# Simulation

### Poster at MCMSki III

December 28, 2010 |

Here is the poster presented at MCMSki III next week by Pierre Jacob about our joint paper on parallelisation: Filed under: R, Statistics, Travel Tagged: Adapski, MCMC, MCMSki, Metropolis-Hastings, Monte Carlo Statistical Methods, parallelisation, pos... [Read more...]

### Questions on the parallel Rao-Blackwellisation

December 21, 2010 |

Pierre Jacob and I got this email from a student about our parallel Rao-Blackwellisation paper. Here are some parts of the questions and our answer: Although I understand how the strategy proposed in the paper helps in variance reduction, I do not understand why you set b=1 (mentioned in Section 3.2) ... [Read more...]

### Computing evidence

November 28, 2010 |

The book Random effects and latent variable model selection, edited by David Dunson in 2008 as a Springer Lecture Note. contains several chapters dealing with evidence approximation in mixed effect models. (Incidentally, I would be interested in the story behind the  Lecture Note as I found no explanation in the backcover ... [Read more...]

### Random graphs with fixed numbers of neighbours

November 24, 2010 |

In connection with Le Monde puzzle #46, I eventually managed to write an R program that generates graphs with a given number n of nodes and a given number k of edges leaving each of those nodes. (My early attempt was simply too myopic to achieve any level of success when ... [Read more...]

### Graphical comparison of MCMC performance [arXiv:1011.445]

November 22, 2010 |

A new posting on arXiv by Madeleine Thompson on a graphical tool for assessing performance. She has developed a software called SamplerCompare, implemented in R and C. The graphical evaluation plots “log density evaluations per iteration times autocorrelation time against a tuning parameter in a grid of plots where rows ... [Read more...]

### Le Monde puzzle [43]

November 7, 2010 |

Here is the puzzle in Le Monde I missed last week: Given a country with 6 airports and a local company with three destinations from each of the six airports, is it possible to find a circular trip with three intermediate stops from one of the airports? From all of the ... [Read more...]

### Galton & simulation

September 27, 2010 |

Stephen Stigler has written a paper in the Journal of the Royal Statistical Society Series A on Francis Galton’s analysis of (his cousin) Charles Darwin’ Origin of Species, leading to nothing less than Bayesian analysis and accept-reject algorithms! “On September 10th, 1885, Francis Galton ushered in a new era of ... [Read more...]

### R tee-shirt

September 21, 2010 |

I gave my introduction to the R course in a crammed amphitheatre of about 200 students today. Had to wear my collectoR teeshirt from Revolution Analytics, even though it only made the kids pay attention for about 30 seconds… The other few “lines” that worked were using the Proctor & Gamble “car 54″ poster ...

### NetLogo-R-Extension

August 1, 2010 |

Here is a bridge between NetLogo and R, which looks very interesting. But I was not able to get it work on my Ubuntu box (running the latest R).

### Stratified sampling

June 9, 2010 |

The recently arXived paper of Goldstein, Rinott and Scarsini studies the impact of refining a partition on the precision of a stratified maximising/integration Monte Carlo approach. Quite naturally, if the partition gets improved, simulating points in each set of the partition can only improve the quality of the approximation, ... [Read more...]

### Random sudokus [p-values]

May 21, 2010 |

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). [...]

### Random [uniform?] sudokus [corrected]

May 19, 2010 |

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 ...

### Random [uniform?] sudokus

May 19, 2010 |

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 ...

### Random sudokus [test]

May 17, 2010 |

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 ...

### Computational Statistics

May 9, 2010 |

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 ...

### Forsythe’s algorithm

May 8, 2010 |

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 ... [Read more...]

### The Bernoulli factory

April 22, 2010 |

A few months ago, Latuszyński, Kosmidis, Papaspiliopoulos and Roberts arXived a paper I should have noticed earlier as its topic is very much related to our paper with Randal Douc on the vanilla Rao-Blackwellisation scheme. It is motivated by the Bernoulli factory problem, which aims at (unbiasedly) estimating f(... [Read more...]

### Sudokus more random than random!

April 18, 2010 |

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 ... [Read more...]

### A von Mises variate…

March 25, 2010 |

Inspired from a mail that came along the previous random generation post the following question rised : How to draw random variates from the Von Mises distribution? First of all let’s check the pdf of the probability rule, it is , for . Ok, I admit that Bessels functions can be a ... [Read more...]

### In search of a random gamma variate…

March 16, 2010 |

One of the most common exersices given to Statistical Computing,Simulation or relevant classes is the generation of random numbers from a gamma distribution. At first this might seem straightforward in terms of the lifesaving relation that exponential and gamma random variables share. So, it’s easy to get a ... [Read more...]
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