Fig. 4 – Boxplots of the evolution [against ε] of ABC approximations to the Bayes factor. The representation is made in terms of frequencies of visits to [accepted proposals from] models MA(1) and MA(2) during an ABC simulation when ε corresponds to the 10,1,.1,.01% quantiles on the simulated autocovariance distances. The data is a time series of 50 points simulated from a MA(2) model. The true Bayes factor is then equal to 17.71, corresponding to posterior probabilities of 0.95 and 0.05 for the MA(2) and MA(1) models, resp.

The survey we wrote with Jean-Michel Marin, Pierre Pudlo, and Robin Ryder is now published in [the expensive] Statistics and Computing (on-line). Beside recycling a lot of Og posts on ABC, this paper has the (personal) appeal of giving us the first hint that all was not so rosy in terms of ABC model choice. I wonder whether or not it will be part of the ABC special issue.