## MCMC at ICMS (3)

**T**he intense pace of the two first days of our workshop on MCMC at ICMS had apparently taken an heavy toll on the participants as a part of the audience was missing this morning! Although not as a consequence of the haggis of the previous night at the conference dinner, nor even as a result of the above pace. In fact, the missing participants had opted ahead of time for leaving the workshop early, which is understandable given everyone’s busy schedule, esp. for those attending both Bristol and Edinburgh workshops, however slightly impacting the atmosphere of the final day. (*Except for Mark Girolami who most unfortunately suffered such a teeth infection that he had to seek urgent medical assistance yesterday afternoon. Best wishes to Mark for a prompt recovery, say I with a dental appointment tomorrow…!)*

**T**he plenary talk of the day was delivered by Heikki Haario, who provided us with a survey of the (adaptive) MCMC advances he and his collaborators had made in the analysis of complex and immensely high-dimensional weather models. This group of Finnish researchers, who started from inverse problem analysis rather than from MCMC, have had a major impact on the design and validation of adaptive MCMC algorithms, especially in the late 1990’s. (Heikki also was a co-organizer of the Adap’ski workshops, workshops that may be continued, stay tuned!) The next talk, by Marko Laine, was also about adaptive MCMC algorithms, with the difference that the application was climate modelling. It contained interesting directions about early stopping (“early rejection”, as opposed to “delayed rejection”) of diverging proposals (gaining 80% in computing time!) and about parallel adaptation. Still in the same theme, Gersende Fort explained the adaptive version of the equi-energy sampler she and co-authors had recently developed. Although she had briefly presented this paper in Banff a month ago, I found the talk quite informative about the implementation of the method and at the perfect technical level *(for me!)*.

**I**n *[what I now perceive as]* another recurrent theme of the workshop, namely the recourse to Gaussian structures like Gaussian processes (see, e.g., Ian Murray’s talk yesterday), Andrew Stuart gave us a light introduction to random walk Metropolis-Hastings algorithms on Hilbert spaces. In particular, he related to Ian Murray’s talk of yesterday as to the definition of a “new” random walk (due to Radford Neal) that makes a proposal

that still preserves the acceptance probability of the original (“old”) random walk proposal. The final talks of the morning were Krys Latuszynski’s and Nick Whiteley’s very pedagogical presentations of the convergence properties of manifold MALA and of particle filters for hidden Markov models. In both cases, the speakers avoided the overly technical details and provided clear intuition in the presented results, a great feat after those three intense days of talks! (Having attended Nick’s talk in Paris two weeks ago helped of course.)

**U**nfortunately, due to very limited flight options (after one week of traveling around the UK) and also being slightly worried at the idea of missing my flight!, I had to leave the meeting along with all my French colleagues right after Jean-Michel Marin’s talk on (hidden) Potts driven mixtures, explaining the computational difficulties in deriving marginal likelihoods. I thus missed the final talk of the workshop by Gareth Tribello. And delivering my final remarks at the lunch break.

**O**verall, when reflecting on those two Monte Carlo workshops, I feel I preferred the pace of the Bristol workshop, because it allowed for more interactions between the participants by scheduling less talks… This being said, the organization at ICMS was superb (as usual!) and the talks were uniformly very good so it also was a very profitable meeting, of a different kind! As written earlier, among other things, it induced (in me) some reflections on a possible new research topic with friends there. Looking forward to visit Scotland again, of course!

April 26, 2012 at 8:37 am

Thanks for the summaries!

A small correction: “that still preserves the acceptance probability of the original (“old”) random walk proposal”. In the proposal that satisfies detailed balance wrt the prior, only the likelihood ratio appears in the acceptance ratio. When the prior is really strong, stopping it from vetoing proposals is really useful.

Of course although I say “prior”, there’s nothing to stop one factoring out any Gaussian distribution from the target distribution. And one can see this method as a special case of more general two-stage acceptance rules (such as early rejection). These were also mentioned a couple of times in the meeting, and have been reinvented a few times. I gave some references in my thesis (p30), and briefly showed how it can be extended to slice sampling (p40).

April 26, 2012 at 10:53 am

Thanks, Iain, I was writing this entry while listening to the talks and missed this point!