**I**n the first issue of this year Biometrika, I spotted a paper with the above title, written by Wang, Kim, and Yang, and thought it was a particular case of ABC. However, when I read it on a rare metro ride to Dauphine, thanks to my hurting knee!, I got increasingly disappointed as the contents had nothing to do with ABC. The purpose of the paper was to derive a consistent and convergent posterior distribution based on a estimator of the parameter θ that is… consistent and convergent under informative sampling. Using for instance a Normal approximation to the sampling distribution of this estimator. Or to the sampling distribution of the pseudo-score function, S(θ) [which pseudo-normality reminded me of Ron Gallant’s approximations and of my comments on them]. The paper then considers a generalisation to the case of estimating equations, U(θ), which may again enjoy a Normal asymptotic distribution. Involving an object that does not make direct Bayesian sense, namely the posterior of the parameter θ given U(θ)…. (The algorithm proposed to generate from this posterior (8) is also a mystery.) Since the approach requires consistent estimators to start with and aims at reproducing frequentist coverage properties, I am thus at a loss as to why this pseudo-Bayesian framework is adopted.

## Archive for RER B

## approximate Bayesian inference under informative sampling

Posted in Books, Statistics, Travel, University life with tags ABC, approximate Bayesian inference, Bayesian semi-parametrics, Bernstein-von Mises theorem, Biometrika, estimating equations, generalised method of moments, RER B, Ron Gallant, sampling on March 30, 2018 by xi'an## simulation in Gare du Nord [jatp]

Posted in Statistics with tags ads, COP 21, France, Gare du Nord, jatp, métro, Paris, RER B, simulation on January 30, 2018 by xi'an## O’Bayes in action

Posted in Books, Kids, Statistics, University life with tags bois de Boulogne, Charles de Gaulle, invariance, Jeffreys priors, La Défense, mathematical puzzle, noninformative priors, O-Bayes 2017, objective Bayes, randomisation, RER B, Roissy, Université Paris Dauphine on November 7, 2017 by xi'an**M**y next-door colleague [at Dauphine] François Simenhaus shared a paradox [to be developed in an incoming test!] with Julien Stoehr and I last week, namely that, when selecting the largest number between a [observed] and b [unobserved], drawing a random boundary on a [meaning that a is chosen iff a is larger than this boundary] increases the probability to pick the largest number above ½2…

When thinking about it in the wretched RER train [train that got immobilised for at least two hours just a few minutes after I went through!, good luck to the passengers travelling to the airport…] to De Gaulle airport, I lost the argument: if a<b, the probability [for this random bound] to be larger than a and hence for selecting b is 1-Φ(a), while, if a>b, the probability [of winning] is Φ(a). Hence the only case when the probability is ½ is when a is the median of this random variable. But, when discussing the issue further with Julien, I exposed an interesting non-informative prior characterisation. Namely, if I assume a,b to be iid U(0,M) and set an improper prior 1/M on M, the conditional probability that b>a given a is ½. Furthermore, the posterior probability to pick the right [largest] number with François’s randomised rule is also ½, no matter what the distribution of the random boundary is. Now, the most surprising feature of this coffee room derivation is that these properties only hold for the prior 1/M. Any other power of M will induce an asymmetry between a and b. (The same properties hold when a,b are iid Exp(M).) Of course, this is not absolutely unexpected since 1/M is the invariant prior and since the “intuitive” symmetry only holds under this prior. Power to O’Bayes!

When discussing again the matter with François yesterday, I realised I had changed his wording of the puzzle. The original setting is one with two cards hiding the unknown numbers a and b and of a player picking one of the cards. If the player picks a card at random, there is indeed a probability of ½ of picking the largest number. If the decision to switch or not depends on an independent random draw being larger or smaller than the number on the observed card, the probability to get max(a,b) in the end hits 1 when this random draw falls into (a,b) and remains ½ outside (a,b). Randomisation pays.

## trip to München

Posted in Mountains, Statistics, Travel, University life, Wines with tags ABC, Astrophysics, Bavaria, Charles de Gaulle, dark matter, Eisbier, Germany, Max Planck Institute, Munich, particle physics, population Monte Carlo, RER B, Roissy, Wener-Heisenberg-Institut on October 19, 2015 by xi'an**W**hile my train ride to the fabulous De Gaulle airport was so much delayed that I had less than ten minutes from jumping from the carriage to sitting in my plane seat, I handled the run through security and the endless corridors of the airport in the allotted time, and reached Munich in time for my afternoon seminar and several discussions that prolonged into a pleasant dinner of Wiener Schnitzel and Eisbier. This was very exciting as I met physicists and astrophysicists involved in population Monte Carlo and parallel MCMC and manageable harmonic mean estimates and intractable ABC settings (because simulating the data takes eons!). I wish the afternoon could have been longer. And while this is the third time I come to Munich, I still have not managed to see the centre of town! Or even the nearby mountains. Maybe an unsuspected consequence of the Heisenberg principle…

## art brut

Posted in pictures, Travel with tags 3460, advertising, métro, Paris, pipe, RER B, Saint-Michel on August 5, 2015 by xi'an## life and death along the RER B, minus approximations

Posted in Statistics, Travel with tags Bagneux, boulevard périphérique, France, France Inter, inequalities, Luxembourg, national public radio, Orsay, Paris, Paris suburbs, Périphéries, RER B, Saint-Michel, Stade de France, Yvette on June 30, 2015 by xi'an**W**hile cooking for a late Sunday lunch today [sweet-potatoes röstis], I was listening as usual to the French Public Radio (France Inter) and at some point heard the short [10mn] Périphéries that gives every weekend an insight on the suburbs [on the “other side’ of the Parisian Périphérique boulevard]. The idea proposed by a geographer from Montpellier, Emmanuel Vigneron, was to point out the health inequalities between the wealthy 5th arrondissement of Paris and the not-so-far-away suburbs, by following the RER B train line from Luxembourg to La Plaine-Stade de France…

The disparities between the heart of Paris and some suburbs are numerous and massive, actually the more one gets away from the lifeline represented by the RER A and RER B train lines, so far from me the idea of negating this opposition, but the presentation made during those 10 minutes of Périphéries was quite approximative in statistical terms. For instance, the mortality rate in La Plaine is 30% higher than the mortality rate in Luxembourg and this was translated into the chances for a given individual from La Plaine to die in the coming year are 30% higher than if he [or she] lives in Luxembourg. Then a few minutes later the chances for a given individual from Luxembourg to die are 30% lower than he [or she] lives in La Plaine…. Reading from the above map, it appears that the reference is the mortality rate for the Greater Paris. (Those are 2010 figures.) This opposition that Vigneron attributes to a different access to health facilities, like the number of medical general practitioners per inhabitant, does not account for the huge socio-demographic differences between both places, for instance the much younger and maybe larger population in suburbs like La Plaine. And for other confounding factors: see, e.g., the equally large difference between the neighbouring stations of Luxembourg and Saint-Michel. There is no socio-demographic difference and the accessibility of health services is about the same. Or the similar opposition between the southern suburban stops of Bagneux and [my local] Bourg-la-Reine, with the same access to health services… Or yet again the massive decrease in the Yvette valley near Orsay. The analysis is thus statistically poor and somewhat ideologically biased in that I am unsure the data discussed during this radio show tells us much more than the sad fact that suburbs with less favoured populations show a higher mortality rate.

## Paris Machine Learning Meeting #10 Season 2

Posted in Books, Kids, pictures, Statistics, University life with tags Berlin, data, Jussieu, machine learning, Matlab, Paris Machine Learning Applications group, RER B, robots, Toronto, Université Pierre et Marie Curie, Vowpal on June 17, 2015 by xi'an**T**onight, I am invited to give a speed-presenting talk at the Paris Machine Learning last meeting of Season 2, with the themes of DL, Recovering Robots, Vowpal Wabbit, Predcsis, Matlab, and Bayesian test [by yours truly!] The meeting will take place in Jussieu, Amphi 25, Here are my slides for the meeting:

As it happened, the meeting was quite crowded with talks and plagued with technical difficulties in transmitting talks from Berlin and Toronto, so I came to talk about three hours after the beginning, which was less than optimal for the most technical presentation of the evening. I actually wonder if I even managed to carry the main idea of replacing Bayes factors with posteriors of the mixture weight! *[I had plenty of time to reflect upon this on my way back home as I had to wait for several and rare and crowded RER trains until one had enough room for me and my bike!]*