As an organiser of the ABC session (along with Paul Fearnhead), I was already aware of most results behind the talks, but nonetheless got some new perspectives from the presentations. Ewan Cameron discussed a two-stage ABC where the first step is actually an indirect inference inference, which leads to a more efficient ABC step. With applications to epidemiology. Lu presented extensions of his work with Paul Fearnhead, incorporating regression correction à la Beaumont to demonstrate consistency and using defensive sampling to control importance sampling variance. (While we are working on a similar approach, I do not want to comment on the consistency part, but I missed how defensive sampling can operate in complex ABC settings, as it requires advanced knowledge on the target to be effective.) And Ted Meeds spoke about two directions for automatising ABC (as in the ABcruise), from incorporating the pseudo-random generator into the representation of the ABC target, to calling for deep learning advances. The inclusion of random generators in the transform is great, provided they can remain black boxes as otherwise they require recoding. (This differs from quasi-Monte Carlo ABC, which aims at reducing the variability due to sheer noise.) It took me a little while, but I eventually understood why Jan Haning saw this inclusion as a return to fiducial inference!
Merlise Clyde gave a wide-ranging plenary talk on (linear) model selection that looked at a large range of priors under the hat of generalised confluent hypergeometric priors over the mixing scale in Zellner’s g-prior. Some were consistent under one or both models, maybe even for misspecified models. Some parts paralleled my own talk on the foundations of Bayesian tests, no wonder since I mostly give a review before launching into a criticism of the Bayes factor. Since I think this may be a more productive perspective than trying to over-come the shortcomings of Bayes factors in weakly informative settings. Some comments at the end of Merlise’s talk were loosely connected to this view in that they called for an unitarian perspective [rather than adapting a prior to a specific inference problem] with decision-theoretic backup. Conveniently the next session was about priors and testing, obviously connected!, with Leo Knorr-Held considering g-priors for the Cox model, Kerrie Mengersen discussing priors for over-fitted mixtures and HMMs, and Dan Simpson entertaining us with his quest of a prior for a point process, eventually reaching PC priors.