Publications by xi'an
multiplying the bars
The latest Riddler makes the remark that the expression |-1|-2|-3| has no unique meaning (and hence value) since it could be | -1x|-2|-3 | = 5 or |-1| – 2x|-3| = -5 depending on the position of the multiplication sign and asks for all the possible values of |-1|-2|…|-9| which can be explored by a recursive R function for computing |-i...
1082 sym R (557 sym/2 pcs)
chain of lynx and drove of hares
A paper (and an introduction to the paper) in Nature this week seems to have made progress on the existence of indefinite predator-prey cyles. As in the lynx/hare dataset available on R. The paper is focusing on another pair, an invertebrate and its prey, an algae. For which the authors managed a 50 cycle sequence. What I do not get about this ex...
1433 sym 2 img
!ABC%in%Grenoble
Most regrettably, the incoming ABC in Grenoble, planned on 19-20 March 2020 is now postponed till a yet unspecified date, like next Summer or next Fall. Due to travel disruptions all over the World and to gathering restrictions in France, courtesy of the Covid-19 virus. Not particularly surprising given the avalanche of cancellations, but unfortu...
1683 sym 2 img
one or two?
A superposition of two random walks from The Riddler: Starting from zero, a random walk is produced by choosing moves between ±1 and ±2 at each step. If the choice between both is made towards maximising the probability of ending up positive after 100 steps, what is this probability? Although the optimal path is not necessarily made of moves th...
1237 sym R (446 sym/6 pcs)
Le Monde puzzle [#1134]
A weekly Monde current mathematical puzzle on gcd’s and scm’s: If one replaces a pair (a,b) of integers with the pair (g,s) of their greatest common denominator and smallest common multiple, how long at most before the sequence ends. Same question when considering a collection of five integers where two are selected by the pair (g,s) of thei...
1068 sym R (409 sym/1 pcs) 2 img
Probability and Bayesian modeling [book review]
Probability and Bayesian modeling is a textbook by Jim Albert and Jingchen Hu that CRC Press sent me for review in CHANCE. (The book is also freely available in bookdown format.) The level of the textbook is definitely most introductory as it dedicates its first half on probability concepts (with no measure theory involved), meaning mostly focusi...
7658 sym 4 img
Le Monde puzzle [#1133]
A weekly Monde current mathematical puzzle that reminded me of an earlier one (but was too lazy to check): If ADULE-ELUDE=POINT, was is the largest possible value of POINT? With the convention that all letters correspond to different digits and no digit can start with 0. Same question when ADULE+ELUDE=POINT. The run of a brute force R search re...
900 sym R (495 sym/3 pcs) 2 img
wrapped Normal distribution
One version of the wrapped Normal distribution on (0,1) is expressed as a sum of Normal distributions with means shifted by all relative integers which, while a parameterised density, has imho no particular statistical appeal over the use of other series. It was nonetheless the centre of a series of questions on X validated in the past weeks. Cu...
1579 sym R (399 sym/1 pcs) 10 img
a computational approach to statistical learning [book review]
This book was sent to me by CRC Press for review for CHANCE. I read it over a few mornings while [confined] at home and found it much more computational than statistical. In the sense that the authors go quite thoroughly into the construction of standard learning procedures, including home-made R codes that obviously help in understanding the nit...
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random generators produce ties
“…an essential part of understanding how many ties these RNGs produce is to understand how many ties one expects in 32-bit integer arithmetic.” A sort of a birthday-problem paper for random generators by Markus Hofert on arXiv as to why they produce ties. As shown for instance in the R code (inspired by the paper): sum(duplicated(runif(1e6...
1526 sym R (29 sym/1 pcs)