BNP13 is set in this incredible location on a massive lake (almost as large as Lac Saint Jean!) facing several tantalizing snow-capped volcanoes… My trip from Paris to Puerto Varas was quite smooth if relatively longish (but I slept close to 8 hours on the first leg and busied myself with Biometrika submissions the rest of the way). Leaving from Paris at midnight proved a double advantage as this was one of the last flights leaving, with hardly anyone in the airport. On Sunday, I arrived early enough to take a quick dip in Lake Llanquihue which was fairly cold and choppy!

Overall the conference is quite exhilarating as all talks are of interest and often covering on-going research. This may be one of the most engaging meetings I have attended in the past years! Plus a refreshing variety of topics and seniority in the speakers.

To start with a bang!, Sonia Petrone (Bocconi) gave a very nice plenary lecture in the most auspicious manner, covering her recent works on Bayesian prediction as an alternative way to run Bayesian inference (in connection with the incoming Read Paper by Fong et al.). She covered so much ground that I got lost before long (jetlag did not help!). However, an interesting feature underlying her talk is that, under exchangeability, the sequence of predictives converges to a random probability measure, a de Finetti way to construct the prior that is based on predictives. Avoiding in a sense the model and the prior on the parameters of that process. (The parameter is derived from the infinite exchangeable [or conditionally iid] sequence, but the sequence of predictives need be defined.) The drawback is that this approach involves infinite sequences, with practical truncation to a finite horizon being an approximation whose precision / error may prove elusive to characterise. The predictive approach also allows to recover a limiting Normal distribution (not a Bernstein-von Mises type!) and hence credible intervals on parameters and distributions.

While this is indeed a BNP conference (!), I was surprised to see lot of talks paying attention to clustering and even to mixtures, with again a recurrent imprecision on the meaning of a cluster. (Maybe this was already the case for BNP11 in Paris but I may have been too busy helping with catering to notice!) For instance, Brian Trippe (MIT) gave a quick intro on his (AISTATS 2022) work on parallel MCMC with coupling. As unbiased MCMC strongly improving upon naïve parallel MCMC relative to the computing cost. With an interesting example where coupling is agnostic to the labeling of random partitions in clustering problems, involving optimal transport, manageable in O(K³log(K)) time when K is the number of clusters.