**L**ast day at MCMskv! Not yet exhausted by this exciting conference, but this was the toughest day with one more session and a tutorial by Art Own on quasi Monte-Carlo. (Not even mentioning the night activities that I skipped. Or the ski break that I did not even consider.) Krys Latunszynski started with a plenary on exact methods for discretised diffusions, with a foray in Bernoulli factory problems. Then a neat session on adaptive MCMC methods that contained a talk by Chris Sherlock on delayed acceptance, where the approximation to the target was built by knn trees. (The adaptation was through the construction of the tree by including additional evaluations of the target density. Another paper sitting in my to-read list for too a long while: the exploitation of the observed values of π towards improving an MCMC sampler has always be “obvious” to me even though I could not see any practical way of doing so. )

It was wonderful that Art Owen accepted to deliver a tutorial at MCMskv on quasi-random Monte Carlo. Great tutorial, with a neat coverage of the issues most related to Monte Carlo integration. Since quasi-random sequences have trouble with accept/reject methods, a not-even-half-baked idea that came to me during Art’s tutorial was that the increased computing power granted by qMC could lead to a generic integration of the Metropolis-Hastings step in a Rao-Blackwellised manner. Art mentioned he was hoping that in a near future one could switch between pseudo- and quasi-random in an almost automated manner when running standard platforms like R. This would indeed be great, especially since quasi-random sequences seem to be available at the same cost as their pseudo-random counterpart. During the following qMC session, Art discussed the construction of optimal sequences on sets other than hypercubes (with the surprising feature that projecting optimal sequences from the hypercube does not work). Mathieu Gerber presented the quasi-random simulated annealing algorithm he developed with Luke Bornn that I briefly discussed a while ago. Or thought I did as I cannot trace a post on that paper! While the fact that annealing also works with quasi-random sequences is not astounding, the gain over random sequences shown on two examples is clear. The session also had a talk by Lester Mckey who relies Stein’s discrepancy to measure the value of an approximation to the true target. This was quite novel, with a surprising connection to Chris Oates’ talk and the use of score-based control variates, if used in a dual approach.

Another great session was the noisy MCMC one organised by Paul Jenkins (Warwick), with again a coherent presentation of views on the quality or lack thereof of noisy (or inexact) versions, with an update from Richard Everitt on inexact MCMC, Felipe Medina Aguayo (Warwick) on sufficient conditions for noisy versions to converge (and counterexamples), Jere Koskela (Warwick) on a pseudo-likelihood approach to the highly complex Kingman’s coalescent model in population genetics (of ABC fame!), and Rémi Bardenet on the tall data approximations techniques discussed in a recent post. Having seen or read most of those results previously did not diminish the appeal of the session.