ABC model choice via random forests [and no fire]

While my arXiv newspage today had a puzzling entry about modelling UFOs sightings in France, it also broadcast our revision of Reliable ABC model choice via random forests, version that we resubmitted today to Bioinformatics after a quite thorough upgrade, the most dramatic one being the realisation we could also approximate the posterior probability of the selected model via another random forest. (With no connection with the recent post on forest fires!) As discussed a little while ago on the ‘Og. And also in conjunction with our creating the abcrf R package for running ABC model choice out of a reference table. While it has been an excruciatingly slow process (the initial version of the arXived document dates from June 2014, the PNAS submission was rejected for not being enough Bayesian, and the latest revision took the whole summer), the slow maturation of our thoughts on the model choice issues led us to modify the role of random forests in the ABC approach to model choice, in that we reverted our earlier assessment that they could only be trusted for selecting the most likely model, by realising this summer the corresponding posterior could be expressed as a posterior loss and estimated by a secondary forest. As first considered in Stoehr et al. (2014). (In retrospect, this brings an answer to one of the earlier referee’s comments.) Next goal is to incorporate those changes in DIYABC (and wait for the next version of the software to appear). Another best-selling innovation due to Arnaud: we added a practical implementation section in the format of FAQ for issues related with the calibration of the algorithms.