A straightforward but probabilistic riddle this week in the Riddler, which is to find the expected order of integer i when the sequence {1,2,…,n} is partitioned at random into two sets, A and B, each of which is then sorted before both sets are merged. For instance, if {1,2,3,4} is divided ...

An interesting question about stratified sampling came up on X validated last week, namely how to optimise a Monte Carlo estimate based on two subsequent simulations, one, X, from a marginal and one or several Y from the corresponding conditional given X, when the costs of producing those two simulations ...

The next AISTATS conference is taking place in Florida, Fort Lauderdale, on April 20-22. (The website keeps the same address one conference after another, which means all my links to the AISTATS 2016 conference in Cadiz are no longer valid. And that the above sunset from Florida is named… cadiz.jpg!) ...

[A review of Bayesian Essentials that appeared in Technometrics two weeks ago, with the first author being rechristened Jean-Michael!] “Overall this book is a very helpful and useful introduction to Bayesian methods of data analysis. I found the use of R, the code in the book, and the companion R ...

As I was previously unaware of this book coming up, my surprise and excitement were both extreme when I received it from CRC Press a few weeks ago! John Chambers, one of the fathers of S, precursor of R, had just published a book about extending R. It covers some ...

Following my post of yesterday about the missing condition in Lynch’s R code, Gérard Letac sent me a paper he recently wrote with Luc Devroye on correlation matrices and copulas. Paper written for the memorial volume in honour of Marc Yor. It considers the neat problem of the ...

A s I figured out while working with astronomer colleagues last week, a strange if understandable difficulty proceeds from the simplest and most studied statistical model, namely the Normal model x~N(θ,1) Indeed, if one reparametrises this model as x~N(υ⁻¹,1) with υ__0, a single observation x brings very little information ...

Quite a coincidence! I just came across another bug in Lynch’s (2007) book, Introduction to Applied Bayesian Statistics and Estimation for Social Scientists. Already discussed here and on X validated. While working with one participant to the post-ISBA softshop, we were looking for efficient approaches to simulating correlation matrices and ...

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 ...