Archive for Siméon Poisson

Laplace great⁶-grand child!

Posted in Kids, pictures, Statistics, University life with tags , , , , , , , , , on August 3, 2015 by xi'an

eulerchild1laplacechildLooking at the Family Tree application (I discovered via Peter Coles’ blog), I just found out that I was Laplace’s [academic] great-great-great-great-great-great-great-grand-child! Through Poisson and Chasles. Going even further, as Simeon Poisson was also advised by Lagrange, my academic lineage reaches Euler and the Bernoullis. Pushing always further, I even found William of Ockham along one of the “direct” branches! Amazing ancestry, to which my own deeds pay little homage if any… (However, I somewhat doubt the strength of the links for the older names, since pursuing them ends up at John the Baptist!)

I wonder how many other academic descendants of Laplace are alive today. Too bad Family Tree does not seem to offer this option! Given the longevity of both Laplace and Poisson, they presumably taught many students, which means a lot of my colleagues and even of my Bayesian colleagues should share the same illustrious ancestry. For instance, I share part of this ancestry with Gérard Letac. And both Jean-Michel Marin and Arnaud Guillin. Actually, checking with the Mathematics Genealogy Project, I see that Laplace had… one student!, but still a grand total of [at least] 85,738 descendants… Incidentally, looking at the direct line, most of those had very few [recorded] descendants.

the Poisson transform

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , on June 19, 2014 by xi'an

In obvious connection with an earlier post on the “estimation” of normalising constants, Simon Barthelmé and Nicolas Chopin just arXived a paper on The Poisson transform for unormalised statistical models. Obvious connection because I heard of the Guttmann and Hyvärinen (2012) paper when Simon came to CREST to give a BiP talk on this paper a few weeks ago. (A connected talk he gave in Banff is available as a BIRS video.)

Without getting too much into details, the neat idea therein is to turn the observed likelihood

\sum_{i=1}^n f(x_i|\theta) - n \log \int \exp f(x|\theta) \text{d}x

into a joint likelihood

\sum_{i=1}^n[f(x_i|\theta)+\nu]-n\int\exp[f(x|\theta)+\nu]\text{d}x

 which is the likelihood of a Poisson point process with intensity function

\exp\{ f(x|\theta) + \nu +\log n\}

This is an alternative model in that the original likelihood does not appear as a marginal of the above. Only the modes coincide, with the conditional mode in ν providing the normalising constant. In practice, the above Poisson process likelihood is unavailable and Guttmann and Hyvärinen (2012) offer an approximation by means of their logistic regression.

Unavailable likelihoods inevitably make me think of ABC. Would ABC solutions be of interest there? In particular, could the Poisson point process be simulated with no further approximation? Since the “true” likelihood is not preserved by this representation, similar questions to those found in ABC arise, like a measure of departure from the “true” posterior. Looking forward the Bayesian version! (Marginalia: Siméon Poisson died in Sceaux, which seemed to have attracted many mathematicians at the time, since Cauchy also spent part of his life there…)