sweet 60’s

The traditional group picture at the end of Eric Moulines’ 60th anniversary celebration, at IHP, Paris. Some of the participants had already left (and I am carefully hidding in the background). Among the celebrating talks reflecting the huge thematic diversity of EM’s carreer, Patrick Flandrin gave a great historical account of a certain Édouard-Léon Scott de Martinville and his invention of a sound recording device that did not meet with the same success as the later phonograph by Edison. A song he had registered in 1860 was retrieved in 2008 by a team of the Lawrence Berkeley National Laboratory, making it the earliest known intelligible voice recording in existence! Jean-François Cardoso explained how the team at Institut d’Astrophysique de Paris produced a near optimal estimate of the Cosmic Microwave Background (CMB) by linear projections preserving normality. Sara Filippi exposed a variational Bayes approach to selecting groups of variables in a GLM. Gareth Roberts illustrated retrospective sampling with his recent foray with Jeff Rosenthal in the lack of uniformity in the FIFA World Cup draws. Anatoli Iouditski spoke about a recent work on polyhedral estimation in statistical linear inverse problems. And Elisabeth Gassiat strolled through recent works on inference for hidden Markov models, including one at NeurIPS 2021 with Aapo Hyvärinen and others on nonlinear ICA. This was quite a fun meeting, with plenty of anecdotes and a few older pictures (even though I could not find any prior to 2005, which may have been the year I bought my first digital camera!)

nested sampling: any prior anytime?!

A recent arXival by Justin Alsing and Will Handley on “nested sampling with any prior you like” caught my attention. If only because I was under the impression that some priors would not agree with nested sampling. Especially those putting positive weight on some fixed levels of the likelihood function, as well as improper priors.

“…nested sampling has largely only been practical for a somewhat restrictive class of priors, which have a readily available representation as a transform from the unit hyper-cube.”

Reading from the paper, it seems that the whole point is to demonstrate that “any proper prior may be transformed onto the unit hypercube via a bijective transformation.” Which seems rather straightforward if the transform is not otherwise constrained: use a logit transform in every direction. The paper gets instead into the rather fashionable direction of normalising flows as density representations. (Which suddenly reminded me of the PhD dissertation of Rob Cornish at Oxford, which I examined last year. Even though nested was not used there in the same understanding.) The purpose appearing later (in the paper) or in fine to express a random variable simulated from the prior as the (generative) transform of a Uniform variate, f(U). Resuscitating the simulation from an arbitrary distribution from first principles.

“One particularly common scenario where this arises is when one wants to use the (sampled) posterior from one experiment as the prior for another”

But I remained uncertain at the requirement for this representation in implementing nested sampling as I do not see how it helps in bypassing the hurdles of simulating from the prior constrained by increasing levels of the likelihood function. It would be helpful to construct normalising flows adapted to the truncated priors but I did not see anything related to this version in the paper.

The cosmological application therein deals with the incorporation of recent measurements in the study of the ΛCDM cosmological model, that is, more recent that the CMB Planck dataset we played with 15 years ago. (Time flies, even if an expanding Universe!) Namely, the Baryon Oscillation Spectroscopic Survey and the SH₀ES collaboration.

a bad graph about Hubble discrepancies

Here is a picture seen in a Nature Reviews Physics paper I came across, on  the Hubble constant being consistently estimated as large now than previously. I have no informed comment to make on the paper, which thinks that these discrepancies support altering the composition of the Universe shortly before the emergence of the Cosmological Background Noise (CMB), but the way it presented the confidence assessments of the same constant H⁰ based on 13 different experiments is rather ghastly, from using inclined confidence intervals, to adding a USA Today touch to the graph via a broken bridge and a river below, to resorting to different scales for both parts of the bridge…  

big bang/data/computers

I missed this astrostatistics conference announcement (and the conference itself, obviously!), occurring next door… Actually, I would have had (wee) trouble getting there as I was (and am) mostly stuck at home with a bruised knee and a doctor ban on any exercise in the coming day, thanks to a bike fall last Monday! (One of my 1991 bike pedals broke as I was climbing a steep slope and I did not react fast enough… Just at the right time to ruin my training preparation of the Argentan half-marathon. Again.) Too bad because there was a lot of talks that were of interest to me!

550 billion particles

“Space,” it says, “is big. Really big. You just won’t believe how vastly, hugely, mindbogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space, listen…” The Hitchhiker’s Guide to the Galaxy, Douglas Adams

“There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened.” The Hitchhiker’s Guide to the Galaxy, Douglas Adams

Following a link on Science Daily when looking at this 64 kcal mystery, I found an interesting annoucement about the most complete simulation of the evolution of the Universe from the Big Bang till now. The cosmology research unit in charge of the project is furthermore called DEUS (for Dark Energy Universe Simulation!), mostly located at Université Paris-Diderot, and its “goal is to investigate the imprints of dark energy on cosmic structure formation through high-performance numerical simulations”. It just announced the “simulation of the full observable universe for the concordance ΛCDM model”, which allows for the comparison of several cosmological models. (Data is freely available.) Besides the sheer scientific appeal of the project, the simulation side is also fascinating, although quite remote from Monte Carlo principles, in that the approach relies on very few repetitions of the simulation. The statistics are based on a single simulation, for a completely observed (simulated) Universe.

“If life is going to exist in a Universe of this size, then the one thing it cannot afford to have is a sense of proportion…” The Hitchhiker’s Guide to the Galaxy, Douglas Adams

The amounts involved in this simulation are simply mindboggling: 92 000 CPUs,  150 PBytes of data, 2 (U.S.) quadrillion flops (2 PFlop/s), the equivalent of 30 million computing hours, each particle has the size of the Milky Way, and so on… Here is a videoed description of the project (make sure to turn the sounds off if, like me, you simply and definitely hate Strauss’ music, and even if you like it, since the pictures do not move at the same pace as the music!):