Several interesting questions were raised during my seminar talk at Oxford. First, David Cox suggested I looked at the collection of the two p-values in the Poisson and geometric cases to check whether or not they could point out at a disagreement. (I am however unsure at how the p-values should be computed in this case, maybe as a likelihood-ratio test…) Chris Holmes asked about what happened to the ABC Bayes factor when both models were wrong. I had not thought of this earlier and will look into it: my first impression is that there is no reason for the same model to be chosen. It depends on the relative tail behaviour of the distribution of the summary statistics under both models… Stephen Lauritzen mentioned prior to the seminar a highly relevant book by a Copenhagen mathematician, whose definition of conditional densities was perfectly suited for constructing a convergence proof for ABC (to be incorporated in my Roma slides, if feasible). During the talk, he also pointed out at other (counter)examples of models where sufficient statistics remained sufficient across models: e.g., contingency tables with pairwise interactions. Arnaud Doucet got back to the Potts model (counter)example to stress that we needed perfect sampling to make it work and that our MCMC alternative could be adding another level of approximation to the process, which is quite right!
On the less academic side, I was in Oxford only for a short while, being due back in Paris for a presentation of our Statistics Master: I stil managed a short run in the morning in a nearby park where I saw a heron (blurred above!), as well as hints of the coming Spring (left) but I wish I had had more time (and indications!) to run along the rowers as I did in Cambridge. (I also wish I had had time to visit Tolkien’s favourite pub! Although I had a beer at the Lamb and Flag, which served as a meeting place for the later members of the Inklings…)
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