Archive for January, 2010

Congruential generators all are RANDUs!

Posted in R, Statistics, University life with tags , , , , , on January 31, 2010 by xi'an

In case you did not read all the slides of Regis Lebrun’s talk on pseudo-random generators I posted yesterday, one result from Marsaglia’s (in a 1968 PNAS paper) exhibited my ignorance during Regis’ Big’ MC seminar on Thursday. Marsaglia indeed showed that all multiplicative congruential generators

r_{i+1}= kr_i \text{modulo }m

lie on a series of hyperplanes whose number gets ridiculously small as the dimension d increases! If you turn the r_i‘s into uniforms u_i and look at the d dimensional vectors


they are on a small number of hyperplanes, at most (d!m)^{1/m}, which gives 41 hyperplanes when m=2^{32}… So in this sense all generators share the same poor property as the infamous RANDU which is such that that (u_{i},u_{i+1},u_{i+2}) is always over one of 16 hyperplanes, an exercise we use in both Introducing Monte Carlo Methods with R and Monte Carlo Statistical Methods (but not in our general audience out solution manual). I almost objected to the general result being irrelevant as the \pi_i‘s share u_j‘s, but of course the subsequence \pi_1,\pi_d,\pi_{2d},... also share enjoys this property!

The Night Angel Trilogy

Posted in Books with tags , , , , , , on January 31, 2010 by xi'an

“There was no thesis, counterpointed with antithesis, harmonized into synthesis. It wasn’t that kind of music. The music of logic was too patrician for the streets, too subtle, the nuances all wrong.” Brent Weeks, Shadow’s Edge

I have finished the Night Angel Trilogy quite a while ago but felt so far little inclination to comment on it as I was quite disappointed by the series. The third volume, Beyond the Shadows, is quite unappealing and at some point it turns into such a bleak story of rape and slaughter that I was close to give up on the book. (This is when one of the main and so far “good” characters turns into a mad homicidal and sadistic Godking. Maybe a necessary part of the plot but unpleasant nonetheless, especially because Weeks makes it sound so reasonable…)

“You realize it might make a quantitative rather than qualitative difference?” “Huh?” Brent Weeks, Beyond the Shadows

As posted earlier, I did like the first volume The Way of Shadows as it truly made for a compelling and unusual read. But the characters do not evolve nor take much depth in the subsequent volumes, Shadow’s Edge and Beyond the Shadows (except for the female assassin Vi who alas often acts as a lovelorn teenager…) The interesting parallel structure of the thief society all but disappears once the new king comes to power, the influential (Aes Sedai or Bene Gesserit like) sisterhood is almost invisible and thus hardly influential. The fight for survival of the (future) king Logan in the dungeon filled with psychopaths is a better-written part, but the psychopaths turn up being a wee too nice to be credible! The central character Elene who was creating the (rather predictable) tension about the antagonistic inclinations of the other central character Kylar, torn between a prospect for family life and a magical assassin’s career, mostly drops from the last volume, Beyond the Shadows, only to reappear at the end to save the day. While the disappearance of major characters is a good novelist’s trick to keep the pace going and the reader hooked, I find the slaughter of many main characters overdone.  At last, the crudity and cruelty of the story, which were innovative in the first volume, end up wearing up in the following ones. Unless you specialise into gory fantasy (!), I would thus not recommend the Night Angel Trilogy. (There is an interview of Brent Weeks by Patrick Rothfuss that does not bring much about the books… Patrick Rothfuss should better be working on the sequel of The Name of the Wind I am desperate for! I also just found Linus Torvald, yes THE Linus Torvald!, recommended the trilogy two years ago…)

Anonymous fame: all wrong!

Posted in Statistics, University life with tags , , on January 30, 2010 by xi'an

Yesterday, the French daily Liberation ran a story about an appeal trial. As I happened to contribute to an expertise about this murder, I went pestering my office neighbours in Dauphine with the story and my two words of “fame” («très probablement»). The funniest thing is that our conclusion is quoted all wrong! We determined (by a simple Bayesian conjugate analysis of a Binomial experiment) that a cell-phone call was very unlikely to have been given from the place the main suspect said she was, given the antenna that got this call, while Liberation [and maybe the court] reports that the suspect was very likely to be at the location of the murder… No wonder when considering that statistics nor probability is taught in Law schools. Nor directly used in trials, as far as I know.

Ps- It is also comes as a surprise to me that this trial is still going on when considering that the murder took place in 1997 and that we sent our report in early 2000.

Big’MC seminar

Posted in R, Statistics, University life with tags , , , , on January 30, 2010 by xi'an

Two very interesting talks at the Big’ MC seminar on Thursday:

Phylogenetic models and MCMC methods for the reconstruction of language history by Robin Ryder

Uniform and non-uniform random generators by Régis Lebrun

which are both on topics close to my interest, evolution of languages (I’ll be a philologist in another life!) and uniform random generators.

The Search for Certainty: a book review

Posted in Books, Statistics with tags , , on January 29, 2010 by xi'an

As I have spent some time reading Krzysztof Burdzy’s The Search for Certainty over the past weeks and putting my thoughts together into a structured (?) review, I have written a full book review that I have submitted to Bayesian Analysis. And arXived as well. Hopefully, we can start a written discussion in the journal with diverging (?) opinions about the book. Starting with a debate about the probability and therefore the nature of the event represented on the front picture!

I gave Andrew Gelman the book yesterday night (on a sidewalk by the Luxembourg gardens) and he managed to produce a review within a few hours, concluding that the book is harmless and does little mischief in terms in statistical practice (a point I cannot but agree with).


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