About incoherent inference

TL;DR

This paper critiques Templeton (2010)'s claims about the mathematical correctness of ABC algorithms, clarifying that the issues are rooted in Bayesian foundations rather than computational methods.

Contribution

It clarifies the statistical errors in Templeton (2010) and defends the validity of ABC algorithms against foundational criticisms.

Findings

Identifies errors in Templeton (2010)'s critique of ABC

Reaffirms the mathematical correctness of ABC methods

References broader rebuttal by Beaumont et al. (2010)

Abstract

In Templeton (2010), the Approximate Bayesian Computation (ABC) algorithm (see, e.g., Pritchard et al., 1999, Beaumont et al., 2002, Marjoram et al., 2003, Ratmann et al., 2009) is criticised on mathematical and logical grounds: "the [Bayesian] inference is mathematically incorrect and formally illogical". Since those criticisms turn out to be bearing on Bayesian foundations rather than on the computational methodology they are primarily directed at, we endeavour to point out in this note the statistical errors and inconsistencies in Templeton (2010), refering to Beaumont et al. (2010) for a reply that is broader in scope since it also covers the phylogenetic aspects of nested clade versus a model-based approach.