re-re-relevant statistics for ABC model choice

After a very, very long delay, we eventually re-revised our paper about necessary and sufficient conditions on summary statistics to be relevant for model choice (i.e. to lead to consistent tests). Reasons, both good and bad, abound for this delay! Some (rather bad) were driven by the completion of a certain new edition… Some (fairly good) are connected with the requests from the Series B editorial team, towards improving our methodological input.  As a result we put more emphasis on the post-ABC cross-checking for the relevance of the summary choice, via a predictive posterior evaluation of the means of the summary statistic under both models and a test for mean equality. And re-ran a series of experiments on a three population population genetic example. Plus, on the side, simplified some of our assumptions. I dearly hope the paper can make it through but am also looking forward the opinion of the Series B editorial team  The next version of Relevant statistics for Bayesian model choice should be arXived by now (meaning when this post appears!).