Sousaphonic graph!

Notre-Dame-de-Paris analysed by Andrew [not a book review]

As reported in Le Monde, Alexander van Geen, Yuling Yao, Tyler Ellis, and Andrew Gelman wrote a paper analysing the impact of the destruction of Notre-Dame last year in terms of lead concentration in the ground. As 460 tons of lead from the roof melted overnight. Based on  100 samples of surface soil collected by one author (not Andrew!) from tree pits, parks, and other sites in all directions within 1 km of the cathedral. Here is a plain language summary of the findings.

“This study attempts to estimate the extent to which the population of Paris was exposed to lead as a result of the Notre‐Dame cathedral fire of April 15, 2019. The concern stems from the large quantity of lead that covered the cathedral, some of which was injected into the air by the fire for several hours. In order to evaluate how much lead rising from the fire was redeposited nearby, surface soil samples were collected in all directions within a 1 km radius of the cathedral. Elevated levels of lead observed downwind of the cathedral indicate that surface soil preserved the mark of lead fallout from the fire. Although the estimated amount of lead redeposited within 1 km corresponds to only a small fraction of the total covering the cathedral, it could have posed a health hazard to children located downwind for a limited amount of time. Environmental testing on a larger scale immediately after the fire could have provided a more timely assessment of the scale of the problem and resulted in more pointed advice to the surrounding population on how to limit exposure to the fallout of lead.”

The statistical modelling is one of a spatial pattern of the lead distribution, using a mean-zero Gaussian process prior. And of a discretisation of the neighbourhood of the cathedral into uniform 30×30 locations. Without any further input, the model identifies properly the direction of the wind on that fateful evening. And logically concludes to a higher exposure than measured weeks after the fire. (Minor quibbles: a bias in self-declared test toward “a more educated, wealthier segment of the population” is unlikely in the immediate neighbourhood of Notre-Dame where the average flat sells at 16,000 euros per m², and the LCPP (Laboratoire Central de la Préfecture de Police) is not affiliated with the City of Paris but the Ministry of the Interior.)

truncated Gumbels

As I had to wake up pretty early on Easter morning to give my daughter a ride, while waiting I came upon this calculus question on X validated of computing the conditional expectation of a Gumbel variate, conditional on its drifted version being larger than another independent Gumbel variate with the same location-scale parameters. (Just reminding readers that a Gumbel G(0,1) variate is a double log-uniform, i.e., can be generated as X=-log(-log(U)).) And found after a few minutes (and a call to Wolfram Alpha integrator) that

which is simple enough to make me wonder if there is a simpler derivation than the call to the exponential integral Ei(x) function. (And easy to check by simulation.)

Incidentally, I discovered that Emil Gumbel had applied statistical analysis to the study of four years of political murders in the Weimar Republic, demonstrating the huge bias of the local justice towards right-wing murders. When he signed the urgent call [for the union of the socialist and communist parties] against fascism in 1932, he got expelled from his professor position in Heidelberg and emigrated to France, which he had to leave again for the USA on the Nazi invasion in 1940. Where he became a professor at Columbia.

a vignette on Metropolis

Over the past week, I wrote a short introduction to the Metropolis-Hastings algorithm, mostly in the style of our Introduction to Monte Carlo with R book, that is, with very little theory and worked-out illustrations on simple examples. (And partly over the Atlantic on my flight to New York and Columbia.) This vignette is intended for the Wiley StatsRef: Statistics Reference Online Series, modulo possible revision. Again, nothing novel therein, except for new examples.

back from New York

A greatly enjoyable [if a wee bit tight] visit to Columbia University for my  seminar last Monday! (And a reasonably smooth trip if I forget about the screaming kids on both planes…!) Besides discussing with several faculty on our respective research interests, and explaining our views on replacing Bayes factors and posterior probabilities, views that were not strongly challenged by the seminar audience, maybe because it sounded too Bayesiano-Bayesian!, I had a great time catching up (well, almost!) with Andrew, running for one hour by the river both mornings, and even biking—does not feel worse than downtown Paris!—with Andrew a few miles to a terrific tiny Mexican restaurant in South Bronx, El Atoradero where I had a home-made tortilla (or pupusa) filled with beans and covered with hot chorizo! (The restaurant was selected as the 2014 best Mexican restaurant in New York City by The Village Voice, whatever that means. And also has a very supportive review in The New York Times.) It was so good I (very exceptionally) ordered a second serving of spicy pork huarache, which was almost as good. And kept me well-fed till the next day, when I arrived in Paris. And with enough calories to fight the cold melted snow that fell when biking back to the office at Columbia. I also had an interesting morning in a common room at Columbia, working next to graduate students and hearing their conversations about homeworks and advisors (nothing to gossip about as their comments were invariably laudatory!, maybe because they suspected me of being a mole!)