The next Mostly Monte Carlo seminar will be this very Friday, 10/04/26, at PariSanté Campus. With Shiva Darshan and Pierre Monmarché speaking on the following topics:
15h: Shiva Darshan Maximal-reflection couplings on manifolds: some specific examplesExplicit Markovian couplings can be used to build Markov Chain Monte Carlo methods such unbiased MCMC or coupling based control variates. For sampling from probability measures supported on Euclidean space, one typically uses a synchronous coupling, a maximal-reflection coupling (also known as a discrete-time sticky coupling), or some variant of the two. For probability measures supported on Riemannian manifolds, the situation is less clear cut. While the Kendall-Cranston coupling of Brownian motions on manifolds has been successfully applied in theoretical works, it is ill-suited for building explicit algorithms. In this talk, we will discuss some of the obstacles to extending Euclidean maximal-reflection couplings to manifolds and present some special cases for which these obstacles can be easily overcome. With applications to Stereographic MCMC in mind, we detail particular couplings of random walks on the sphere.16h: Pierre Monmarché A post-sampling reweighting method for multi-modal target measuresEven when the modes are identified and sampled locally with MCMC methods, a difficulty to sample multi-modal measures is to correctly estimate the relative probabilities of each of these modes, which requires to observe many transitions between them (which are rare events). We will present an approach based on variational inference which exploits the local samples, aiming only at estimating the relative weights between them. When the modes are well separated, this amount to some entropy estimations.
Bob then spoke about the latest version of NUTS, the within-orbit adaptive NUTS (WALNUTS) sampler, which adapts the step size at every leapfrog step in order to conserve the Hamiltonian and keep the path stable enough. The adaptation is facilitated by incorporating this step size as an extra parameter with an attached distribution, that the authors call Gibbs self tuning (GIST), for coupling tuning parameters and conditionally Gibbs-sampling them per iteration in Hamiltonian Monte Carlo. This has been done in the past, incl. in some of my papers (e.g., Andrieu & Robert, 2004), but I could not cite a particular reference during the seminar.
Further light reflections that came to mind during Bob’s talk:
I am quite excited about 
