Publications by xi'an
Wrong puzzle of the week [w10]?!
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 on a precise mathematical argument (something to do with graph theo...
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t-walk on the banana side
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. Here is an output from...
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Solving the rectangle puzzle
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 for a grid. His theorem is based on the theory of projecti...
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Vanilla Rao-Blackwellisation for revision
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 point to the empirical results as being s...
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Course in San Antonio, Texas
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 Bayesia...
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Savage-Dickey [talk]
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 are at the core of the “paradox”. Filed under: R, Statistics, Tra...
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Le Monde rank test
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 rank test statistic. I don’t know whether o...
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Le Monde rank test (cont’d)
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) that the ranks are reordered for each group (meaning that the g...
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Le Monde rank test (corr’d)
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 on produces > lm(log(meme...
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An obscure integral
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 on page 74, that describes the marginal likelihood, simplifies ...
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