Articles by xi'an

An obscure integral

April 7, 2010 |

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 ... [Read more...]

Le Monde rank test (corr’d)

April 6, 2010 |

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 ... [Read more...]

Le Monde rank test (cont’d)

April 5, 2010 |

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) ... [Read more...]

Le Monde rank test

April 4, 2010 |

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 ... [Read more...]

Savage-Dickey [talk]

March 19, 2010 |

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 ... [Read more...]

Course in San Antonio, Texas

March 18, 2010 |

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 ... [Read more...]

Vanilla Rao-Blackwellisation for revision

March 17, 2010 |

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 ... [Read more...]

Solving the rectangle puzzle

March 15, 2010 |

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 ... [Read more...]

t-walk on the banana side

March 14, 2010 |

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. ... [Read more...]

Wrong puzzle of the week [w10]?!

March 12, 2010 |

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 ... [Read more...]

t-walk on the wild side

March 11, 2010 |

When I read in the abstract of the recent A General Purpose Sampling Algorithm for Continuous Distributions, published by Christen and Fox in Bayesian Analysis that We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning. I am slightly bemused. The proposal of the ... [Read more...]

Puzzle of the week [w10]

March 10, 2010 |

The puzzle in last Saturday edition of Le Monde is made of two parts: Given a 10×10 grid, what is the maximum number of nodes one can highlight before creating a parallelogram with one side parallel to one of the axes of the grid? What is the maximum number of nodes ... [Read more...]

Introducing R on video

March 9, 2010 |

Darren Wraith pointed out to me this site proposing a whole series of videos introducing to R. (Unfortunately in a Windows environment.) This can be handy when facing students with no R background… Filed under: R, Statistics, University life Tagged: course, video [Read more...]

Chinese versus Japanese editions

March 8, 2010 |

Last week, I got news from Springer Verlag about possibly two new editions of my books, one in Chinese and one in Japanese. These were bad news and good news: the bad news was that the Chinese edition was actually a reprint of our original book,  Monte Carlo Statistical Method, ... [Read more...]

schoolmath

March 6, 2010 |

In connection with the Le Monde puzzle of last week, I was looking for an R function that would give me the prime factor decomposition of any integer. Such a function exists within the package schoolmath, developped by Joerg Schlarmann and Josef Wienand. It is called prime.factor and it ... [Read more...]

Posterior likelihood

March 6, 2010 |

At the Edinburgh mixture estimation workshop, Murray Aitkin presented his proposal to compare models via the posterior distribution of the likelihood ratio. As already commented in a post last July, the positive aspect of looking at this quantity rather than at the Bayes factor is that the priors are then ... [Read more...]

March 4, 2010 |

As a coincidence, or not, I received the following email just before starting our mixture estimation workshop (the above is Ben Nevis on Monday, whose skyline really looks like a three component mixture!) and giving a discussion on label switching: I am implementing a Markov-Chain Monte Carlo method for Gibbs ... [Read more...]

New Le Monde puzzle

March 3, 2010 |

When I first read Le Monde puzzle this weekend, I though it was even less exciting than the previous one: find and , such that is a multiple of . The solution is obtained by brute-force checking through an R program: and then the a next solution is (with several values for ... [Read more...]

How to use mcsm

February 27, 2010 |

Within the past two days, I received this email Dear Prof.Robert I have just bought your recent book on Introducing Monte Carlo Methods with R.  Although I have checked your web page for the R programs (bits of the code in the book, codes for generating the figures and ...