Publications by xi'an
thinning a Markov chain, statistically
Art Owen has arXived a new version of his thinning MCMC paper, where he studies how thinning or subsampling can improve computing time in MCMC chains. I remember quite well the message set by Mark Berliner and Steve MacEachern in an early 1990’s paper that subsampling was always increasing the variance of the resulting estimators. We actually h...
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[un]solved riddles
On the Riddler of last week, first a birthday puzzle: Given a group of 23 persons, what is the probability of observing three pairs of identical birthdays? which can be found by a quick simulation as ave=0 for (t in 1:1e6){ dupz=dates[duplicated(sample(1:365,23,rep=TRUE))] ave=ave+as.integer((length(dupz)==3)& (length(unique(dupz))==3)...
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easy riddle
From the current Riddler, a problem that only requires a few lines of code and a few seconds of reasoning. Or not. N households each stole the earnings from one of the (N-1) other households, one at a time. What is the probability that a given household is not burglarised? And what are the expected final earnings of each household in the list, a...
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RNG impact on MCMC [or lack thereof]
Following the talk at MCM 2017 about the strange impact of the random generator on the outcome of an MCMC generator, I tried in Montréal airport the following code on the banana target of Haario et al. (1999), copied from Soetaert and Laine and using the MCMC function of the FME package: library(FME) Banana <- function (x1, x2) { return(x2 - ...
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Le Monde puzzle [#1707]
A geometric Le Monde mathematical puzzle: Given a pizza of diameter 20cm, what is the way to cut it by two perpendicular lines through a point distant 5cm from the centre towards maximising the surface of two opposite slices? Using the same point as the tip of the four slices, what is the way to make four slices with equal arcs in four cuts f...
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sequence riddle
The riddle this week on The Riddler was about finding the largest sequence of integers between 1 and 100 such that each integer is only used once and always followed by a multiple or a factor. A basic R code searching at random [and programmed during a massive downpour on Skye] led to a solution of 69: although there is no certainty this is the ...
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Le Monde puzzle [#1018]
An arithmetic Le Monde mathematical puzzle (that first did not seem to involve R programming because of the large number of digits in the quantity involved): An integer x with less than 100 digits is such that adding the digit 1 on both sides of x produces the integer 99x. What are the last nine digits of x? And what are the possible numbers o...
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Le Monde puzzle [#1020]
A collection of liars in this Le Monde mathematical puzzle: A circle of 16 liars and truth-tellers is such that everyone states that their immediate neighbours are both liars. How many liars can there be? A circle of 12 liars and truth-tellers is such that everyone state that their immediate neighbours are one liar plus one truth-teller. How ma...
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Le Monde puzzle [#1021]
A puzzling Le Monde mathematical puzzle for which I could find no answer in the allotted time!: A most democratic electoral system allows every voter to have at least one representative by having each of the N voters picking exactly m candidates among the M running candidates and setting the size n of the representative council towards this goal,...
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mea culpa!
An entry about our Bayesian Essentials book on X validated alerted me to a typo in the derivation of the Gaussian posterior..! When deriving the posterior (which was left as an exercise in the Bayesian Core), I just forgot the term expressing the divergence between the prior mean and the sample mean. Mea culpa!!!Filed under: Books, Kids, R, Stati...
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