Archive for Université Paris Dauphine

Couplings and Monte Carlo [advanced graduate course at Dauphine by Pierre Jacob]

Posted in Kids, pictures, Statistics, Travel with tags , , , , , , on January 20, 2020 by xi'an

As a visiting professor at Paris-Dauphine next month, Pierre Jacob will give a series of lectures on coupling and Monte Carlo. Next month on Feb. 12, 25, 26, 27, at Université Paris-Dauphine, all starting at 13:45 (room yet to be announced). Attendance is open to all and material will be made available on the lecture webpage.

repulsive postdoc!

Posted in Statistics with tags , , , , , , , , , , on December 20, 2019 by xi'an

Rémi Bardenet has been awarded an ERC grant on Monte Carlo integration via repulsive point processes and is now looking for a postdoc starting next March. (Our own ABSINT ANR grant still has an open offer of a postdoctoral position on approximate Bayesian methods, feel free to contact me if potentially interested.)

an arithmetic mean identity

Posted in Books, pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , , , on December 19, 2019 by xi'an

A 2017 paper by Ana Pajor published in Bayesian Analysis addresses my favourite problem [of computing the marginal likelihood] and which I discussed on the ‘Og, linking with another paper by Lenk published in 2012 in JCGS. That I already discussed here last year. Lenk’s (2009) paper is actually using a technique related to the harmonic mean correction based on HPD regions Darren Wraith and myself proposed at MaxEnt 2009. And which Jean-Michel and I presented at Frontiers of statistical decision making and Bayesian analysis in 2010. As I had only vague memories about the arithmetic mean version, we discussed the paper together with graduate students in Paris Dauphine.

The arithmetic mean solution, representing the marginal likelihood as the prior average of the likelihood, is a well-known approach used as well as the basis for nested sampling. With the improvement consisting in restricting the simulation to a set Ð with sufficiently high posterior probability. I am quite uneasy about P(Ð|y) estimated by 1 as the shape of the set containing all posterior simulations is completely arbitrary, parameterisation dependent, and very random since based on the extremes of this posterior sample. Plus, the set Ð converges to the entire parameter space with the number of posterior simulations. An alternative that we advocated in our earlier paper is to take Ð as the HPD region or a variational Bayes version . But the central issue with the HPD regions is how to construct these from an MCMC output and how to compute both P(Ð) and P(Ð|y). It does not seem like a good idea to set P(Ð|x) to the intended α level for the HPD coverage. Using a non-parametric version for estimating Ð could be in the end the only reasonable solution.

As a test, I reran the example of a conjugate normal model used in the paper, based on (exact) simulations from both the prior and  the posterior, and obtained approximations that were all close from the true marginal. With Chib’s being exact in that case (of course!), and an arithmetic mean surprisingly close without an importance correction:

> print(c(hame,chme,came,chib))
[1] -107.6821 -106.5968 -115.5950 -115.3610

Both harmonic versions are of the right order but not trustworthy, the truncation to such a set Ð as the one chosen in this paper having little impact.

sampling the mean

Posted in Kids, R, Statistics with tags , , , , , on December 12, 2019 by xi'an

A challenge found on the board of the coffee room at CEREMADE, Université Paris Dauphine:

When sampling with replacement three numbers in {0,1,…,N}, what is the probability that their average is (at least) one of the three?

With a (code-golfed!) brute force solution of

mean(!apply((a<-matrix(sample(0:n,3e6,rep=T),3)),2,mean)-apply(a,2,median))

producing a graph pretty close to 3N/2(N+1)² (which coincides with a back-of-the-envelope computation):temp

unbiased MCMC discussed at the RSS tomorrow night

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on December 10, 2019 by xi'an

The paper ‘Unbiased Markov chain Monte Carlo methods with couplings’ by Pierre Jacob et al. will be discussed (or Read) tomorrow at the Royal Statistical Society, 12 Errol Street, London, tomorrow night, Wed 11 December, at 5pm London time. With a pre-discussion session at 3pm, involving Chris Sherlock and Pierre Jacob, and chaired by Ioanna Manolopoulou. While I will alas miss this opportunity, due to my trip to Vancouver over the weekend, it is great that that the young tradition of pre-discussion sessions has been rekindled as it helps put the paper into perspective for a wider audience and thus makes the more formal Read Paper session more profitable. As we discussed the paper in Paris Dauphine with our graduate students a few weeks ago, we will for certain send one or several written discussions to Series B!

digital humanities meet artificial intelligence [course]

Posted in Statistics with tags , , , , , , , , , , on December 6, 2019 by xi'an

Paris Sciences & Lettres University (PSL) is organising next semester a special one-week training on the topic “Digital Humanities Meet Artificial Intelligence”. This course is open to Master and PhD students, as well and researchers, subject to availability (and free). This intensive training will cover theoretical, numerical and applicative topics at the intersection between both fields. The dates are March 30-April 3, 2020, the course is located in downtown Paris, and the pre-registration form is already on-line. The courses are given by

back from HKU

Posted in Kids, pictures, Travel, University life with tags , , , , , , , , , on November 16, 2019 by xi'an