Cédric Villani elected

Posted in Statistics with tags , , , , , , on June 19, 2017 by xi'an

generalised bouncy particle sampler

Posted in Statistics with tags on June 19, 2017 by xi'an

My PhD student, Wu Changye, just completed a paper on an extension of the bouncy particle sampler, to which he associated me as we had discussed the contents and especially the proofs together, although I did not participate in the redaction of the paper. The bouncy particle sampler belongs to the collection of piecewise deterministic samplers, which also contains the recent zig-zag sampler of Joris Bierkens, Paul Fearnhead, and Gareth Roberts (Warwick).  It was introduced by Alexandre Bouchard-Côté, Sebastian Vollmer (Warwick) and Arnaud Doucet, to appear in JASA, and uses one particle that is characterised by the pair (position, velocity), the velocity only changing at random times determined by the target density. The change is also deterministic. Which may lead to a lack of irreducibility in the process and is solved by an extra Poisson process in the original paper. In the generalisation imagined by Changye, the bounce becomes partly random in the direction orthogonal to the gradient. The stationarity results of Bouchard-Côté, Vollmer and Doucet then extend to this setting. As does the ability to subsample and compute faster versions of the likelihood function.

La Rochambelle, 25000⁺ coureuses! [39:29, 24⁰, 164th & 7th V2…]

Posted in Kids, pictures, Running, Travel with tags , , , , , , , , , , on June 18, 2017 by xi'an

As almost every year in the last decade, I have run the 10K in Caen for Courants de la Liberté, with 5000⁺ runners, on a new route completely in the city of Caen, partly downhill..! It did not go well (although I started in 3:44 on the first three k’s) as I ended up at a poor position (8th) in my category, which is not surprising with some runners now 8 years younger than I! (The runner next to me is the second V3.) And a fairly hot weather, especially for a Norman early morning…. Several runners fainted on the race or upon arrival and the faces of most runners showed the strain. But I first and primarily want to congratulate my mom for walking the 6⁻ km the previous evening despite serious health issues in the previous months, as well as my mother in-law who walked with her.

Infomocracy [book review]

Posted in Books, Travel with tags , , , , , , , , , on June 17, 2017 by xi'an

Infomocracy is a novel by Malka Older set in a near future where most of the Earth is operating under a common elective system where each geographical unit of 100,000 people elect a local representative that runs this unit according to the party’s program and contributes to elect a Worldwide government, except for some non-democratic islets like Saudi Arabia. The whole novel revolves around the incoming election, with different parties trying to influence the outcome in their favour, some to the point of instating a dictature. Which does not sound that different from present times!, with the sligth difference that the whole process is controlled by Information, a sort of World Wide Web that seems to operate neutrally above states and parties, although the book does not elaborate on how this could be possible. The story is told through four main (and somewhat charicaturesque) characters, working for or against the elections and crossing paths along the novel. Certainly worth reading if not outstanding. (And definitely not “one of the greatest literary debuts in recent history”!)

The book is more interesting as a dystopia on electoral systems and the way the information revolution can produce a step back in democracy, with the systematisation of fake news and voters’ manipulation, where the marketing research group YouGov has become a party, than as a science-fiction (or politics-fiction) book. Indeed, it tries too hard to replicate The cyberpunk reference, William Gibson’s Neuromancer, with the same construct of interlacing threads, the same fascination for Japan, airports, luxury hotels, if not for brands, and a similar ninja-geek pair of characters. And with very little invention about the technology of the 21st Century.  (And a missed opportunity to exploit artificial intelligence themes and the prediction of outcomes when Information builds a fake vote database but does not seem to mind about Benford’s Law.) The acknowledgement section somewhat explains this imbalance, in that the author worked many years in humanitarian organisations and is currently completing a thesis at Science Po’ (Paris).

Rouen noir [jatp]

Posted in pictures, Travel with tags , , , , on June 16, 2017 by xi'an

convergence of MCMC

Posted in Statistics with tags , , , , , , , , , on June 16, 2017 by xi'an

Michael Betancourt just posted on arXiv an historical  review piece on the convergence of MCMC, with a physical perspective.

“The success of these of Markov chain Monte Carlo, however, contributed to its own demise.”

The discourse proceeds through augmented [reality!] versions of MCMC algorithms taking advantage of the shape and nature of the target distribution, like Langevin diffusions [which cannot be simulated directly and exactly at the same time] in statistics and molecular dynamics in physics. (Which reminded me of the two parallel threads at the ICMS workshop we had a few years ago.) Merging into hybrid Monte Carlo, morphing into Hamiltonian Monte Carlo under the quills of Radford Neal and David MacKay in the 1990’s. It is a short entry (and so is this post), with some background already well-known to the community, but it nonetheless provides a perspective and references rarely mentioned in statistics.

Bayesian decision riddle

Posted in Books, Kids, Statistics with tags , , , , on June 15, 2017 by xi'an

The current puzzle on The Riddler is a version of the secretary problem with an interesting (?) Bayesian solution.

Given four positive numbers x¹, x², x³, x⁴, observed sequentially, the associated utility is the value of x at the stopping time. What is the optimal stopping rule?

While nothing is mentioned about the distribution of the x’s, I made the assumption that they were iid and uniformly distributed over (0,M), with M unknown and tried a Bayesian resolution with the non-informative prior π(M)=1/M. And failed. The reason for this failure is that the expected utility is infinite at the first step: while the posterior expected utility is finite with three and two observations, meaning I can compare stopping and continuing at the second and third steps, the predicted expected reward for continuing after observing x¹ does not exist because the expected value of max(x¹,x²) given x¹ does not exist. As the predictive density of x² is max(x¹,x²)⁻²…  Several alternatives are possible to bypass this impossible resolution, from changing the utility function to picking another reference prior.

For instance, using a prior like π(M)=1/M² l(and the same monetary return utility) leads to a proper optimal solution, namely

  1. always wait for the second observation x²
  2. stop at x² if x²>11x¹/12, else wait for x³
  3. stop at x³ if x³>23 max(x¹,x²)/24, else observe x⁴

obtained analytically on a bar table in Rouen (and checked numerically later).

Another approach is to try to optimise the probability to pick the largest amount of the four x’s, but this is not leading to an interesting solution, since it corresponds to picking the first maximum after x¹, while picking the largest among remaining ones leads to a somewhat convoluted solution I have no patience to produce here! Plus this is not a really pertinent loss function as it does not discriminate enough against waiting…