Publications by xi'an
simulated annealing and logistic regression to the max
A Riddler puzzle on the three binary and sequential questions one should ask three players hiding their respective U(0,1) realisation, U, V, and W, to best guess which player holds the largest number, max{U,V,W}. Assuming questions of the type Is U, &tc., the challenge boils down to selecting seven bounds (one for U, two for V, and four for W) in o...
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powering a probability [a Bernoulli factory tale]
Starting from an X validated question on finding an unbiased estimator of an integral raised to a non-integer power, I came across a somewhat interesting Bernoulli factory solution! Thanks to Peter Occil’s encyclopedic record of cases, pointing out to Mendo’s (2019) solution for functions of ρ that can be expressed as power series. Like ργ s...
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partial rankings and aggregate ranks
When interviewing impressive applicants from a stunning variety of places and background for fellows in our Data Science for Social Good program (in Warwick and Kaiserslautern) this summer, we came through the common conundrum of comparing ranks while each of us only meeting a subset of the candidates. Over a free morning, I briefly thought of the ...
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JAGS Workshop [10-14 July 2023]
Hey, JAGS users and would-be users, be warned that registration is now open for the annual JAGS workshop on probabilistic modelling for cognitive science. The tenth instalment of this workshop takes place July 10–14, 2023 in Amsterdam and online. This workshop is meant for researchers who want to learn how to apply Bayesian inference in practice....
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alone in Napoli
A combinatorics puzzle from The Riddler about a Napoli solitaire where 4 x 10 cards numbered from 1 to 10 are shuffled and the game is lost when a number (1,2, or 3) is equal to its position modulo 3 (1,2 or 3). A simple R code shows that the probability of winning is around 0.00831: N=40 for(t in 1:1e6)F=F+!sum(!(sample((1:N)%%10)-(1:N)%%3)) Ch...
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The Effect [book review]
While it sounds like the title of a science-fiction catastrophe novel or of a (of course) convoluted nouveau roman, this book by Nick Huntington-Klein is a massive initiation to econometrics and causality. As explained by the subtitle, An Introduction to Research Design and Causality. This is a hüûüge book, actually made of two parts that could ...
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Diophantine riddle
The weekly riddle from The Riddler is to find solutions to the Diophantine equation c³-c=b²+4 (when b and c are positive integers). First, forget about ChatGPT since it states this is a Pell equation. With a wrong argument. Second, when running a basic R code, using as.double to handle larger integers, the only solution less than 10⁶ this code ...
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latest math stats exam
As I finished grading our undergrad math stats exam (in Paris Dauphine) over the weekend, which was very straightforward this year, the more because most questions had already been asked on weekly quizzes or during practicals, some answers stroke me as atypical (but ChatGPT is not to blame!). For instance, in question 1, (c) received a fair share...
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another drawer of socks
A socks riddle from the Riddler but with no clear ABC connection! Twenty-eight socks from fourteen pairs of socks are taken from a drawer, one by one, and laid on a surface that only fit nine socks at a time, with complete pairs removed. What is the probability that all pairs are stored without running out of space? No orphan socks then!! Writing...
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Tribonacci sequence
A simplistic puzzle from The Riddler when applying brute force: A Tribonacci sequence is based on three entry integers a ≤ b ≤ c, and subsequent terms are the sum of the previous three. Among Tribonacci sequences containing 2023, which one achieves the smallest fourth term, a+b+c ? The R code tri<-function(a,b,e){ while(F<2023){ F=a+b...
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