Bertorelle, Benazzo and Mona have published a nice survey about ABC in Molecular Ecology. It is available on-line and can be downloaded. The nine steps are summarised in the above graph. Step 6 corresponds to ABC model selection, but Step 7 follows the suggestion found in DIYABC to generate pseudo-observed data (pods) to evaluate the “type I – type II” errors of the procedure. In Step 9, a second quality control is proposed via ABC posterior predictive tests. The survey also makes an interesting link with an early version of ABC published by Weiss and von Haessler (1998, Genetics).
My only criticisms are, beyond the lack of confidence in ABC model selection, about an unclear discussion of the “controversial results” about ABC-MCMC and ABC-PMC. The fact that reference tables as those produced by DIYABC can be recycled with “limited additional effort” is however a good point in favour of Monte Carlo evaluations of estimation and model selection procedures.