**W**e just [arXived and] submitted to Statistics & Computing special issue on ABC a paper on ABC model assessment with Olli Ratman, Pierre Pudlo and Sylvia Richardson. The central idea is to incorporate the errors within the ABC simulation, thanks to an extra prior and a kernel acceptance probability on those errors. The existing ABC algorithms can be modified to this effect. This short paper thus extends the earlier PNAS paper by Olli et al. to include the MH and SIS ABC extensions, and to test those on several applications: network, dynamical systems, and population genetics. In the later case, while the ABC estimated Bayes factor agrees with an importance sampling approximation, we show that the measure of discrepancy provided by our approach highlights a poor fit of both models under comparison. Although we (Natesh Pillai, Jean-Michel Marin, Judith Rousseau and myself) are currently making progress towards an indicator of worth for the ABC Bayes factor approximation, these exploratory tools are quite valuable to defend an ABC approach to model evaluation and to model choice.

## Archive for June, 2011

## ABC model assessment

Posted in Statistics with tags ABC, Bayesian model choice on June 30, 2011 by xi'an## LaTeX search

Posted in Statistics, University life with tags Bayes theorem, LaTeX on June 30, 2011 by xi'an**W**hen visiting Springer site, I spotted a window advertising LaTeX Search. This is a webpage that produces (Springer published) papers involving the LaTeX code entered by the user. The idea is nice. However, given the number of ways one can type a LaTeX command, (and the limited number of LaTeX “snippets” available, a modest 3 millions…), I wonder about the final utility of this (free) product! For instance, when typing

\pi(\theta|x_1,\ldots,x_n) \propto \pi(\theta)

I could not find any relevant document. Even

\pi(\theta|x_1,\ldots,x_n) \propto \pi(\theta)

did not show an exact equivalence. Even though Bayes’ formula eventually showed up

\pi(\theta|{\mathbf{x}}) = \frac{\pi(\theta)L(\theta|{\mathbf{x}})} {\int_{\Uptheta} \pi(\theta)L(\theta|{\mathbf{x}}) \hbox{d}\theta} \propto \pi(\theta)L(\theta|{\mathbf{x}})

I therefore remain unconvinced by the relevance of the concept! Unless one looks for a very specific and concise object.

## Hotel with a blog

Posted in pictures, Travel, University life with tags Berlin, Richard von Mises, Unter den Linden on June 29, 2011 by xi'an**F**or my visit to Berlin tomorrow, I am staying in the Circus Hotel, which happens to have a true blog…! Amazing! Looking forward my visit to Berlin…

## Quantile distributions

Posted in Statistics, University life with tags ABC, quantile distribution on June 29, 2011 by xi'an**K**errie Mengersen, who is visiting CREST and Dauphine this month, showed me a 2009 paper she had published in ** Statistics and Computing** along with D. Allingham and R. King on an application of ABC to quantile distributions. Those distributions are defined by a closed-form quantile function, which makes them easy to simulate by a simple uniform inversion, and a mostly unavailable density function, which makes any approach but ABC difficult or at least costly to implement. For instance, the

*g*-and-

*k*distribution is given by

hence can be simulated by a single call to a normal simulation. This is therefore a good benchmark for realistic albeit simple examples to use in ABC calibration and we are currently experimenting with it.

## From my office

Posted in pictures, University life with tags bois de Boulogne, La Défense, Université Paris Dauphine on June 28, 2011 by xi'an## density()

Posted in R, Statistics with tags ABC, Bayesian model choice, density, histogram, R on June 28, 2011 by xi'an**F**ollowing my earlier posts on the revision of Lack of confidence, here is an interesting outcome from the derivation of the exact marginal likelihood in the Laplace case. Computing the posterior probability of a normal model versus a Laplace model in the normal (gold) and the Laplace (chocolate) settings leads to the above histogram(s), which show(s) that the Bayesian solution is discriminating (in a frequentist sense), even for 21 observations. If instead I use R density() over the posterior probabilities, I get this weird and unmotivated flat density in the Laplace case. It looked as if the (frequentist) density of the posterior probability under the alternative was uniform, although there is no reason for this phenomenon!

## Bayesian Fall school in La Rochelle

Posted in Kids, R, Statistics, Travel, University life with tags Bayesian statistics, BUGS, INRA, La Rochelle, R, school on June 27, 2011 by xi'an**T**he French agronomy research institute INRA is organising a Fall school in La Rochelle, Nov. 28 – Dec. 02, on Bayesian methods, oriented towards the applications in food sciences, environmental sciences, and biology. The provisional program (in French) is

■ Initiation aux outils informatiques R et WinBUGS (TP et réalisation de projets sur ordinateur)

■ Rappels en probabilité et initiation aux modèles graphiques

■ Introduction de la démarche bayésienne à travers des exemples simples

■ Quelques aspects et anecdotes sur l’histoire passée et récente de la statistique bayésienne

■ Estimation des distributions a posteriori à l’aide de méthodes numériques (MCMC etc.)

■ Evaluation et sélection de modèles en statistique bayésienne

■ Distributions a priori et élicitation

■ Exposés prospectifs sur les méthodes bayésiennes

**T**he instructors will be Sophie Ancelet, Chantal Guihenneuc-Jouyaux, and Jean-Michel Marin. There are still a few places available and the registration deadline is June 30. *(The above picture is a painting by Henri-Paul Motte of Richelieu during the year long siege of La Rochelle in 1628, painting that was included in my primary school history book and that I then found fascinating…)*