Blog Archives

Random [uniform?] sudokus [corrected]

May 19, 2010
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Random [uniform?] sudokus [corrected]

As the discrepancy 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 true distribution and the

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Random [uniform?] sudokus

May 19, 2010
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Random [uniform?] sudokus

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 adequation with a basic chi-square

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Confusing slice sampler

May 18, 2010
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Confusing slice sampler

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, how you determine the

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Random sudokus [test]

May 17, 2010
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Random sudokus [test]

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 on the block diagonal

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Random sudokus

May 16, 2010
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Random sudokus

After thinking about random sudokus for a few more weeks, I eventually came to read the paper by Newton and DeSalvo about the entropy of sudoku matrices. As written earlier, if we consider (as Newton and DeSakvo) a uniform distribution where the sudokus are drawn uniformly over the set of all sudokus, the entropy of

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Typo in Bayesian Core [again]

May 15, 2010
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Typo in Bayesian Core [again]

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 if the omission of

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pimax(mcsm)

May 12, 2010
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pimax(mcsm)

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 manual, and it gave

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A ridiculous email

May 10, 2010
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A ridiculous email

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, launched alongside Mathematica 6 in

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Computational Statistics

May 9, 2010
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Computational Statistics

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 can write a short

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Forsythe’s algorithm

May 8, 2010
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Forsythe’s algorithm

In connection with the Bernoulli factory post of last week, Richard Brent arXived a short historical note recalling George Forsythe’s algorithm for simulating variables with density when (the extension to any upper bound is straightforward). The idea is to avoid computing the exponential function by simulating uniforms until since the probability of this event is

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