Kids, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , on April 16, 2015 by xi'an

Amster4On Monday, I went to Amsterdam to give a seminar at the University of Amsterdam, in the department of psychology. And to visit Eric-Jan Wagenmakers and his group there. And I had a fantastic time! I talked about our mixture proposal for Bayesian testing and model choice without getting hostile or adverse reactions from the audience, quite the opposite as we later discussed this new notion for several hours in the café across the street. I also had the opportunity to meet with Peter Grünwald [who authored a book on the minimum description length principle] pointed out a minor inconsistency of the common parameter approach, namely that the Jeffreys prior on the first model did not have to coincide with the Jeffreys prior on the second model. (The Jeffreys prior for the mixture being unavailable.) He also wondered about a more conservative property of the approach, compared with the Bayes factor, in the sense that the non-null parameter could get closer to the null-parameter while still being identifiable.

Amster6Among the many persons I met in the department, Maarten Marsman talked to me about his thesis research, Plausible values in statistical inference, which involved handling the Ising model [a non-sparse Ising model with O(p²) parameters] by an auxiliary representation due to Marc Kac and getting rid of the normalising (partition) constant by the way. (Warning, some approximations involved!) And who showed me a simple probit example of the Gibbs sampler getting stuck as the sample size n grows. Simply because the uniform conditional distribution on the parameter concentrates faster (in 1/n) than the posterior (in 1/√n). This does not come as a complete surprise as data augmentation operates in an n-dimensional space. Hence it requires more time to get around. As a side remark [still worth printing!], Maarten dedicated his thesis as “To my favourite random variables , Siem en Fem, and to my normalizing constant, Esther”, from which I hope you can spot the influence of at least two of my book dedications! As I left Amsterdam on Tuesday, I had time for a enjoyable dinner with E-J’s group, an equally enjoyable early morning run [with perfect skies for sunrise pictures!], and more discussions in the department. Including a presentation of the new (delicious?!) Bayesian software developed there, JASP, which aims at non-specialists [i.e., researchers unable to code in R, BUGS, or, God forbid!, STAN] And about the consequences of mixture testing in some psychological experiments. Once again, a fantastic time discussing Bayesian statistics and their applications, with a group of dedicated and enthusiastic Bayesians!Amster12

a week in Oxford

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on January 26, 2015 by xi'an

1sprI spent [most of] the past week in Oxford in connection with our joint OxWaSP PhD program, which is supported by the EPSRC, and constitutes a joint Centre of Doctoral Training in  statistical science focussing on data-­intensive environments and large-­scale models. The first cohort of a dozen PhD students had started their training last Fall with the first year spent in Oxford, before splitting between Oxford and Warwick to write their thesis.  Courses are taught over a two week block, with a two day introduction to the theme (Bayesian Statistics in my case), followed by reading, meetings, daily research talks, mini-projects, and a final day in Warwick including presentations of the mini-projects and a concluding seminar.  (involving Jonty Rougier and Robin Ryder, next Friday). This approach by bursts of training periods is quite ambitious in that it requires a lot from the students, both through the lectures and in personal investment, and reminds me somewhat of a similar approach at École Polytechnique where courses are given over fairly short periods. But it is also profitable for highly motivated and selected students in that total immersion into one topic and a large amount of collective work bring them up to speed with a reasonable basis and the option to write their thesis on that topic. Hopefully, I will see some of those students next year in Warwick working on some Bayesian analysis problem!

On a personal basis, I also enjoyed very much my time in Oxford, first for meeting with old friends, albeit too briefly, and second for cycling, as the owner of the great Airbnb place I rented kindly let me use her bike to go around, which allowed me to go around quite freely! Even on a train trip to Reading. As it was a road racing bike, it took me a trip or two to get used to it, especially on the first day when the roads were somewhat icy, but I enjoyed the lightness of it, relative to my lost mountain bike, to the point of considering switching to a road bike for my next bike… I had also some apprehensions with driving at night, which I avoid while in Paris, but got over them until the very last night when I had a very close brush with a car entering from a side road, which either had not seen me or thought I would let it pass. Gave me the opportunity of shouting Oï!

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