## Archive for Carl Friedrich Gauss

## Gaußplatz [jatp]

Posted in pictures, Running, Travel with tags Austria, Carl Friedrich Gauss, Gaussplatz, jatp, running, Vienna, Wien on September 22, 2017 by xi'an## from least squares to signal processing and particle filtering

Posted in Books, Kids, Statistics, University life with tags Andrei Kolmogorov, auxiliary particle filter, Carl Friedrich Gauss, importance sampling, Kalman filter, R.E. Kálmán, Shannon, signal processing, stochastic processes on June 6, 2017 by xi'an**N**ozer Singpurwalla, Nick. Polson, and Refik Soyer have just arXived a remarkable survey on the history of signal processing, from Gauß, Yule, Kolmogorov and Wiener, to Ragazzini, Shanon, Kálmán [who, I was surprised to learn, died in Gainesville last year!], Gibbs sampling, and the particle filters of the 1990’s.

## Gauss to Laplace transmutation interpreted

Posted in Books, Kids, Statistics, University life with tags Box-Muller algorithm, Carl Friedrich Gauss, convolution, correlation, cross validated, Laplace distribution, Pierre Simon de Laplace on November 9, 2015 by xi'an**F**ollowing my earlier post [induced by browsing X validated], on the strange property that the product of a Normal variate by an Exponential variate is a Laplace variate, I got contacted by Peng Ding from UC Berkeley, who showed me how to derive the result by a mere algebraic transform, related with the decomposition

(X+Y)(X-Y)=X²-Y² ~ 2XY

when X,Y are iid Normal N(0,1). Peng Ding and Joseph Blitzstein have now arXived a note detailing this derivation, along with another derivation using the moment generating function. As a coincidence, I also came across another interesting representation on X validated, namely that, when X and Y are Normal N(0,1) variates with correlation ρ,

XY ~ R(cos(πU)+ρ)

with R Exponential and U Uniform (0,1). As shown by the OP of that question, it is a direct consequence of the decomposition of (X+Y)(X-Y) and of the polar or Box-Muller representation. This does not lead to a standard distribution of course, but remains a nice representation of the product of two Normals.

## re-re-relevant statistics for ABC model choice

Posted in Books, Statistics, University life with tags ABC, arXiv, Carl Friedrich Gauss, Pierre Simon de Laplace, relevant statistics, Series B, summary statistics on March 18, 2013 by xi'an**A**fter a very, very long delay, we eventually re-revised our paper about necessary and sufficient conditions on summary statistics to be relevant for model choice (i.e. to lead to consistent tests). Reasons, both good and bad, abound for this delay! Some (rather bad) were driven by the completion of a certain new edition… Some (fairly good) are connected with the requests from the *Series B* editorial team, towards improving our methodological input. As a result we put more emphasis on the post-ABC cross-checking for the relevance of the summary choice, via a predictive posterior evaluation of the means of the summary statistic under both models and a test for mean equality. And re-ran a series of experiments on a three population population genetic example. Plus, on the side, simplified some of our assumptions. I dearly hope the paper can make it through but am also looking forward the opinion of the Series B editorial team The next version of *Relevant statistics for Bayesian model choice* should be arXived by now *(meaning when this post appears!)*.

## 17 equations that changed the World (#1)

Posted in Books, Statistics, University life with tags 17 equations That Changed the World, book review, Carl Friedrich Gauss, Descartes, Euler, Galileo, Henri Poincaré, Ian Stewart, Intelligence Genes and Success, Isaac Newton, Molière, space travel, The Bell Curve, The Universe in zero words, Thomas Bayes on October 15, 2012 by xi'an**I** do not know if it is a coincidence or if publishers were competing for the same audience: after reviewing ** The universe in zero word: The story of mathematics as told through equations**, in this post (and in CHANCE, to appear in 25(3)!), I noticed Ian Stewart’s

**, published in 2011, and I bought a copy to check the differences between both books.**

*17 equations That Changed the World***I** am quite glad I did so, as I tremendously enjoyed this book, both for its style and its contents, both entertaining and highly informative. This does not come as a big surprise, given Stewart’s earlier books and their record, however this new selection and discussion of equations is clearly superior to ** The universe in zero word**! Maybe because it goes much further in its mathematical complexity, hence is more likely to appeal to the mathematically inclined (to borrow from my earlier review). For one thing, it does not shy away from inserting mathematical formulae and small proofs into the text, disregarding the risk of cutting many halves of the audience (I know, I know, high powers of (1/2)…!) For another,

**uses the equation under display to extend the presentation much much further than**

*17 equations That Changed the World***. It is also much more partisan (in an overall good way) in its interpretations and reflections about the World.**

*The universe in zero word*** I**n opposition with ** The universe in zero word**, formulas are well-presented, each character in the formula being explained in layman terms. (Once again, the printer could have used better fonts and the LaTeX word processor.) The (U.K. edition, see tomorrow!) cover is rather ugly, though, when compared with the beautiful cover of

**. But this is a minor quibble! Overall, it makes for an enjoyable, serious and thought-provoking read that I once again undertook mostly in transports (planes and métros). Continue reading**

*The universe in zero word*