**J**ust yet another perfect day in Providence! Especially when I thought it was going to be a half-day: After a longer and slightly warmer run in the early morning around the peninsula, I attended the lecture by Eric Moulines on his recent results on adaptive MCMC and the equi-energy sampler. At this point, we were told that, since Peter Glynn was sick, the afternoon talks were drifted forward. This meant that I could attend Mylène Bédard’s talk in the morning and most of Xiao-Li Meng’s talk, before catching my bus to the airport, making it a full day in the end!

**T**he research presented by Mylène (and coauthored with Randal Douc and Eric Moulines) was on multiple-try MCMC and delayed-rejection MCMC, with optimal scaling results and a comparison of the efficiency of those involved schemes. I had not seen the work before and got quite impressed by the precision of the results and the potential for huge efficiency gains. One of the most interesting tricks was to use an antithetic move for the second step, considerably improving the acceptance rate in the process. An aside exciting point was to realise that the hit-and-run solution was also open to wide time-savings thanks to some factorisation.

**W**hile Xiao-Li’s talk had connections with his earlier illuminating talk in New York last year, I am quite desolate to have missed [the most novel] half of it (and still caught my bus by a two minute margin!), esp. because it connected beautifully with the constant estimation controverse! Indeed, Xiao-Li started his presentation with the pseudo-paradox that the likelihood cannot be written as a function of the normalising constant, simply because this is not a free parameter. He then switched to his usual theme that the dominating measure was to be replaced with a substitute and estimated.The normalising constant being a function of the dominating measure, it is a by-product of this estimation step. And can even be endowed within a Bayesian framework. Obviously, one can always argue against the fact that the dominating measure is truly unknown, however this gives a very elegant safe-conduct to escape the debate about the constant that did not want to be estimated…So to answer Xiao-Li’s question as I was leaving the conference room, I have now come to a more complete agreement with his approach. And think further advances could be contemplated along this path…

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