## mea culpa!

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , on October 9, 2017 by xi'an

An entry about our Bayesian Essentials book on X validated alerted me to a typo in the derivation of the Gaussian posterior..! When deriving the posterior (which was left as an exercise in the Bayesian Core), I just forgot the term expressing the divergence between the prior mean and the sample mean. Mea culpa!!!

## LaTeX issues from Vienna

Posted in Books, Statistics, University life with tags , , , , , , , , , , , on September 21, 2017 by xi'an

When working on the final stage of our edited handbook on mixtures, in Vienna, I came across unexpected practical difficulties! One was that by working on Dropbox with Windows users, files and directories names suddenly switched from upper case to lower cases letters !, making hard-wired paths to figures and subsections void in the numerous LaTeX files used for the book. And forcing us to change to lower cases everywhere. Having not worked under Windows since George Casella gave me my first laptop in the mid 90’s!, I am amazed that this inability to handle both upper and lower names is still an issue. And that Dropbox replicates it. (And that some people see that as a plus.)

The other LaTeX issue that took a while to solve was that we opted for one chapter one bibliography, rather than having a single bibliography at the end of the book, mainly because CRC Press asked for this feature in order to sell chapters individually… This was my first encounter with this issue and I found the solutions to produce individual bibliographies incredibly heavy handed, whether through chapterbib or bibunits, since one has to bibtex one .aux file for each chapter. Even with a one line bash command, this is annoying to the extreme!

## zurück nach Wien

Posted in pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , on September 16, 2017 by xi'an

Today, I am travelling to Vienna for a few days, primarily for assessing a grant renewal for a research consortium federating most Austrian research groups on a topic for which Austria is a world-leader. (Sorry for being cryptic but I am unsure how much I can disclose about this assessment!) And taking advantage on being in Vienna, for a two-day editing session with Sylvia Früwirth-Schnatter and Gilles Celeux on our Handbook of mixtures analysis project. Which started a few years ago with another meeting in Vienna. And taking further advantage on being in Vienna, for an evening at the Volksoper, conveniently playing Die Zauberflöte!

## an elegant result on exponential spacings

Posted in Statistics with tags , , , , , , , , , , , , , on April 19, 2017 by xi'an

A question on X validated I spotted in the train back from Lyon got me desperately seeking a reference in Devroye’s Generation Bible despite the abyssal wireless and a group of screeching urchins a few seats away from me… The question is about why

$\sum_{i=1}^{n}(Y_i - Y_{(1)}) \sim \text{Gamma}(n-1, 1)$

when the Y’s are standard exponentials. Since this reminded me immediately of exponential spacings, thanks to our Devroye fan-club reading group in Warwick,  I tried to download Devroye’s Chapter V and managed after a few aborts (and a significant increase in decibels from the family corner). The result by Sukhatme (1937) is in plain sight as Theorem 2.3 and is quite elegant as it relies on the fact that

$\sum_{i=1}^n y_i=\sum_{j=1}^n (n-j+1)(y_{(j)}-y_{(j-1)})=\sum_{j=2}^n (y_{(j)}-y_{(1)})$

hence sums up as a mere linear change of variables! (Pandurang Vasudeo Sukhatme (1911–1997) was an Indian statistician who worked on human nutrition and got the Guy Medal of the RSS in 1963.)

## simulation by hand

Posted in Books, Kids, pictures, Statistics, Travel with tags , , , , , , , on November 28, 2016 by xi'an

A rather weird question on X validated this week was about devising a manual way to simulate (a few) normal variates. By manual I presume the author of the question means without resorting to a computer or any other business machine. Now, I do not know of any real phenomenon that is exactly and provably Normal. As analysed in a great philosophy of science paper by Aidan Lyon, the standard explanations for a real phenomenon to be Normal are almost invariably false, even those invoking the Central Limit Theorem. Hence I cannot think of a mechanical device that would directly return Normal generations from a Normal distribution with known parameters. However, since it is possible to simulate by hand Uniform U(0,1) variates [up to a given precision] using a chronometre or a wheel, calls to versions of the Box-Müller algorithm that do not rely on logarithmic or trigonometric functions are feasible, for instance by generating two Exponential variates, x and y, until 2y>(1-x)², x being the output. And generating Exponential variates is easy provided a radioactive material with known half-life is available, along with a Geiger counter. Or, if not, by calling von Neumann’s exponential generator. As detailed in Devroye’s simulation book.

After proposing this solution, I received a comment from the author of the question towards a simpler solution based, e.g., on the Central Limit Theorem. Presumably for simple iid random variables such as coin tosses or dice experiments. While I used the CLT for simulating Normal variables in my very early days [just after programming on punched cards!], I do not think this is a very good or efficient method, as the tails grow very slowly to normality. By comparison, using the same amount of coin tosses to create a sufficient number of binary digits of a Uniform variate produces a computer-precision exact Uniform variate, which can be exploited in Box-Müller-like algorithms to return exact Normal variates… Even by hand if necessary. [For some reason, this question attracted a lot of traffic and an encyclopaedic answer on X validated, despite being borderline to the point of being proposed for closure.]

## Introduction à Monte Carlo en R

Posted in Books, R, Statistics with tags , , , , , , , on November 12, 2009 by xi'an

Following a proposal by Springer-Verlag Paris, I have decided to translate Introducing Monte Carlo Methods with R with George Casella into French, since a new collection of R books (in French) is planed for the Spring of 2010. The translation will a priori be done by Joachim Robert and Robin Ryder, under my supervision and with the support of Springer-Verlag Paris. I have already translated the first chapter as I needed to cut most of the R coverage, since this collection assumes a prior knowledge of R and aims at a smaller number of pages (around 200) to keep the price as low as possible.

## The twilight zone!

Posted in Statistics with tags , , on November 26, 2008 by xi'an

I had the weirdest impression this morning when, while looking at entries on defensive sampling on Google, I ended up on a webpage that suspiciously looked like my own work! After getting over the first shock (it was way too early for shouting out loud!), I went up the directory hierarchy to understand at last that my entry into the collective book Computational Statistics by James E. Gentle, Wolfgang Härdle, and Yuichi Mori has a free version available on the Web, as all entries of this book have…. This available web-book can be quite useful as additional material when teaching an introductory course on computational statistics.