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MCqMC 2016 [#4]

Posted in Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on August 21, 2016 by xi'an

In his plenary talk this morning, Arnaud Doucet discussed the application of pseudo-marginal techniques to the latent variable models he has been investigating for many years. And its limiting behaviour towards efficiency, with the idea of introducing correlation in the estimation of the likelihood ratio. Reducing complexity from O(T²) to O(T√T). With the very surprising conclusion that the correlation must go to 1 at a precise rate to get this reduction, since perfect correlation would induce a bias. A massive piece of work, indeed!

The next session of the morning was another instance of conflicting talks and I hoped from one room to the next to listen to Hani Doss’s empirical Bayes estimation with intractable constants (where maybe SAME could be of interest), Youssef Marzouk’s transport maps for MCMC, which sounds like an attractive idea provided the construction of the map remains manageable, and Paul Russel’s adaptive importance sampling that somehow sounded connected with our population Monte Carlo approach. (With the additional step of considering transform maps.)

An interesting item of information I got from the final announcements at MCqMC 2016 just before heading to Monash, Melbourne, is that MCqMC 2018 will take place in the city of Rennes, Brittany, on July 2-6. Not only it is a nice location on its own, but it is most conveniently located in space and time to attend ISBA 2018 in Edinburgh the week after! Just moving from one Celtic city to another Celtic city. Along with other planned satellite workshops, this occurrence should make ISBA 2018 more attractive [if need be!] for participants from oversea.

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MCqMC [#3]

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , on August 20, 2016 by xi'an

On Thursday, Christoph Aistleiter [from TU Gräz] gave a plenary talk at MCqMC 2016 around Hermann Weyl’s 1916 paper, Über die Gleichverteilung von Zahlen mod. Eins, which demonstrates that the sequence a, 22a, 32a, … mod 1 is uniformly distributed on the unit interval when a is irrational. Obviously, the notion was not introduced for simulation purposes, but the construction applies in this setting! At least in a theoretical sense. Since for instance the result that the sequence (a,a²,a³,…) mod 1 being uniformly distributed for almost all a’s has not yet found one realisation a. But a nice hour of history of mathematics and number theory: it is not that common we hear the Riemann zeta function mentioned in a simulation conference!

The following session was a nightmare in that I wanted to attend all four at once! I eventually chose the transport session, in particular because Xiao-Li advertised it at the end of my talk. The connection is that his warp bridge sampling technique provides a folding map between modes of a target. Using a mixture representation of the target and folding all components to a single distribution. Interestingly, this transformation does not require a partition and preserves the normalising constants [which has a side appeal for bridge sampling of course]. In a problem with an unknown number of modes, the technique could be completed by [our] folding in order to bring the unobserved modes into the support of the folded target. Looking forward the incoming paper! The last talk of this session was by Matti Vihola, connecting multi-level Monte Carlo and unbiased estimation à la Rhee and Glynn, paper that I missed when it got arXived last December.

The last session of the day was about probabilistic numerics. I have already discussed extensively about this approach to numerical integration, to the point of being invited to the NIPS workshop as a skeptic! But this was an interesting session, both with introductory aspects and with new ones from my viewpoint, especially Chris Oates’ description of a PN method for handling both integrand and integrating measure as being uncertain. Another arXival that went under my decidedly deficient radar.

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MCqMC 2016 [#2]

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , on August 17, 2016 by xi'an

In her plenary talk this morning, Christine Lemieux discussed connections between quasi-Monte Carlo and copulas, covering a question I have been considering for a while. Namely, when provided with a (multivariate) joint cdf F, is there a generic way to invert a vector of uniforms [or quasi-uniforms] into a simulation from F? For Archimedian copulas (as we always can get back to copulas), there is a resolution by the Marshall-Olkin representation,  but this puts a restriction on the distributions F that can be considered. The session on synthetic likelihoods [as introduced by Simon Wood in 2010] put together by Scott Sisson was completely focussed on using normal approximations for the distribution of the vector of summary statistics, rather than the standard ABC non-parametric approximation. While there is a clear (?) advantage in using a normal pseudo-likelihood, since it stabilises with much less simulations than a non-parametric version, I find it difficult to compare both approaches, as they lead to different posterior distributions. In particular, I wonder at the impact of the dimension of the summary statistics on the approximation, in the sense that it is less and less likely that the joint is normal as this dimension increases. Whether this is damaging for the resulting inference is another issue, possibly handled by a supplementary ABC step that would take the first-step estimate as summary statistic. (As a side remark, I am intrigued at everyone being so concerned with unbiasedness of methods that are approximations with no assessment of the amount of approximation!) The last session of the day was about multimodality and MCMC solutions, with talks by Hyungsuk Tak, Pierre Jacob and Babak Shababa, plus mine. Hunsuk presented the RAM algorithm I discussed earlier under the title of “love-hate” algorithm, which was a kind reference to my post! (I remain puzzled by the ability of the algorithm to jump to another mode, given that the intermediary step aims at a low or even zero probability region with an infinite mass target.) And Pierre talked about using SMC for Wang-Landau algorithms, with a twist to the classical stochastic optimisation schedule that preserves convergence. And a terrific illustration on a distribution inspired from the Golden Gate Bridge that reminded me of my recent crossing! The discussion around my folded Markov chain talk focussed on the extension of the partition to more than two sets, the difficulty being in generating automated projections, with comments about connections with computer graphic tools. (Too bad that the parallel session saw talks by Mark Huber and Rémi Bardenet that I missed! Enjoying a terrific Burmese dinner with Rémi, Pierre and other friends also meant I could not post this entry on time for the customary 00:16. Not that it matters in the least…)

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MCqMC 2016 [#1]

Posted in Statistics, Travel, University life with tags , , , , , , , , on August 16, 2016 by xi'an

mcqmc1This week, I attend the MCqMC 2016 conference in Stanford, which is quite an exciting gathering of researchers involved in various aspects of Monte Carlo methods. As Art Owen put it in his welcoming talk, the whole Carlo family is there! (Not to mention how pleasant the Stanford Campus currently is, after the scorching heat we met the past week in Northern California inlands.) My talk is on folded Markov chains, which is a proposal Randal and I have been working on for quite a while, with Gareth joining us more recently. The basic idea was inspired from a discussion I had about a blog post, so long ago that I cannot even trace it! Namely, when defining an inside set A and an outside set, such that the outside set can be projected onto the inside set, one can fold both the target and the proposal, essentially looking at a collection of values for each step of the Markov chain. In other words, the problem can be reduced to A at essentially no cost and with the benefits of a compact support A and of a possibly uniformly ergodic Markov chain. We are still working on the paper, but the idea is both cool and straightforward, so we decided to talk about it at Nordstat 2016 and now MCqMC 2016.

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MCqMC 2016 acknowledgement

Posted in Statistics, Travel, University life with tags , , , , on August 1, 2016 by xi'an

mcqmc

Here is a very nice inclusion about the ‘Og by the organisers of MCqMC 2016.

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