Archive for noisy Metropolis-Hastings algorithm

MCMskv #5 [future with a view]

Posted in Kids, Mountains, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , on January 12, 2016 by xi'an

As I am flying back to Paris (with an afternoon committee meeting in München in-between), I am reminiscing on the superlative scientific quality of this MCMski meeting, on the novel directions in computational Bayesian statistics exhibited therein, and on the potential settings for the next meeting. If any.

First, as hopefully obvious from my previous entries, I found the scientific program very exciting, with almost uniformly terrific talks, and a coverage of the field of computational Bayesian statistics that is perfectly tuned to my own interest. In that sense, MCMski is my “top one” conference! Even without considering the idyllic location. While some of the talks were about papers I had already read (and commented here), others brought new vistas and ideas. If one theme is to emerge from this meeting it has to be the one of approximate and noisy algorithms, with a wide variety of solutions and approaches to overcome complexity issues. If anything, I wish the solutions would also incorporate the Boxian fact that the statistical models themselves are approximate. Overall, a fantastic program (says one member of the scientific committee).

Second, as with previous MCMski meetings, I again enjoyed the unique ambience of the meeting, which always feels more relaxed and friendly than other conferences of a similar size, maybe because of the après-ski atmosphere or of the special coziness provided by luxurious mountain hotels. This year hotel was particularly pleasant, with non-guests like myself able to partake of some of their facilities. A big thank you to Anto for arranging so meticulously all the details of such a large meeting!!! I am even more grateful when realising this is the third time Anto takes over the heavy load of organising MCMski. Grazie mille!

Since this is a [and even the!] BayesComp conference, the current section program chair and board must decide on the  structure and schedule of the next meeting. A few suggestions if I may: I would scrap entirely the name MCMski from the next conference as (a) it may sound like academic tourism for unaware bystanders (who only need to check the program of any of the MCMski conferences to stand reassured!) and (b) its topic go way beyond MCMC. Given the large attendance and equally large proportion of young researchers, I would also advise against hosting the conference in a ski resort for both cost and accessibility reasons [as we had already discussed after MCMskiv], in favour of a large enough town to offer a reasonable range of accommodations and of travel options. Like Chamonix, Innsbruck, Reykjavik, or any place with a major airport about one hour away… If nothing is available with skiing possibilities, so be it! While the outdoor inclinations of the early organisers induced us to pick locations where skiing over lunch break was a perk, any accessible location that allows for a concentration of researchers in a small area and for the ensuing day-long exchange is fine! Among the novelties in the program, the tutorials and the Breaking news! sessions were quite successful (says one member of the scientific committee). And should be continued in one format or another. Maybe a more programming thread could be added as well… And as we had mentioned earlier, to see a stronger involvement of the Young Bayesian section in the program would be great! (Even though the current meeting already had many young researcher  talks.)

stability of noisy Metropolis-Hastings

Posted in Books, Statistics, Travel, University life with tags , , , on April 3, 2015 by xi'an

UWpondFelipe Medina-Aguayo, Anthony Lee and Gareths Roberts, all from Warwick, arXived last Thursday a paper on the stability properties of noisy Metropolis-Hastings algorithms. The validation of unbiased estimators of the target à la Andrieu and Roberts (2009, AoS)—often discussed here—is in fact obvious when following the auxiliary variable representation of Andrieu and Vihola (2015, AoAP). Assuming the unbiased estimator of the target is generated conditional on the proposed value in the original Markov chain. The noisy version of the above means refreshing the unbiased estimator at each iteration. It also goes under the name of Monte Carlo within Metropolis. The difficulty with this noisy version is that it is not exact, i.e., does not enjoy the true target as its marginal stationary distribution. The paper by Medina-Aguayo, Lee and Roberts focusses on its validation or invalidation (with examples of transient noisy versions). Under geometric ergodicity of the marginal chain, plus some stability in the weights, the noisy version is also geometrically ergodic. A drift condition on the proposal kernel is also sufficient. Under (much?) harder conditions, the limiting distribution of the noisy chain is asymptotically in the number of unbiased estimators the true target. The result is thus quite interesting in that it provides sufficient convergence conditions, albeit not always easy to check in realistic settings.