Publications by xi'an
Le Monde puzzle [#29]
This week, the puzzle from the weekend edition of Le Monde was easy to state: in the sequence (8+17n), is there a 6th power? a 7th? an 8th? If so, give the first occurrence. So I first wrote an R code for a function testing whether an integer is any power: ispower=function(x){ ispo=FALSE logx=log(x) i=trunc(logx/log(2)) while((i>1)&&(!ispo)){ j=t...
1885 sym R (720 sym/5 pcs) 18 img
JSM 2011 [3]
Monday August 01 was the first full day of JSM 2011 and full is the appropriate word to describe the day! It started for me at 7am with a round table run by Marc Suchard on parallel computing (or at 3am if I am considering the time I woke up!). I was rather out of my depth there, given that my link with parallel computing is rather formal, having...
5581 sym 20 img
Number of components in a mixture
I got a paper (unavailable online) to referee about testing for the order (i.e. the number of components) of a normal mixture. Although this is an easily spelled problem, namely estimate k in I came to the conclusion that it is a kind of ill-posed problem. Without a clear definition of what a component is, i.e. without a well-articulated prior d...
2067 sym 20 img
Bayes factors and martingales
A surprising paper came out in the last issue of Statistical Science, linking martingales and Bayes factors. In the historical part, the authors (Shafer, Shen, Vereshchagin and Vovk) recall that martingales were popularised by Martin-Löf, who is also influential in the theory of algorithmic randomness. A property of test martingales (i.e., marti...
2539 sym R (280 sym/1 pcs) 28 img
expectation-propagation and ABC
“It seems quite absurd to reject an EP-based approach, if the only alternative is an ABC approach based on summary statistics, which introduces a bias which seems both larger (according to our numerical examples) and more arbitrary, in the sense that in real-world applications one has little intuition and even less mathematical guidance on to w...
3193 sym 20 img
le logiciel R
For once, here is a book review I wrote in French about the book Le logiciel R, written by Pierre Lafaye de Micheaux (Université de Montréal), Rémy Drouilhet (Université de Grenoble 2) and Benoît Liquet (Université de Bordeaux 2): Ce livre édité par Springer (dans la même collection que Le Choix Bayesien) propose une couverture exhausti...
3315 sym 18 img
computational difficulties [with notations]
Here is an email I received from Umberto: I have a doubt regarding the tempered transitions method you considered in your JASA article with Celeux and Hurn. On page 961 you detail the several steps for building a proposal for a given distribution by simulating through l tempered power densities. I am slightly confused regarding the interpretatio...
2395 sym 22 img
Numerical analysis for statisticians
“In the end, it really is just a matter of choosing the relevant parts of mathematics and ignoring the rest. Of course, the hard part is deciding what is irrelevant.” Somehow, I had missed the first edition of this book and thus I started reading it this afternoon with a newcomer’s eyes (obviously, I will not comment on the differences wit...
5181 sym 18 img
Le Monde puzzle [#737]
The puzzle in the weekend edition of Le Monde this week can be expressed as follows: Consider four integer sequences (xn), (yn), (zn), and (wn), such that and, if u=(xn,yn,zn,wn), for i=1,…,4, otherwise. Find the first return time n (if any) such that xn=0. Find the value of (y0,z0,w0) that minimises this return time. The difficulty stands wi...
1256 sym R (730 sym/1 pcs) 22 img
Le Monde puzzle [#737 re-read]
As a coincidence, while I was waiting for the solution to puzzle #737 published this Friday in Le Monde, the delivery (wo)man forgot to include the weekend magazine and I had to buy it this morning with my baguette (as if anyone cares!). The solution is (y0,z0,w0)=(38,40,46) and…it does not work! The value of (x1,y1,z1,w1) is indeed (19,39,43,...
1278 sym R (494 sym/3 pcs) 22 img