Articles by xi'an

dynamic mixtures [at NBBC15]

June 17, 2015 | xi'an

A funny coincidence: as I was sitting next to Arnoldo Frigessi at the NBBC15 conference, I came upon a new question on Cross Validated about a dynamic mixture model he had developed in 2002 with Olga Haug and Håvård Rue [whom I also saw last week in Valencià]. The ...

the Flatland paradox [#2]

May 26, 2015 | xi'an

Another trip in the métro today (to work with Pierre Jacob and Lawrence Murray in a Paris Anticafé!, as the University was closed) led me to infer—warning!, this is not the exact distribution!—the distribution of x, namely since a path x of length l(x) will corresponds ...

another viral math puzzle

May 24, 2015 | xi'an

After the Singapore Maths Olympiad birthday problem that went viral, here is a Vietnamese primary school puzzle that made the frontline in The Guardian. The question is: Fill the empty slots with all integers from 1 to 9 for the equality to hold. In other words, find a,b,c,d,e,...

quantile functions: mileage may vary

May 11, 2015 | xi'an

When experimenting with various quantiles functions in R, I was shocked [ok this is a bit excessive, let us say surprised] by how widely the execution times would vary. To the point of blaming a completely different feature of R. Borrowing from Charlie Geyer’s webpage on the topic of ... [Read more...]

arbitrary distributions with set correlation

May 10, 2015 | xi'an

A question recently posted on X Validated by Antoni Parrelada: given two arbitrary cdfs F and G, how can we simulate a pair (X,Y) with marginals F and G, and with set correlation ρ? The answer posted by Antoni Parrelada was to reproduce the Gaussian copula solution: produce (X’,Y’) ...

corrected MCMC samplers for multivariate probit models

May 5, 2015 | xi'an

“Moreover, IvD point out an error in Nobile’s derivation which can alter its stationary distribution. Ironically, as we shall see, the algorithms of IvD also contain an error.” Xiyun Jiao and David A. van Dyk arXived a paper correcting an MCMC sampler and R package MNP for the multivariate ...

take those hats off [from R]!

May 4, 2015 | xi'an

This is presumably obvious to most if not all R programmers, but I became aware today of a hugely (?) delaying tactic in my R codes. I was working with Jean-Michel and Natesh [who are visiting at the moment] and when coding an MCMC run I was telling them that I ...

Le Monde puzzle [#909]

April 30, 2015 | xi'an

Another of those “drop-a-digit” Le Monde mathematical puzzle: Find all integers n with 3 or 4 digits an single interior zero digit, such that removing that zero digit produces a divider of x. As in puzzle #904, I made use of the digin R function: and simply checked all integers up to 10⁶: which ...

the most patronizing start to an answer I have ever received

April 29, 2015 | xi'an

Another occurrence [out of many!] of a question on X validated where the originator (primitivus petitor) was trying to get an explanation without the proper background. On either Bayesian statistics or simulation. The introductory sentence to the question was about “trying to understand how the choice of priors affects a ... [Read more...]

scale acceleration

April 23, 2015 | xi'an

Kate Lee pointed me to a rather surprising inefficiency in matlab, exploited in Sylvia Früwirth-Schnatter’s bayesf package: running a gamma simulation by rgamma(n,a,b) takes longer and sometimes much longer than rgamma(n,a,1)/b, the latter taking advantage of the scale nature of b. I ...

simulating correlated Binomials [another Bernoulli factory]

April 20, 2015 | xi'an

This early morning, just before going out for my daily run around The Parc, I checked X validated for new questions and came upon that one. Namely, how to simulate X a Bin(8,2/3) variate and Y a Bin(18,2/3) such that corr(X,Y)=0.5. (No reason or motivation provided for this ...

Bernouilli, Montmort and Waldegrave

April 14, 2015 | xi'an

In the last issue of Statistical Science, David Belhouse [author of De Moivre’s biography] and Nicolas Fillion published an accounting of a discussion between Pierre Rémond de Montmort, Nicolaus Bernoulli—”the” Bernoulli associated with the St. Petersburg paradox—, and Francis Waldegrave, about the card game of Le Her (... [Read more...]

failures and uses of Jaynes’ principle of transformation groups

April 13, 2015 | xi'an

This paper by Alon Drory was arXived last week when I was at Columbia. It reassesses Jaynes’ resolution of Bertrand’s paradox, which finds three different probabilities for a given geometric event depending on the underlying σ-algebra (or definition of randomness!). Both Poincaré and Jaynes argued against Bertrand that there ...

a vignette on Metropolis

April 12, 2015 | xi'an

Over the past week, I wrote a short introduction to the Metropolis-Hastings algorithm, mostly in the style of our Introduction to Monte Carlo with R book, that is, with very little theory and worked-out illustrations on simple examples. (And partly over the Atlantic on my flight to New York and ... [Read more...]

an email exchange about integral representations

April 7, 2015 | xi'an

I had an interesting email exchange [or rather exchange of emails] with a (German) reader of Introducing Monte Carlo Methods with R in the past days, as he had difficulties with the validation of the accept-reject algorithm via the integral in that it took me several iterations [as shown in ...

scalable Bayesian inference for the inverse temperature of a hidden Potts model

April 6, 2015 | xi'an

Matt Moores, Tony Pettitt, and Kerrie Mengersen arXived a paper yesterday comparing different computational approaches to the processing of hidden Potts models and of the intractable normalising constant in the Potts model. This is a very interesting paper, first because it provides a comprehensive survey of the main methods used ... [Read more...]

Le Monde puzzle [#905]

March 31, 2015 | xi'an

A recursive programming Le Monde mathematical puzzle: Given n tokens with 10≤n≤25, Alice and Bob play the following game: the first player draws an integer1≤m≤6 at random. This player can then take 1≤r≤min(2m,n) tokens. The next player is then free to take 1≤s≤min(2r,n-r) ...

MCMskv, Lenzerheide, Jan. 5-7, 2016

March 30, 2015 | xi'an

Following the highly successful [authorised opinion!, from objective sources] MCMski IV, in Chamonix last year, the BayesComp section of ISBA has decided in favour of a two-year period, which means the great item of news that next year we will meet again for MCMski V [or MCMskv for short], this ...

intuition beyond a Beta property

March 29, 2015 | xi'an

A self-study question on X validated exposed an interesting property of the Beta distribution: If x is B(n,m) and y is B(n+½,m) then √xy is B(2n,2m) While this can presumably be established by a mere change of variables, I could not carry the derivation ...

Le Monde puzzle [#904.5]

March 25, 2015 | xi'an

About this #904 arithmetics Le Monde mathematical puzzle: Find all plural integers, namely positive integers such that (a) none of their digits is zero and (b) removing their leftmost digit produces a dividing integer. a slight modification in the R code allows for a faster exploration, based on the fact that ...

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