I reran the program checking the distribution of the digits over 9 “diagonals” (obtained by acceptable permutations of rows and column) and this test again results in mostly small p-values. Over a million iterations, and the nine (dependent) diagonals, four p-values were below 0.01, three were below 0.1, and two were above (0.21 and 0.42). [...]

As the discrepancy [from 1] in the sum of the nine probabilities seemed too blatant to be attributed to numerical error given the problem scale, I went and checked my R code for the probabilities and found a choose(9,3) instead of a choose(6,3) in the last line… The fit between the ...

A longer run of the R code of yesterday with a million sudokus produced the following qqplot. It does look ok but no perfect. Actually, it looks very much like the graph of yesterday, although based on a 100-fold increase in the number of simulations. Now, if I test the ...

Most embarrassingly, Liaosa Xu from Virginia Tech sent the following email almost a month ago and I forgot to reply: I have a question regarding your example 7.11 in your book Introducing Monte Carlo Methods with R.  To further decompose the uniform simulation by sampling a and b step by step, ...

Robin Ryder pointed out to me that 3 is indeed the absolute minimum one could observe because of the block constraint (bon sang, mais c’est bien sûr !). The distribution of the series of 3 digits being independent over blocks, the theoretical distribution under uniformity can easily be simulated: #uniform distribution ...

Reza Seirafi from Virginia Tech sent me the following email about Bayesian Core, which alas is pointing out a real typo in the reversible jump acceptance probability for the mixture model: With respect to the expression provided on page 178 for the acceptance probability of the split move, I was wondering ...

The function pimax from our package mcsm is used in to reproduce Figure 5.11 of our book Introducing Monte Carlo Methods with R. (The name comes from using the Pima Indian R benchmark as the reference dataset.) I got this email from Josué I ran the ‘pimax’ example from the mcsm ...

Wolfram Research presumably has a robot that sends automated email following postings on arXiv: Your article, “Evidence and Evolution: A review”, caught the attention of one of my colleagues, who thought that it could be developed into an interesting Demonstration to add to the Wolfram Demonstrations Project. The Demonstrations Project, ...

Do not resort to Monte Carlo methods unnecessarily. When I received this 2009 Springer-Verlag book, Computational Statistics, by James Gentle a while ago, I briefly took a look at the table of contents and decided to have a better look later… Now that I have gone through the whole book, I ...

Glancing perchance at the back of my Amstat News, I was intrigued by the SAS advertisement Bayesian Methods Specify Bayesian analysis for ANOVA, logistic regression, Poisson regression, accelerated failure time models and Cox regression through the GENMOD, LIFEREG and PHREG procedures. Analyze a wider variety of models with the MCMC ...