Although some of the participants of the workshop left for ICML²⁶ or the 4th Bayesian Nonparametrics networking workshop, both taking place in Seoul this week, the following days of the workshop were as intense and captivating as the first two, with a return to MCMC “basics” but also more geometrical and maethematical aspects.
To wit, Radu Craiu talked on MCMC for DAG processes with revisiting the landmark paper of Geyer & Møller (1994) on replacing discrete time MCMC with a birth & death process and cutting on complexity by restricted set imposing some edges, set from a redetermined run. Galin Jones presented some (novel) Lower bounds on the rate of convergence for accept-reject-based Markov chains in Wasserstein and total variation distances, showing the massive dependence of the convergence rates on the scaling factors of the proposal, especially in relation with the data size n when considering posterior targets. James Flegal discussed Simultaneous confidence bands for (MC)MC simulations that aimed at returning a confidence band on marginal density estimates; it reminded me of our 2005 simultaneous coverage paper with Wilfrid Kendall and Jean-Michel Marin and got me wondering why not going full Bayes by adopting a GP prior modelling.
Michiko Okudo spoke about Applications of information geometry to Bayesian prediction and estimation in curved exponential families, returning to point estimation with a mention of Marchand & Strawderman (2025)! Marta Catalano presented results on Distances on random measures for Bayesian nonparametrics, involving random measures like Dirichlet processes, that was connected with Hugo Lavenant’s talk at ISBA, but more focussed on the mathematical aspects albeit algorithmic aspects were mentioned. With highly intuitive arguments (making the accronym WoW for Wasserstein on Wasserstein quite appropriate!).
Takemasa Miyoshi made a presentation of the Osaka Expo 2025 Weather [prediction] on Fugaku: Synergizing Big Data Assimilation and AIRIKEN, with impressive predictive abilities achieved using RIKEN super-computer (but no technical details). Björn Sprung exposed how they obtained Dimension-independent MCMC [convergence speed] on the sphere, using retroprojections of random walks outside the sphere (as in Frederica’s talk yesterday), which comes as a surprise given the deterioration of random walk performances with increasing dimensions.
Geoffrey Wolfer’s Characterization of Exponential Families of Lumpable Stochastic Matrices was a very mathematical talk set firmly in the Japanese probability school, going too fast with too many new definitions for my abilities (and attention span) but setting the scene for exponential families on stochastic matrices and being one of the rate cases I eve rsaw lumpability à la Kemeny & Snell (1983) mentionned! Daniel Paulin followed with Stochastic gradient Langevin dynamics: convergence and bias, via an UBU algorithm using splitting integrators that sound very much like the leapfrog for an HMC with unscented Langevin steps where the gradient is replaced with an unbiased estimator (connecting to the poster of Jack Jewson on Sunday, when he mentioned the opposition between pseudo-marginal MCMC, requiring an unbiased estimator of the target, and schemes using the log-target, for which unbiased estimators of the log can be used). Shahab Asoodeh concluded Monday with Recent Advances in Metropolis-Hastings Algorithms, actually developing multi-marginal coupling with freely coupling chains.
On the final morning, Weiming Feng showed results about a Faster mixing of the Jerrum-Sinclair chain, reminding me of the 1989 paper, with a Metropolis algorithm on graphs allowing for specific mixing time results with spectral gap and log-Sobolev inequalities (and a Poincáre typo!). Michael Choi produced convergence properties by Optimising two-block averaging kernels to speed up Markov chains, with a (rather formal) Gibbs sampler on orbits (in a finite state space) again connecting to Jerrum.
Yuga Iguchi discussed Diffusion models for high-dimensional clustered data: Intrinsic-dimension adaptivity via Bayesian classification, producing a rigorous characterisation of the phase transition property of their diffusion denoising probabilistic model when the target is a mixture with separation constraints on the components, phase transition meaning that eventually concentrating on a single cluster as the forward diffusion moves toward pure noise. (Although being fully awake, having mostly recovered from the longest jetlag period ever, I had trouble understanding the process per se.) Edric Tam discussed Fundamental Limits to Neural Monte Carlo by returning to standard variance reduction techniques like stratifying and antithetic-ying (!) and applying normalising flows on them. Victor Elvira concluded the meeting by Rethinking self-normalized importance sampling, with a fun interlude of Eric Veach’s Oscars joke, but I unfortunately had to miss the end to gather my bags and leave for the Alps! But Victor should be in Paris in the Fall and hopfefully giving a talk at mostly Monte Carlo!
This workshop was most efficiently supported by the Institute of Statistical Mathematics and its staff, including over the weekend days! On a personal foodie note, the coffee breaks featured the same unbelievable matcha cakes (“Chez Kobe”) as at ISBA²⁶, we enjoyed a terrific full tofu dinner at Umenohana Tachikawa shop and there were plenty French (or pseudo-French) bakeries in Tachekima, enough to find rye (raimugi) bread for breakfast!
A few days before the 
After another morning cycle of 2Xing Porte della Libertà (under a light and pleasant rain) and swimming in Sant’ Alviso (in too warm a water), I did not make it for the beginning of the Bayesian deep learning session, breakfast oblige!, and cumulated with different percolation events (ie, meeting friend after friend on my way to the classroom), I could not get enough of the session to report anything even barely useful!
Also, I chaired the 
