A rather exotic question on X validated: since π can be approximated by random sampling over a unit square, is there an equivalent for approximating e? This is an interesting question, as, indeed, why not focus on e rather than π after all?! But very quickly the very artificiality of the problem ...

Another boardgame in Le Monde mathematical puzzle : Given an 8×8 chequerboard,  consider placing 2×2 tiles over this chequerboard until (a) the entire surface is covered and (b) removing a single 2×2 tile exposes some of the original chequerboard. What is the maximal number of 2×2 tiles one can set according to this scheme? And ...

Hyungsuk Tak, Xiao-Li Meng and David van Dyk just arXived a paper on a multiple choice proposal in Metropolis-Hastings algorithms towards dealing with multimodal targets. Called “A repulsive-attractive Metropolis algorithm for multimodality” [although I wonder why XXL did not jump at the opportunity to use the “love-hate” denomination!]. The proposal ...

When discussing high dimension models with Ingmar Schüster Schuster [blame my fascination for accented characters!] the other day, we came across the following paradox with Metropolis-Hastings algorithms. If attempting to simulate from a multivariate standard normal distribution in a large dimension, when starting from the mode of the target, ...

After the MCqMC 2014 conference in Leuven I enjoyed very much, the MCqMC 2016 instalment takes place in Stanford this (late) summer. I cannot alas attend it, as I will be in Australia all summer winter, but the program looks terrific! As Art’s tutorial so brilliantly showed at MCMskv last week, ...

While browsing Images des Mathématiques, I came across this article [in French] that studies the impact of round-off errors on number representations in a dynamical system and checked how much this was the case for MCMC algorithms like the slice sampler (recycling some R code from Monte Carlo Statistical ...

As I am flying back to Paris (with an afternoon committee meeting in München in-between), I am reminiscing on the superlative scientific quality of this MCMski meeting, on the novel directions in computational Bayesian statistics exhibited therein, and on the potential settings for the next meeting. If any. First, ...

After presenting this work in both London and Lenzerheide, Kaniav Kamary, Kate Lee and I arXived and submitted our paper on a new parametrisation of location-scale mixtures. Although it took a long while to finalise the paper, given that we came with the original and central idea about a year ...

Tuesday at MCMSkv was a rather tense day for me, from having to plan the whole day “away from home” [8km away] to the mundane worry of renting ski equipment and getting to the ski runs over the noon break, to giving a poster over our new mixture paper with ...

If you remember the previous post, I had two interpretations about Le Monde mathematical puzzle #639: Find all integers with less than 11 digits that are perfect squares and can be written as a(a+6), a being an integer. and: Find all integers with less than 11 digits that are perfect squares and ...

A Le Monde mathematical puzzle about special integers: Find all integers with less than 11 digits that are perfect squares and can be written as a(a+6), a being an integer. Eleven digits being too much for a brute force exploration of the form `for (t in 1:1e11)`…, some preliminary  analysis ...

One student of mine coded by mistake an independent Metropolis-Hastings algorithm with too small a variance in the proposal when compared with the target variance. Here is the R code of this implementation: It produces outputs of the following shape which is quite amazing because of the small variance. The ...

[Here are some comments sent to me by Aki Vehtari in the sequel of the previous posts.] The following is mostly based on our arXived paper with Andrew Gelman and the references mentioned  there. Koopman, Shephard, and Creal (2009) proposed to make a sample based estimate of the existence of the ...

“In this article it is shown that in a fairly general setting, a sample of size approximately exp(D(μ|ν)) is necessary and sufficient for accurate estimation by importance sampling.” Sourav Chatterjee and Persi Diaconis arXived yesterday an exciting paper where they study the proper sample size in an importance sampling ...

A combinatoric Le Monde mathematical puzzle that resembles many earlier ones: Given a pool of 30 interns allocated to three person night-shifts, is it possible to see 31 consecutive nights such that (a) all the shifts differ and (b) there are no pair of shifts with a single common intern? In fact, ...

By some piece of luck, I came upon the book Think Bayes: Bayesian Statistics Made Simple, written by Allen B. Downey and published by Green Tea Press [which I could relate to No Starch Press, focussing on coffee!, which published Statistics Done Wrong that I reviewed a while ago] which ...