Category: Kids

posterior distribution missing the MLE

An X validated question as to why the MLE is not necessarily (well) covered by a posterior distribution. Even for a flat prior… Which in restrospect highlights the fact that the MLE (and the MAP) are invasive species in a Bayesian ecosystem. Since they do not account for the dominating measure. And hence do not […]

Le Monde puzzle [#1094]

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+(min(stringr::str_count(j,paste(0:9)))==1)} > combien [1] 3456 And […]

survivalists [a Riddler’s riddle]

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 one to die. […]

Gone…!

Even stronger and farther-reaching a symbol of Paris than the Eiffel Tower, the Notre-Dame-de-Paris cathedral is now burning down. Only Hugo can make for the memory of this monumental loss: “Sur la face de cette vieille reine de noscathédrales, à côté d’une ride on trouve toujours une cicatrice. Tempua edax, homo edacior; ce que je […]

ERC panel [step #2]

Another post that was written ages ago, about the second round of the European Research Council (ERC) panel on starting grants for mathematics in which I took part as an expert and not as an applicant. While anonymity possibly fell apart for the several dozens of applicants who were shortlisted for interview, in particular more […]

Metropolis gets off the ground

An X validated discussion that toed-and-froed about an incomprehension of the Metropolis-Hastings algorithm. Which started with a blame of George Casella‘s and Roger Berger’s Statistical Inference (p.254), when the real issue was the inquisitor having difficulties with the notation V ~ f(v), or the notion of random variable [generation], mistaking identically distributed with identical. Even […]

no country for old liars

A puzzle from the Riddler about a group of five persons, A,..,E, where all and only people strictly older than L are liars, all making statements about others’ ages: A: B>20 and D>16 B: C>18 and E<20 C: D<22 and A=19 D: E≠20 and B=20 E: A>21 and C<18 The Riddler is asking for the […]

Le Monde puzzle [#1088]

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 targ=function(tabz){ sum(tabz[-c(1,9),-c(1,9)]-1.2*(tabz[-c(1,9),-c(1,9)]*tabz[-c(8,9),-c(1,9)] +tabz[-c(1,9),-c(1,9)]*tabz[-c(1,2),-c(1,9)] […]

(x=scan())%in%(2*4^(n=0:x)-2^n-1)

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 […]

La peste et la vigne [book review]

During my trip to Cambodia, I read the second volume of this fantasy cycle in French. Which I liked almost as much as the first volume since the author continues to explore the mystery of the central character Syffe and its relations with some magical forces at play in his universe. As in most stories […]

ERC panel [step #1]

Although this post was written ages ago, regulations of the European Research Council (ERC) prevented me from posting it until now, for confidentiality reasons. I was indeed nominated as an expert member of the ERC panel on starting grants for mathematics [a denomination including statistics, obviously, but also quantum physics or some aspects of it], […]

sorcerer to the Crown [book review]

Sorcerer to the Crown is an historical fantasy book by Zen Cho I got into buying by reading a review linking most positively it to Jonathan Strange & Mr. Norrell. Obviously I should have known better, given that Jonathan Strange & Mr. Norrell was several years in the making, with both a very convincing reconstitution […]

Siem Reap conference

As I returned from the conference in Siem Reap. on a flight avoiding India and Pakistan and their [brittle and bristling!] boundary on the way back, instead flying far far north, near Arkhangelsk (but with nothing to show for it, as the flight back was fully in the dark), I reflected how enjoyable this conference […]

error bars [reposted]

A definitely brilliant entry on xkcd that reflects upon the infinite regress of producing error evaluations that are based on estimates. A must for the next class when I introduce error bars and confidence intervals!

Le Monde puzzle [#1087]

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. I first attempted a brute force random filling […]

and it only gets worse…

” A recent survey by Bankrate.com found that just 40% of US households have enough money to cover a $1,000 in emergency expenses.” The Guardian, Feb 2, 2019 ““Until we heard those cheers coming from Albany, we thought states were moving beyond such barbaric practices.” Mr. Pence offered his argument as a litmus test of […]

simulation fodder for future exams

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 and non-standard, but a simple bound on the conditional density is the corresponding […]