Following my earlier post on the terrible performances of ChatGPT for a grasshopping riddle, Bob Carpenter sent me his interaction with GPT4, using the same entry. Here is the python code outcome he obtained. The code is running  and the answer is correct. BC: Thanks. Can you write a python ...

Since the solution to the previous riddle from The Riddler on the maximum of  different terms in the composed operation a∅b∅c∅d∅e∅f depending on the bracketing ordering and the meaning of each ∅ among one of the six elementary operations got posted today as 974,860, I got back ...

A riddle from The Riddler on how many different numbers one could at most produce from six initial values and the four basic operations. In other words, how many values could the terms in a∅(b∅{c∅[d∅(e∅f)]}) could take? (With each ∅ being one of the four operations ...

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

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 ...

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 ...

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 ...

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 […]

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, ...

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 ...

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, ...

My friend EJ Wagenmaker pointed me towards an entire book on the BF by Bozza (from Ca’Foscari, Venezia), Taroni and Biederman. It is providing a sort of blueprint for using Bayes factors in forensics for both investigative and evaluative purposes. With R code and free access. I am of ...

A riddle about leap years: a solar year consists of approximately 365.24217 mean solar days, which is why there is a leap year approximately every four years. Approximately because the Gregorian calendar plans 97 and not 100 leap years over 400 years. Is this the optimal solution? No, since the Gregorian difference is 3.3 10⁻⁴ […]

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 ...

A backward question from X validated as to why the above is a valid Normal generator based on exponential generations. Which can be found in most textbooks (if not ours). And in The Bible, albeit as an exercise. The validation proceeds from the (standard) Exponential density dominating the (standard) Normal ...

A riddle from the Riddler where N cars going at random (iid) speeds drive a road with a slow and a fast lane, each car choosing the fast lane iff any of the cars ahead in the slow lane is slowerthan them. With the question of the average number of ...

A zorbing puzzle from the Riddler: cover the plane with four non-intersecting disks of radius one towards getting the highest probability (under the standard bivariate Normal distribution). As I could not see a simple connection between the disks and the standard Normal, beyond the probability of a disk being given ...

The Kelly criterion is a way to optimise an unlimited sequence of bets under the following circumstances: a probability p of winning each bet, a loss of a fraction a of the sum bet, a gain of a fraction b of the sum bet, and a fraction f of the ...