Publications by xi'an
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...
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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...
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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...
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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...
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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...
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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...
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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...
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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,...
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another lottery coincidence
Once again, meaningless figures are published about a man who won the French lottery (Le Loto) for the second time. The reported probability of the event is indeed one chance out of 363 (US) trillions (i.e., billions in the metric system. or 1012)… This number is simply the square of which is the number of possible loto grids. Thus, the probab...
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Posts of the year
Like last year, here are the most popular posts since last August: Home page 92,982 In{s}a(ne)!! 6,803 “simply start over and build something better” 5,834 Julien on R shortcomings 2,373 Parallel processing of independent Metropolis-Hastings algorithms 1,455 Do we need an integrated Bayesian/likelihood inference? 1,361 Coincidence in lotter...
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