Two fairy different riddles on the weekend Riddler. The first one is (in fine) about Egyptian fractions: I understand the first one as Find the Egyptian fraction decomposition of 2 into 11 distinct unit fractions that maximises the smallest fraction. And which I cannot solve despite perusing this amazing webpage on Egyptian ...

Following our arXival of ABC-Gibbs, Dennis Prangle pointed out to us a 2016 paper by Athanasios Kousathanas, Christoph Leuenberger, Jonas Helfer, Mathieu Quinodoz, Matthieu Foll, and Daniel Wegmann, Likelihood-Free Inference in High-Dimensional Model, published in Genetics, Vol. 203, 893–904 in June 2016. This paper contains a version of ABC Gibbs where parameters are sequentially ...

Having discovered codegolf on Stack Exchange a few weeks ago, I spotted a few interesting puzzles since then but only got the opportunity at a try over a quiet and rainy weekend (and Robin being on vacation)! The challenge was to write an R code for deciding whether or not ...

The riddle of the week is rather standard probability calculus If N points are generated at random places on the perimeter of a circle, what is the probability that you can pick a diameter such that all of those points are on only one side of the newly halved circle? ...

A question on X validated led me to wonder at the point made by Christopher Bishop in his Pattern Recognition and Machine Learning book about the MLE of the Normal variance being biased. As it is illustrated by the above graph that opposes the true and green distribution of the ...

A simple 2×2 Le Monde mathematical puzzle: Arielle and Brandwein play a game out of two distinct even integers between 1500 and 2500,  and y. Providing one another with either the pair (x/2,y+x/2) or the pair (x+y/2,y/2) until they run out of even possibilities or exceed 6 rounds. When x=2304, ...

A rather blah number Le Monde mathematical puzzle: Find all integer multiples of 11111 with exactly one occurrence of each decimal digit.. Which I solved by brute force, by looking at the possible range of multiples (and  borrowing stringr:str_count from Robin!) __ combien=0 __ for (i in 90001:900008){ j=i*11111 combien=combien+(...

A neat question from The Riddler on a multi-probability survival rate: Nine processes are running in a loop with fixed survivals rates .99,….,.91. What is the probability that the first process is the last one to die? Same question with probabilities .91,…,.99 and the probability that the last process is the last ...

The full program is now available on the conference webpage of BayesComp 20, next 7-10 Jan 2020. There are eleven invited sessions, including one j-ISBA session, and a further thirteen contributed sessions were selected by the scientific committee. Calls are still open for tutorials on Tuesday 07 January (with two already planed on ...

A board (Ising!) Le Monde mathematical puzzle in the optimisation mode, again: On a 7×7 board, what is the maximal number of locations that one can occupy when imposing at least two empty neighbours ? Which I tried to solve by brute force and simulated annealing (what else?!), first defining a target ...

One challenge on code golf is to find the shortest possible code to identify whether or not an integer belongs to the binary cyclops numbers which binary expansion is 0, 101, 11011, 1110111, 111101111, &tc. The n-th such number being this leads to the above solution in R (26 bits). The same length as the […]

A board-like Le Monde mathematical puzzle in the digit category: Given a (k,m) binary matrix, what is the maximum number S of entries with only one neighbour equal to one? Solve for k=m=2,…,13, and k=6,m=8. For instance, for k=m=2, the matrix is producing the maximal number 4. ...

A call to all potential participants to the incoming BayesComp 2020 conference at the University of Florida in Gainesville, Florida, 7-10 January 2020, to submit proposals [to me] for contributed sessions on everything computational or training labs [to David Rossell] on a specific language or software. The deadline is April 1 and the ...

Here are two nice exercises for a future simulation exam, seen and solved on X validated.The first one is about simulating a Gibbs sampler associated with the joint target exp{-|x|-|y|-a(y-x|} defined over IR² for a≥0 (or possibly a__-1). The conditionals are identical ...

A new Le Monde mathematical puzzle in the digit category: Given 13 arbitrary relative integers chosen by Bo, Abigail can select any subset of them to be drifted by plus or minus one by Bo, repeatedly until Abigail reaches the largest possible number N of multiples of 5. What is the minimal ...

A Le Monde mathematical puzzle that seems hard to solve without the backup of a computer (and just simple enough to code on a flight to Montpellier): Given the number N=2,019, find a decomposition of N as a sum of non-trivial powers of integers such that (a) the number of ...

A puzzling riddle from The Riddler (as Le Monde had a painful geometry riddle this week): this number with 114 digits 530,131,801,762,787,739,802,889,792,754,109,70?,139,358,547,710,066,257,652,050,346,294,484,433,323,974,747,960,297,803,292,989,236,183,040,000,000,000 is missing one digit and is a product of some of the integers between 2 and 99. By comparison, 76! and 77! have 112 and 114 digits, respectively. While 99! has 156 digits. […]

Although it may sound like an excessive notion of optimality, one can hope at obtaining an estimator δ of a unidimensional parameter θ that is always closer to θ that any other parameter. In distribution if not almost surely, meaning the cdf of (δ-θ) is steeper than for other estimators enjoying the same ...