## Defence of model-based inference

A tribune—to which I contributed—about the virtues of statistical inference in phylogeography  just appeared in Molecular Ecology. (The whole paper seems to be available on line as I can access it.) It has been written by 22 (!) contributors in response to Templeton’s recent criticism of ABC (and his defence of Nested Clade Analysis) in the same journal. My contribution to the paper is mostly based on the arguments posted here last March, namely that the paper was confusing ABC (which is a computational method) with Bayesian statistics. The paper as a whole goes beyond a “Bayesian defence” since not all authors are Bayesian. It supports a statistics based approach to phyleogeography, as reported in the abstract

Recent papers have promoted the view that model-based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested Clade Phylogeographic Analysis (NCPA) offers the best approach in statistical phylogeography. In order to remove the confusion and misconceptions introduced by these papers, we justify and explain the reasoning behind model-based inference. We argue that ABC is a statistically valid approach, alongside other computational statistical techniques that have been successfully used to infer parameters and compare models in population genetics. We also examine the NCPA method and highlight numerous deficiencies, either when used with single or multiple loci. We further show that the ages of clades are carelessly used to infer ages of demographic events, that these ages are estimated under a simple model of panmixia and population stationarity but are then used under different and unspecified models to test hypotheses, a usage the invalidates these testing procedures. We conclude by encouraging researchers to study and use model-based inference in population genetics.

This will most presumably fail to end the debate between the proponents and the opponents of model-based inference in phylogenics and elsewhere, but the point was worth making…

### 8 Responses to “Defence of model-based inference”

1. Is there any formal proof of the convergence (in what sense??) of ABC methods under certain regularity conditions?

Regards.

• Javier: the elementary proof is that, when the tolerance $\epsilon$ goes to zero, the ABC density goes to the true posterior (pointwise convergence)… Other than that, I do not know of a more advanced result.

2. […] rebuttal to Templeton’s (2008, Molecular Ecology) critique of the Bayesian approach by Beaumont et al. (2010, Molecular Ecology) that is broader in scope, since it also covers the phylogenetic aspects […]

3. […] mostly those found in an earlier paper of his’ and discussed in this post as well as in the defence of model based inference twenty-to of us published in Molecular Ecology a few months ago, the paper […]

4. The link in this post doesn’t work.

Second, I find the snapshots previews highly annoying. Food for thought.

• Thanks, Steve. I have corrected the link (this was an early on-line version from Mol. Ecol.) and will see what I can do about the snapshots. (I actually was looking for a way of doing the opposite, as in Andrew Gelman’s blog!) Christian

5. […] that the requirement of Bayesian testing on alternatives is a drawback [as we also argued in the Molecular Ecology disputing paper]. But, tahnks to all its provocative aspects, this was an enjoyable talk and I […]

6. Impressive list of authors! Scott and you in the same paper, nice! :)

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