Posts Tagged ‘ Monte Carlo ’

The Chosen One

August 30, 2010
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The Chosen One

Toss one hundred different balls into your basket. Shuffle them up and select one with equal probability amongst the balls. That ball you just selected, it’s special. Before you put it back, increase its weight by 1/100th. Then put it back, mix up the balls and pick again. If you do this enough, at some

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Random sudokus [p-values]

May 21, 2010
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Random sudokus [p-values]

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).

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ACM Transactions on Modeling and Computer Simulation

May 20, 2010
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ACM Transactions on Modeling and Computer Simulation

Pierre Lecuyer is the new editor of the ACM Transactions on Modeling and Computer Simulation (TOMACS) and he has asked me to become an Area Editor for the new area of simulation in Statistics. I am quite excited by this new Æditor’s hat, since this is a cross-disciplinary journal: The ACM Transactions on Modeling and

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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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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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Sudokus more random than random!

April 18, 2010
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Sudokus more random than random!

Darren Wraith pointed out this column about sudokus to me. It analyses the paper by Newton and De Salvo published in the Proceedings of the Royal Academy of Sciences A that I cannot access from home. The discussion contains this absurd sentence “Sudoku matrices are actually more random than randomly-generated matrices” which shows how mistreated

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Already a competitor?!

December 11, 2009
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Already a competitor?!

When looking around on Amazon, I found that “Introducing Monte Carlo Methods with R” was associated with another very recently published (same day as ours!) book, “Understanding Computational Bayesian Statistics“, by William Bolstad, that seems to mostly cover the same ground as us (with some connections with Bayesian Core for prior modelling in regression and

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Introduction à Monte Carlo en R

November 11, 2009
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Introduction à Monte Carlo en R

Following a proposal by Springer-Verlag Paris, I have decided to translate Introducing Monte Carlo Methods with R with George Casella into French, since a new collection of R books (in French) is planed for the Spring of 2010. The translation will a priori be done by Joachim Robert and Robin Ryder, under my supervision and

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