Another ABC rebuttal
“Given that some logical overlap is common when dealing with complex models, this means that much of the literature using ABC is invalid.” Alan Templeton, July 2010.
I had not noticed another reply to Templeton’s PNAS diatribe against ABC that was published by Csilléry, Blum, Gaggiotti and François in Trends in Ecology and Evolution. This reply follows a letter written by Templeton to this journal and published last July. Alan Templeton takes issue with the inclusion of a box in the nice survey of Csilléry et al. entitled Controversy surrounding ABC. The letter reproduces earlier arguments I already discussed, in particular the “logical impossibility” to have larger models enjoying smaller posterior probabilities than smaller models [that are special cases]. The conclusion that
“1) ABC can and does produce results that are mathematically impossible; 2) the ‘posterior probabilities’ of ABC cannot possibly be true probability measures; and 3) ABC is statistically incoherent (incoherent methods can violate the constraints of formal logic)” Alan Templeton, July 2010.
is thus bringing no novelty to the debate. It is nonetheless mildly irritating to see that Alan Templeton is still advancing “mathematical errors” as his main argument, despite detailed rebuttals published by mathematicians and mathematical statisticians. As demonstrated by the repeated argument that BIC should replace ABC (!), or the decomposition of in the PNAS reply, he is out of his depth on mathematical grounds. However, that he manages to publish a paper like the PNAS diatribe without the journal having a mathematician checking the “mathematical flaws” is more of an issue.