**O**n Day 2, Carsten Hartmann used a representation of the log cumulant as solution to a minimisation problem over a collection of importance functions (by the Vonsker-Varadhan principle), with links to X entropy and optimal control, a theme also considered by Alain Dunmus when considering the uncorrected discretised Langevin diffusion with a decreasing sequence of discretisation scale factors (Jordan, Kinderlehrer and Otto) in the spirit of convex regularisation à la Rockafellar. Also representing ULA as an inexact gradient descent algorithm. Murray Pollock (Warwick) presented a new technique called fusion to simulate from products of d densities, as in scalable MCMC (but not only). With an (early) starting and startling remark that when simulating one realisation from each density in the product and waiting for all of them to be equal means simulating from the product, in a strong link to the (A)BC fundamentals. This is of course impractical and Murray proposes to follow d Brownian bridges all ending up in the average of these simulations, constructing an acceptance probability that is computable and validating the output.

The second “hand-on” lecture was given by Gareth Roberts (Warwick) on the many aspects of scaling MCMC algorithms, which started with the famous 0.234 acceptance rate paper in 1996. While I was aware of some of these results (!), the overall picture was impressive, including a notion of complexity I had not seen before. And a last section on PDMPs where Gareth presented very recent on the different scales of convergence of Zigzag and bouncy particle samplers, mostly to the advantage of Zigzag.In the afternoon, Jeremy Heng presented a continuous time version of simulated tempering by adding a drift to the Langevin diffusion with time-varying energy, which must be solution to the Liouville pde . Which connects to a flow transport problem when solving the pde under additional conditions. Unclear to me was the creation of the infinite sequence. This talk was very much at the interface in the spirit of the workshop! (Maybe surprisingly complex when considering the endpoint goal of simulating from a given target.) Jonathan Weare’s talk was about quantum chemistry which translated into finding eigenvalues of an operator. Turning in to a change of basis in a inhumanly large space (10¹⁸⁰ dimensions!). Matt Moore presented the work on Raman spectroscopy he did while a postdoc at Warwick, with an SMC based classification of the peaks of a spectrum (to be used on Mars?) and Alessandra Iacobucci (Dauphine) showed us the unexpected thermal features exhibited by simulations of chains of rotors subjected to both thermal and mechanical forcings, which we never discussed in Dauphine beyond joking on her many batch jobs running on our cluster!

And I remembered today that there is currently and in parallel another BIRS workshop on statistical model selection [and a lot of overlap with our themes] taking place in Banff! With snow already there! Unfair or rather #unfair, as someone much too well-known would whine..! Not that I am in a position to complain about the great conditions here in Oaxaca (except for having to truly worry about stray dogs rather than conceptually about bears makes running more of a challenge, if not the altitude since both places are about the same).