je reviendrai à Montréal [MCM 2017]

Next summer of 2017, the biennial International Conference on Monte Carlo Methods and Applications (MCM) will take place in Montréal, Québec, Canada, on July 3-7. This is a mathematically-oriented meeting that works in alternance with MCqMC and that is “devoted to the study of stochastic simulation and Monte Carlo methods in general, from the theoretical viewpoint and in terms of their effective applications in different areas such as finance, statistics, machine learning, computer graphics, computational physics, biology, chemistry, and scientific computing in general. It is one of the most prominent conference series devoted to research on the mathematical aspects of stochastic simulation and Monte Carlo methods.” I attended one edition in Annecy three years ago and enjoyed very much the range of topics and backgrounds. The program is under construction and everyone is warmly invited to contribute talks or special sessions, with a deadline on January 20, 2017. In addition, Montréal is a Monte Carlo Mecca of sorts with leading researchers in the field like Luc Devroye and Pierre Lécuyer working there. (And a great place to visit in the summer!)

about randomness (im Hamburg)

True randomness was the topic of the `Random numbers; fifty years later’ talk in DESY by Frederick James from CERN. I had discussed a while ago a puzzling book related to this topic. This talk went along a rather different route, focussing on random generators. James put this claim that there are computer based physical generators that are truly random. (He had this assertion that statisticians do not understand randomness because they do not know quantum mechanics.) He distinguished those from pseudo-random generators: “nobody understood why they were (almost) random”, “IBM did not know how to generate random numbers”… But then spent the whole talk discussing those pseudo-random generators. Among other pieces of trivia, James mentioned that George Marsaglia was the one exhibiting the hyperplane features of congruential generators. That Knuth achieved no successful definition of what randomness is in his otherwise wonderful books! James thus introduced Kolmogorov’s mixing (not Kolmogorov’s complexity, mind you!) as advocated by Soviet physicists to underlie randomness. Not producing anything useful for RNGs in the 60’s. He then moved to the famous paper by Ferrenberg, Landau and Wong (1992) that I remember reading more or less at the time. In connection with the phase transition critical slowing down phenomena in Ising model simulations. And connecting with the Wang-Landau algorithm of flipping many sites at once (which exhibited long-term dependences in the generators). Most interestingly, a central character in this story is Martin Lüscher, based in DESY, who expressed the standard generator of the time RCARRY into one studied by those Soviet mathematicians,

X’=AX

showing that it enjoyed Kolmogorov mixing, but with a very poor Lyapunov coefficient. I partly lost track there as RCARRY was not perfect. And on how this Kolmogorov mixing would relate to long-term dependencies. One explanation by James was that this property is only asymptotic. (I would even say statistical!) Also interestingly, the 1994 paper by Lüscher produces the number of steps necessary to attain complete mixing, namely 15 steps, which thus works as a cutoff point. (I wonder why a 15-step RCARRY is slower, since A¹⁵ can be computed at once… It may be due to the fact that A is sparse while A¹⁵ is not.) James mentioned that Marsaglia’s Die Hard battery of tests is now obsolete and superseded by Pierre Lecuyer’s TestU01.

In conclusion, I did very much like this presentation from an insider, but still do not feel it makes a contribution to the debate on randomness, as it stayed put on pseudorandom generators. To keep the connection with von Neumann, they all produce wrong answers from a randomness point of view, if not from a statistical one. (A final quote from the talk: “Among statisticians and number theorists who are supposed to be specialists, they do not know about Kolmogorov mixing.”) [Discussing with Fred James at the reception after the talk was obviously extremely pleasant, as he happened to know a lot of my Bayesian acquaintances!]

ACM Transactions on Modeling and Computer Simulation

Pierre Lecuyer is the new editor of the ACM Transactions on Modeling and Computer Simulation (TOMACS) and he has asked me to become an Area Editor for the new area of simulation in Statistics. I am quite excited by this new Æditor’s hat, since this is a cross-disciplinary journal:

The ACM Transactions on Modeling and Computer Simulation (TOMACS) provides a single archival source for the publication of high-quality research and developmental results in computer simulation. The subjects of emphasis are discrete event simulation, combined discrete and continuous simulation, as well as Monte Carlo methods. Papers in continuous simulation will also receive serious consideration if their contributions to modeling and simulation in general are substantial.

The use of simulation techniques is pervasive, extending to virtually all the sciences. TOMACS serves to enhance the understanding, improve the practice, and increase the utilization of computer simulation. Submissions should contribute to the realization of these objectives, and papers treating applications should stress their contributions vis-a-vis these objectives.

As an indication of this cross-disciplinarity, I note that most Area Editors and Associate Editors are unknown to me (except for Luc Devroye, of course!). In addition, I savour the irony of being associated with a journal of the Association for Computer Machinery (ACM), given my complete lack of practical skills! So, if you have relevant papers to submit in the field, please consider the ACM Transactions on Modeling and Computer Simulation (TOMACS) as a possible outlet.