A game-related Le Monde mathematical puzzle: Starting with a pile of 10⁴ tokens, Bob plays the following game: at each round, he picks one of the existing piles with at least 3 tokens, takes away one of the tokens in this pile, and separates the remaining ones into two non-empty piles of ...

In what I hope is the first occurrence of a new part of ISBA conferences, Booking.com is launching a data challenge at ISBA 2016 next week. The prize being a trip to take part in their monthly hackathon. In Amsterdam. It would be terrific if our Bayesian conferences, including BayesComp, ...

A new version of the R package abcrf has been posted on Friday by Jean-Michel Marin, in conjunction with the recent arXival of our paper on point estimation via ABC and random forests. The new R functions come to supplement the existing ones towards implementing ABC point estimation: covRegAbcrf, which ...

A not so enticing Le Monde mathematical puzzle: Find the minimal value of a five digit number divided by the sum of its digits. This can formalised as finding the minimum of N/(a+b+c+d+e) when N writes abcde. And solved by brute force. Using a rough ...

Although this is far from a paradox when realising why the phenomenon occurred, it took me a few lines to understand why the empirical average of a log-normal sample is apparently a biased estimator of its mean. And why the biased plug-in estimator does not appear to present a bias. ...

A puzzle on The Riddler last week that is rather similar to an earlier one. Given the probability (1/2,1/3,1/6) on {1,2,3}, what is the mean of the number N of draws to see all possible outcomes and what is the average number of 1’s in those draws? The second question is straightforward, ...

While the last riddle on The Riddler was rather anticlimactic, namely to find the mean of the number Y of empty bins in a uniform multinomial with n bins and m draws, with solution [which still has a link with e in that the fraction of empty bins converges to 1...

Before leaving Helsinki, we arXived [from the Air France lounge!] the paper Jean-Michel presented on Monday at ABCruise in Helsinki. This paper summarises the experiments Louis conducted over the past months to assess the great performances of a random forest regression approach to ABC parameter inference. Thus validating in this ...

As I was checking for software to answer a query on X validated about generic Bayes factor derivation, I came across an R software called BayesFactor, which only applies in regression settings and relies on the Savage-Dickey representation of the Bayes factor when the null hypothesis writes as θ=θ⁰ (and possibly ...

A paper in Nature this week that uses reversible-jump MCMC, phylogenetic trees, and Bayes factors. And that looks at institutionalised or ritual murders in Austronesian cultures. How better can it get?! “by applying Bayesian phylogenetic methods (…) we find strong support for models in which human sacrifice stabilizes social stratification once ...

Travelling through Seville, I arrived in Càdiz on Sunday night, along with a massive depression [weather-speaking!]. Walking through the city from the station was nonetheless pleasant as this is an town full of small streets and nice houses. If with less churches than Seville! Richard Samworth gave the first ...

A riddle from The Riddler where brute-force simulation does not pay: For a given integer N, pick at random without replacement integers between 1 and N by prohibiting consecutive integers until all possible entries are exhausted. What is the frequency of selected integers as N grows to infinity? A simple implementation ...

An arithmetic Le Monde mathematical puzzle: Given an integer k__1, consider the sequence defined by F(1)=1+1 mod k, F²(1)=F(1)+2 mod k, F³(1)=F²(1)+3 mod k, &tc. [With this notation, F is not necessarily a function.] For which value of k is the sequence the entire {0,1,…,k-1} set? This leads ...

Another of those arithmetic Le Monde mathematical puzzle: Find an integer A such that A is the sum of the squares of its four smallest dividers (including1) and an integer B such that B is the sum of the third poser of its four smallest factors. Are there such integers ...

A knapsack Le Monde mathematical puzzle: Given n packages weighting each at most 5.8kg for a total weight of 300kg, is it always possible to allocate these packages  to 12 separate boxes weighting at most 30kg each? weighting at most 29kg each? This can be checked by brute force using the ...

Statistical Rethinking: A Bayesian Course with Examples in R and Stan is a new book by Richard McElreath that CRC Press sent me for review in CHANCE. While the book was already discussed on Andrew’s blog three months ago, and [rightly so!] enthusiastically recommended by Rasmus Bååth on ...

A Le Monde mathematical puzzle with little need of R programming: Does there exist a function f from N to N such that (i) f is (strictly) increasing, (ii) f(n)≥n, and (iii) f²(n)=f(f(n))=3n? Indeed, the constraints imply (i) f²(0)=0, hence that that f(0)=0, (...