art brut

an hectic trip!

The trip to Hamburg had started inauspiciously: a heart attack (someone else’s heart) in the métro (RER) has frozen the train traffic completely on Tuesday and I was lucky to find a taxi that managed to drive me to the airport in the nick of time. As there were warnings of strike in the Hamburg airport today, I decided to pack early and left DESY long enough in advance to reach the aiport by public transportation: it is only once I cleared security and sat at the gate that I realised I had forgotten my PC power box/cord in my room at DESY. What a drag! Anyway, I managed to buy a universal adapter in Paris on my way back from the airport and still to attend Adam Johansen’s seminar on Rao-Blackwellisation of particle filters at the Big’MC seminar. An interesting exploitation of missing variable structures within missing variables in a hidden Markov chain! (I missed the reason for the O(NM) computing time, though.) On the way home, I reflected on how little I had seen of Hamburg: a nice train system, a green and pleasant suburban area south of DESY towards the Elben (Groß Flottbeck), while running this morning, and…the airport! I wish I had had the opportunity and the time to get a glimpse of downtown Hamburg.

Monte Carlo workshop (Tage 1 & 2)

Gathering with simulators from other fields (mostly [quantum] physicists) offers both the appeal of seeing different perspectives on simulation and the diffiulty of having to filter alien vocabulary and presentation styles (generally assuming too much background from the audience). For instance; while the first talk on Tuesday by Gergely Barnaföldi about using GPUs for simulation was quite accessible, showing poor performances of the (CPU based) Mersenne twister., when using Dieharder as the evaluator. (This was in comparison with GPU-based solutions.) This provided an interesting contrapoint to the (later) seminar by Frederik James on random generators. (Of course, I did have some preliminary background on the topic.)

On the opposite, the second talk by Stefan Schäfer involved hybrid Monte Carlo methods but it took a lot of efforts (for me) to translate back to my understanding of the notion, gathered from this earlier Read Paper of Girolami and Calderhead, with the heat-bath and leapfrog algorithms. One extreme talk in this regard was William Lester’s talk on Wednesday morning on quantum Monte Carlo and its applications in computational chemistry where I could not get past the formulas! Too bad because it sounded quite innovative with notions like variational Monte Carlo and diffusion Monte Carlo… Nice movies, though. On the other hand, the final talk of the morning by Gabor Molnar-Saska on option pricing was highly pedagogical, defining everything and using simple examples as illustrations. (It certainly did not cure my misgivings about modelling the evolution of stock prices via pre-defined diffusions like Black-and-Scholes’, but the introduction was welcome, given the heterogeneity of the audience.) Both talks on transportation problems were also more accessible (maybe because they involved no pysics!)

The speakers in the afternoon sessions of Wednesday also made a huge effort to bring the whole audience up-to-date about their topic, like protein folding and high-energy particle physics (although everyone knows about the Higgs boson nowadays!). And ensemble Kalman filters (x2). In particular, Andrew Stuart did a great job with his simulation movies. Even the final talk about path-sampling for quantum simulation was mostly understandable, at least the problematic of it.  Sadly, at this stage, I still cannot put a meaning on “quantum Monte Carlo”… (Incidentally, I do not think my own talk reached much of the audience, missing convincing examples I did not have time to present:)

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!]

nach Hamburg

Today, I will visit Germany again, hopefully with less snow in the airport, in the City of Hamburg, as I am attending an intriguing workshop at the interface between statistics, physics and other sciences (the full title is “Monte Carlo Methods in Natural Sciences, in Engineering and in Economics”) at  DESY (Deutsches Elektronen-Synchrotron). The program of the workshop is a bit tight, but definitely interesting, with mostly speakers unknown to me. (Due to an even tighter schedule, I will miss the guided tour of the structure, unfortunately!)