MCqMC 2014 [day #3]

Leuven2

As the second day at MCqMC 2014, was mostly on multi-level Monte Carlo and quasi-Monte Carlo methods, I did not attend many talks but had a long run in the countryside (even saw a pheasant and a heron), worked at “home” on pressing recruiting evaluations and had a long working session with Pierre Jacob. Plus an evening out sampling (just) a few Belgian beers in the shade of the city hall…

Today was more in my ballpark as there were MCMC talks the whole day! The plenary talk was not about MCMC as Erich Novak presented a survey on the many available results bounding the complexity of approximating an integral based on a fixed number of evaluations of the integrand, some involving the dimension (and its curse), some not, some as fast as √n and some not as fast, all this depending on the regularity and the size of the classes of integrands considered. In some cases, the solution was importance sampling, in other cases, quasi-Monte Carlo, and yet other cases were still unsolved. Then Yves Atchadé gave a new perspective on computing the asymptotic variance in the central limit theorem on Markov chains when truncating the autocovariance, Matti Vihola talked about theoretical orderings of Markov chains that transmuted into the very practical consequence that using more simulations in a pseudo-marginal likelihood approximation improved acceptance rate and asymptotic variances (and this applies to aBC-MCMC as well), Radu Craiu proposed a novel processing of adaptive MCMC by treating various approximations to the true target as food for a multiple-try Metropolis algorithm, and Luca Martino had a go at resuscitating the ARMS algorithm of Gilks and Wild (used for a while in BUGS), although the talk did not dissipate all of my misgivings about the multidimensional version! I had more difficulties following the “Warwick session” which was made of four talks by current or former students from Warwick, although I appreciated the complexity of the results in infinite dimensional settings and novel approximations to diffusion based Metropolis algorithms. No further session this afternoon as the “social” activity was to visit the nearby Stella Artois brewery! This activity made us very social, for certain, even though there was hardly a soul around in this massively automated factory. (Maybe an ‘Og post to come one of those days…)

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