## discussione a Padova

**H**ere are the slides of my talk in Padova for the workshop Recent Advances in statistical inference: theory and case studies (very similar to the slides for the Varanasi and Gainesville meetings, obviously!, with Peter Müller commenting [at last!] that I had picked the wrong photos from Khajuraho!)

**T**he worthy Padova addendum is that I had two discussants, Stefano Cabras from Universidad Carlos III in Madrid, whose slides are :

and Francesco Pauli, from Trieste, whose slides are:

**T**hese were kind and rich discussions with many interesting openings: Stefano’s idea of estimating the pivotal function *h* is opening new directions, obviously, as it indicates an additional degree of freedom in calibrating the method. Esp. when considering the high variability of the empirical likelihood fit depending on the the function *h*. For instance, one could start with a large collection of candidate functions and build a regression or a principal component reparameterisation from this collection… (Actually I did not get point #1 about ignoring *f*: the empirical likelihood is by essence ignoring anything outside the identifying equation, so as long as the equation is valid..) Point #2: Opposing sample free and simulation free techniques is another interesting venue, although I would not say ABC is “sample free”. As to point #3, I will certainly get a look at Monahan and Boos (1992) to see if this can drive the choice of a specific type of pseudo-likelihoods. I like the idea of checking the “coverage of posterior sets” and even more “the likelihood must be the density of a statistic, not necessarily sufficient” as it obviously relates with our current ABC model comparison work… Esp. when the very same paper is mentioned by Francesco as well. ** Grazie, Stefano!** I also appreciate the survey made by Francesco on the consistency conditions, because I think this is an important issue that should be taken into consideration when designing ABC algorithms. (Just pointing out again that, in the theorem of Fearnhead and Prangle (2012) quoting Bernardo and Smith (1992), some conditions are missing for the mathematical consistency to apply.) I also like the agreement we seem to reach about ABC being evaluated per se rather than an a poor man’s Bayesian method. Francesco’s analysis of Monahan and Boos (1992) as validating or not empirical likelihood points out a possible link with the recent coverage analysis of Prangle et al., discussed on the ‘Og a few weeks ago. And an unsuspected link with Larry Wasserman!

*Grazie, Francesco!*
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