Medellin

My nephew Paul and a fellow student made this nice mute video as a final project of his cinema degree in Rennes:

congrats!

This week, our daughter is taking her final exams of her medical studies! Which means competing for the residency specialties and locations at a national level, since the ranking in this competition fully determines the order in selecting one’s residency and hence specialty. Over the past six years, she went though semester exams that were more standard, as well as over thirty externships (as above in the emergency ward at Bicêtre), hence qualified to be a doctor, but this competition is somewhat the most important for medical students who are not considering general practice as a first choice… (In the past years, the least popular specialties were psychiatry, epidemiology, and occupational medicine.) Hence, a particularly stressful moment for them, for which they have been insanely preparing for the past three years. Whatever the outcome of the competition happens to be, congrats to our daughter and her friends for the hard work and the dedication they demonstrated throughout the years, despite the demands imposed by the COVID crisis and despite the absurd features of medical studies in France..!

journal of the [second] plague year [away]

Read Fred Vargas’s Seeking Whom He May Devour (L’Homme à l’envers), which I found on a bookshelf of our vacation rental in Annecy. And got more quickly bored by the story as it is plagued with the same defects as the ones I read before, from a definitive issue with Canadians (!), to an attempt to bring supernatural causes in the story and reveal them as fake by the end of the book, to a collection of implausible and caricaturesque characters surrounded by the usual backcountry morons that would rather fit a Paasilinna novel, and to the incomprehensible intuitions of Inspector Adamsberg. I also went through the sequel to Infomocracy, Null states, albeit this was a real chore as it lacked substance and novelty (the title by itself should have been a warning!).

Watched Night in Paradise (낙원의 밤), another Korean gangster movie, which seems to repeat the trope of bad-guy-on-the-run-meets-lost-girl found in my previously watched Korean Jo-Phil: The Dawning Rage, where the main character, a crooked police officer is radically impacted after failing to save a lost teenager.  (And also in the fascinating The Wild Goose Lake.) The current film is stronger however in creating the bond between the few-words gangster on the run and the reluctant guest Jae-yeon who is on a run of a different magnitude. While the battle scenes are still grand-guignolesque (if very violent) in a Kill Bill spirit, and the gang leaders always caricaturesque, the interplay between the main characters makes Night in Paradise a pretty good film (and explains why it got selected for the Venice Film Festival of 2020). Also went through the appalling Yamakasi by Luc Besson, a macho, demagogical, sexist, simplist, non-story…

more air [&q’s] for MCMC [comments]

[A rich set of comments by Tom Loredo about convergence assessments for MCMC that I feel needs reposting:]

Two quick points:

• By coincidence (and for a different problem), I’ve just been looking at the work of Gorham & Mackey that I believe Pierre is referring to. This is probably the relevant paper: “Measuring Sample Quality with Kernels“.
• Besides their new rank-based R-hat, bloggers on Gelman’s blog have also pointed to another R-hat replacement, R, developed by some Stan team members; it is “based on how well a machine learning classifier model can successfully discriminate the individual chains.” See: “R: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers”.

In addition, here’s an anecdote regarding your comment, “I remain perplexed and frustrated by the fact that, 30 years later, the computed values of the visited likelihoods are not better exploited.”

That has long bothered me, too. During a SAMSI program around 2006, I spent time working on one approach that tried to use the prior*likelihood (I call it q(θ), for “quasiposterior” and because it’s next to “p”!) to compute the marginal likelihood. It would take posterior samples (from MCMC or another approach) and find their Delaunay triangulation. Then, using q(θ) on the nodes of the simplices comprising the triangulation, it used a simplicial cubature rule to approximate the integral of q(theta) over the volume spanned by the samples.

As I recall, I only explored it with multivariate normal and Student-t targets. It failed, but in an interesting way. It worked well in low dimensions, but gave increasingly poor estimates as dimension grew. The problem appeared related to concentration of measure (or the location of the typical set), with the points not sufficiently covering the center or the large volume in the tails (or both; I can’t remember what diagnostics said exactly).

Another problem is that Delaunay triangulation gets expensive quickly with growing dimension. This method doesn’t need an optimal triangulation, so I wondered if there was a faster sub-optimal triangulation algorithm, but I couldn’t find one.

An interesting aspect of this approach is that the fact that the points are drawn from the prior doesn’t matter. Any set of points is a valid set of points for approximating the integral (in the spanned volume). I just used posterior samples because I presumed those would be available from MCMC. I briefly did some experiments taking the samples, and reweighting them to draw a subset for the cubature that was either over- or under-dispersed vs. the target. And one could improve things this way (I can’t remember what choice was better). This suggests that points drawn from q(theta) aren’t optimal for such cubature, but I never tried looking formally for the optimal choice.

I called the approach “adaptive simplicial cubature,” adaptive in the sense that the points are chosen in a way that depends on the integrand.

The only related work I could find at the time was work by you and Anne Philippe on Riemanns sums with MCMC (https://doi.org/10.1023/A:1008926514119). I later stumbled upon a paper on “random Riemann sum estimators” as an alternative to Monte Carlo that seems related but that I didn’t explore further (https://doi.org/10.1016/j.csda.2006.09.041).

I still find it hard to believe that the q values aren’t useful. Admittedly, in an n-dimensional distribution, it’s just 1 more quantity available beyond the n that comprise the sample location. But it’s a qualitatively different type of information from the sample location, and I can’t help but think there’s some clever way to use it (besides emulating the response surface).

genuine Latinsquare rectangle