Here is an email from Thomas I received yesterday about a computation in our book Introducing Monte Carlo Methods with R: I’m currently reading your book “Introduction to Monte Carlo Methods with R” and I quite highly appreciate your work. I’m not able to see how the integral ... [Read more...]

Since my first representation of the rank statistic as paired was incorrect, here is the histogram produced by the simulation perm=sample(1:20) saple[t]=sum(abs(sort(perm[1:10])-sort(perm[11:20]))) when . It is obviously much closer to zero than previously. An interesting change is that the regression of the log-mean ... [Read more...]

Following a comment from efrique pointing out that this statistic is called Spearman footrule, I want to clarify the notation in namely (a) that the ranks of and are considered for the whole sample, i.e. instead of being computed separately for the ‘s and the ‘s, and then (b) ... [Read more...]

In the puzzle found in Le Monde of this weekend, the mathematical object behind the silly story is defined as a pseudo-Spearman rank correlation test statistic, where the difference between the ranks of the paired random variables and is in absolute value instead of being squared as in the Spearman ... [Read more...]

Here are the slides for the Savage-Dickey paradox paper that I gave in San Antonio this morning: (Any suspected coincidence of the first part with earlier talks is for real!) I have tried to spell out as clearly as possible in the second part the issues of version choices that ... [Read more...]

Yesterday, I gave my short (3 hours) introduction to computational Bayesian statistics to a group of 25-30 highly motivated students. I managed to cover “only” the first three chapters, as I included some material on Bayes factor approximation and only barely reached Metropolis-Hastings. Here are the slides, modified from the original ... [Read more...]

The vanilla Rao-Blackwellisation paper with Randal Douc that had been resubmitted to the Annals of Statistics is now back for a revision, with quite encouraging comments: The paper has been reviewed by two referees both of whom comment on the clear exposition and the novelty of the results. Both referees ... [Read more...]

Given the wrong solution provided in Le Monde and comments from readers, I went to look a bit further on the Web for generic solutions to the rectangle problem. The most satisfactory version I have found so far is Mendelsohn’s in Mathematics Magazine, which gives as the maximal number ... [Read more...]

Following my remarks on the t-walk algorithm in the recent A General Purpose Sampling Algorithm for Continuous Distributions, published by Christen and Fox in Bayesian Analysis that acts like a general purpose MCMC algorithm, Darren Wraith tested it on the generic (10 dimension) banana target we used in the cosmology paper. ... [Read more...]

In the weekend supplement to Le Monde, the solution of the rectangle puzzle is given as 32 black squares. I am thus… puzzled!, since my R program there provides a 34 square solution. Am I missing a hidden rectangle in the above?! Given that the solution in Le Monde is not based ... [Read more...]

When I read in the abstract of the recent A General Purpose Sampling Algorithm for Continuous Distributions, published by Christen and Fox in Bayesian Analysis that We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning. I am slightly bemused. The proposal of the ... [Read more...]

The puzzle in last Saturday edition of Le Monde is made of two parts: Given a 10×10 grid, what is the maximum number of nodes one can highlight before creating a parallelogram with one side parallel to one of the axes of the grid? What is the maximum number of nodes ... [Read more...]

Darren Wraith pointed out to me this site proposing a whole series of videos introducing to R. (Unfortunately in a Windows environment.) This can be handy when facing students with no R background… Filed under: R, Statistics, University life Tagged: course, video [Read more...]

Last week, I got news from Springer Verlag about possibly two new editions of my books, one in Chinese and one in Japanese. These were bad news and good news: the bad news was that the Chinese edition was actually a reprint of our original book,  Monte Carlo Statistical Method, ... [Read more...]

In connection with the Le Monde puzzle of last week, I was looking for an R function that would give me the prime factor decomposition of any integer. Such a function exists within the package schoolmath, developped by Joerg Schlarmann and Josef Wienand. It is called prime.factor and it ... [Read more...]

At the Edinburgh mixture estimation workshop, Murray Aitkin presented his proposal to compare models via the posterior distribution of the likelihood ratio. As already commented in a post last July, the positive aspect of looking at this quantity rather than at the Bayes factor is that the priors are then ... [Read more...]

As a coincidence, or not, I received the following email just before starting our mixture estimation workshop (the above is Ben Nevis on Monday, whose skyline really looks like a three component mixture!) and giving a discussion on label switching: I am implementing a Markov-Chain Monte Carlo method for Gibbs ... [Read more...]

When I first read Le Monde puzzle this weekend, I though it was even less exciting than the previous one: find and , such that is a multiple of . The solution is obtained by brute-force checking through an R program: and then the a next solution is (with several values for ... [Read more...]

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Robin Ryder started his new blog with his different solutions to Le Monde puzzle of last Saturday (about the algebraic sum of products…), solutions that are much more elegant than my pedestrian rendering. I particularly like the one based on the Jacobian of a matrix! (Robin is doing a postdoc ... [Read more...]