Archive for Scotland
As much as I love Scotland, or because of it, I would not dream of suggesting to Scots that one side of the referendum sounds better than the other. However, I am rather annoyed at the yoyo-like reactions to the successive polls about the result, because, just like during the US elections, each poll is analysed separately rather than being pooled with the earlier ones in a reasonable meta-analysis… Where is Nate Silver when we need him?!
Alas, thrice alas, the bid we made right after the Banff workshop with Scott Schmidler, and Steve Scott for holding the next World ISBA Conference in 2016 in Banff, Canada was unsuccessful. This is a sad and unforeseen item of news as we thought Banff had a heap of enticing features as a dream location for the next meeting… Although I cannot reveal the location of the winner, I can mention it is much more traditional (in the sense of the Valencia meetings), i.e. much more mare than monti… Since it is in addition organised by friends and in a country I love, I do not feel particularly aggravated. Especially when considering we will not have to organise anything then!
Last Thursday night, after a friendly dinner closing the ICMS workshop, I was rushing back to Pollock Halls to catch some sleep before a very early flight. When crossing North Bridge, on top of Waverley station, I then spotted in the crowd a well-known face of a fellow statistician from Cambridge University, on an academic visit to the University of Edinburgh that was completely unrelated with the workshop. Then, today, on my way back from submitting a visa request at the Indian embassy in Paris, I took the RER train for one stop between Gare du Nord and Chatelet. When I stood up from my seat and looked behind me, a senior (and most famous) mathematician was sitting right there, in deep conversation with a colleague about algorithms… Just two of “those” coincidences. (Edinburgh may be propitious to coincidences: at the last ICMS workshop I attended, I ended up in the same Indian restaurant as Marc Suchard, who also was on an academic visit to the University of Edinburgh that was completely unrelated with the workshop!)
In a somewhat desperate rush (started upon my return from Iceland and terminated on my return from Edinburgh), Marco Banterle, Clara Grazian and I managed to complete and submit our paper by last Friday evening… It is now arXived as well. The full title of the paper is Accelerating Metropolis-Hastings algorithms: Delayed acceptance with prefetching and the idea behind the generic acceleration is (a) to divide the acceptance step into parts, towards a major reduction in computing time that outranks the corresponding reduction in acceptance probability and (b) to exploit this division to build a dynamic prefetching algorithm. The division is to break the prior x likelihood target into a product such that some terms are much cheaper than others. Or equivalently to represent the acceptance-rejection ratio in the Metropolis-Hastings algorithm as
again with significant differences in the computing cost of those terms. Indeed, this division can be exploited by checking for each term sequentially, in the sense that the overall acceptance probability
is associated with the right (posterior) target! This lemma can be directly checked via the detailed balance condition, but it is also a consequence of a 2005 paper by Andrès Christen and Colin Fox on using approximate transition densities (with the same idea of gaining time: in case of an early rejection, the exact target needs not be computed). While the purpose of the recent [commented] paper by Doucet et al. is fundamentally orthogonal to ours, a special case of this decomposition of the acceptance step in the Metropolis–Hastings algorithm can be found therein. The division of the likelihood into parts also allows for a precomputation of the target solely based on a subsample, hence gaining time and allowing for a natural prefetching version, following recent developments in this direction. (Discussed on the ‘Og.) We study the novel method within two realistic environments, the first one made of logistic regression targets using benchmarks found in the earlier prefetching literature and a second one handling an original analysis of a parametric mixture model via genuine Jeffreys priors. [As I made preliminary notes along those weeks using the 'Og as a notebook, several posts on the coming days will elaborate on the above.]
Over a welcomed curry yesterday night in Edinburgh I read this 2008 paper by Koopman, Shephard and Creal, testing the assumptions behind importance sampling, which purpose is to check on-line for (in)finite variance in an importance sampler, based on the empirical distribution of the importance weights. To this goal, the authors use the upper tail of the weights and a limit theorem that provides the limiting distribution as a type of Pareto distribution
over (0,∞). And then implement a series of asymptotic tests like the likelihood ratio, Wald and score tests to assess whether or not the power ξ of the Pareto distribution is below ½. While there is nothing wrong with this approach, which produces a statistically validated diagnosis, I still wonder at the added value from a practical perspective, as raw graphs of the estimation sequence itself should exhibit similar jumps and a similar lack of stabilisation as the ones seen in the various figures of the paper. Alternatively, a few repeated calls to the importance sampler should disclose the poor convergence properties of the sampler, as in the above graph. Where the blue line indicates the true value of the integral.