Tomorrow I am off to Venezia for three days, attending the ESOBE 2016 workshop, where ESOBE stands for European Seminar on Bayesian Econometrics. This year it is indeed taking place in Venezia, Università Ca’ Foscari, in this beautiful building on the Gran Canale, and I have been invited to give a talk. Excited to get back to this unique place, hoping the high water will not be too high to prevent getting around (at random as usual).
One approach to random number generation that had always intrigued me is Kinderman and Monahan’s (1977) ratio-of-uniform method. The method is based on the result that the uniform distribution on the set A of (u,v)’s in R⁺xX such that
induces the distribution with density proportional to ƒ on V/U. Hence the name. The proof is straightforward and the result can be seen as a consequence of the fundamental lemma of simulation, namely that simulating from the uniform distribution on the set B of (w,x)’s in R⁺xX such that
induces the marginal distribution with density proportional to ƒ on X. There is no mathematical issue with this result, but I have difficulties with picturing the construction of efficient random number generators based on this principle.
I thus took the opportunity of the second season of [the Warwick reading group on] Non-uniform random variate generation to look anew at this approach. (Note that the book is freely available on Luc Devroye’s website.) The first thing I considered is the shape of the set A. Which has nothing intuitive about it! Luc then mentions (p.195) that the boundary of A is given by
which then leads to bounding both ƒ and x→x²ƒ(x) to create a box around A and an accept-reject strategy, but I have trouble with this result without making further assumptions about ƒ… Using a two component normal mixture as a benchmark, I found bounds on u(.) and v(.) and simulated a large number of points within the box to end up with the above graph that indeed the accepted (u,v)’s were within this boundary. And the same holds with a more ambitious mixture:
Although I bought this second volume in the Fitz and the Fool trilogy quite a while ago, I only came to read it very recently. And enjoyed it unreservedly! While the novel builds upon the universe Hobb created in the liveship traders trilogy (forget the second trilogy!) and the Assassin and Fool trilogies, the story is compelling enough to bring out excitement and longing for further adventures of Fitz and the Fool. Many characters that were introduced in the earlier volume suddenly take on substance and meaning, while the main characters are no longer heroes of past eras, but also acquire further depth and subtlety. Even long-lasting ones like Chade. I cannot tell whether this new dimension of the plights affecting the Six Duchies and its ruler, King Verity, was conceived from the start or came later to the author, but it really fits seamlessly and increases by several orders of magnitude the epic feeling of the creation. Although it is hard to rank this book against the very first ones, like Royal Assassin, I feel this is truly one of the best of Hobb’s books, with the right mixture of action, plotting, missed opportunities and ambiguous angles about the main characters. So many characters truly come to life in this volume that I bemoan the sluggish pace of the first one even more now. While one could see Fool’s Quest as the fourteenth book in the Realm of the Elderlings series, and hence hint at senseless exploitation of the same saga, there are just too many new threads and perspective there to maintain this posture. A wonderful book and a rarity of a middle book being so. I am clearly looking forward the third instalment!
For ‘Og’s readers interested in lecturer or professor positions in French universities next academic year, including a lecturer position at Paris-Dauphine in applied and computational statistics!, you need to apply for a qualification label by a national committee which strict deadline is next Tuesday, October 25, at 4pm (Paris/CET time). (The whole procedure is exclusively in French!)
On October 11, at Bletchley Park, the Suffrage Science awards in mathematics and computer sciences were awarded for the first time to 12 senior female researchers. Among whom three statisticians, Professor Christl Donnelly from Imperial College London, my colleague at Warwick, Jane Hutton, and my friend and co-author, Sylvia Richardson, from MRC, Cambridge University. This initiative was started by the Medical Research Council in 2011 by Suffrage Science awards for life sciences, followed in 2013 by one for engineering and physics, and this year for maths and computing. The name of the award aims to connect with the Suffragette movement of the late 19th and early 20th Centuries, which were particularly active in Britain. One peculiar aspect of this award is that the recipients are given pieces of jewellery, created for each field, pieces that they will themselves give two years later to a new recipient of their choice, and so on in an infinite regress! (Which suggests a related puzzle, namely to figure out how many years it should take until all female scientists have received the award. But since the number increases as the square of the number of years, this is not going to happen unless the field proves particularly hostile to women scientists!) This jewellery award also relates to the history of the Suffragette movement since the WPSU commissioned their own jewellery awards. A clever additional touch was that the awards were delivered on Ada Lovelace Day, October 11.