My last day (#4) at the workshop, as I had to return to Paris earlier. A rather theoretical morning again, with Morgane Austern on (probabilistic) concentration inequalities on transport distances, far from my comfort zone if lively, Jason Xu on replacing non-convex penalisation factors to distances to the corresponding manifold, which I found most interesting if not directly helpful for simulating over submanifolds, and Hugo Lavenant on studying the impact of prior choice as merging of opinions, in the (Milanese) setting of completely random measures, with the surprise occurrence of a double bent for some choices. The afternoon session saw Andrew Gelman reflecting on multiscale modelling (sans slide et sans tableau) and Chris Holmes introduce the fundamentals of Bayesian conformal prediction, towards reaching well-calibrated (in a frequentist sense) Bayesian procedures by resorting to exchangeability and rank tests. I alas missed the other talks of the day.
In recap, this was a wonderful conference, with a perfect audience size, a diverse if intense program, and a lot of interactions. In addition, the short talk sessions worked very nicely, even at 22:10 after a long day. And attracted very strong audience, even at 22:10! Indeed, they were uniformly well-calibrated, time-wise, and with high clarity messages. To be repeated. As there were many newcomers to CIRM, they discovered the idiosyncrasies of the place and of its surrounding, mostly positively.
On the outdoor front, the week saw an overall moderately hot weather but a constant wind that prevented me from sleeping (well), but which helped with waking up before dawn to cycle or run to my open water pool! The sea remained reasonably choppy, so waves did not prevent my swimming.
The main BayesComp meeting started right after the ABC workshop and went on at a grueling pace, and offered a constant conundrum as to which of the four sessions to attend, the more when trying to enjoy some outdoor activity during the lunch breaks. My overall feeling is that it went on too fast, too quickly! Here are some quick and haphazard notes from some of the talks I attended, as for instance the practical parallelisation of an SMC algorithm by Adrien Corenflos, the advances made by Giacommo Zanella on using Bayesian asymptotics to assess robustness of Gibbs samplers to the dimension of the data (although with no assessment of the ensuing time requirements), a nice session on simulated annealing, from black holes to Alps (if the wrong mountain chain for Levi), and the central role of contrastive learning à la Geyer (1994) in the GAN talks of Veronika Rockova and Éric Moulines. Victor Elvira delivered an enthusiastic talk on our massively recycled importance on-going project that we need to complete asap!
In a not-solely-ABC session, I appreciated Sirio Legramanti speaking on comparing different distance measures via Rademacher complexity, highlighting that some distances are not robust, incl. for instance some (all?) Wasserstein distances that are not defined for heavy tailed distributions like the Cauchy distribution. And using the mean as a summary statistic in such heavy tail settings comes as an issue, since the distance between simulated and observed means does not decrease in variance with the sample size, with the practical difficulty that the problem is hard to detect on real (misspecified) data since the true distribution behing (if any) is unknown. Would that imply that only intrinsic distances like maximum mean discrepancy or Kolmogorov-Smirnov are the only reasonable choices in misspecified settings?! While, in the ABC session, Jeremiah went back to this role of distances for generalised Bayesian inference, replacing likelihood by scoring rule, and requirement for Monte Carlo approximation (but is approximating an approximation that a terrible thing?!). I also discussed briefly with Alejandra Avalos on her use of pseudo-likelihoods in Ising models, which, while not the original model, is nonetheless a model and therefore to taken as such rather than as approximation.
