I thought further about your second point: I do not think comparing Bayes Factors based on two different statistics can operate because in this case there is necessarily a different term in front of the ABC likelihood because of the factorisation theorem… Even in cases when those two statistics are both perfectly sufficient for model comparison.

]]>I am very glad the ABC-user community is aware of this fact, making our “story” a footnote. However I am wondering then why Bayes factors relying on ABC output keep being used in published papers.

]]>So I’d agree with Christian that “this does not sound a particularly novel and fundamental result,” [paraphrasing…] and accordingly the statistical content of this article as it stands is quite weak. I’d suggest that this paper be revised into a more substantial data-analysis article (that is, where primary focus is on the analysis, not the Bayes Factor “story”), and then interweave the above content into it. That is, the current content could be a pertinent footnote to a rather more interesting article than is presently the case.

]]>Basil: The current paper is arXiv:1101.5091 and the earlier paper on Gibbs random fields is discussed in this post and is arXiv:0807.2767. Links to other papers (Toni and Stumpf) can be found in older posts…

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