**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.