Posts Tagged ‘ books ’

Le Monde puzzle [#1021]

September 17, 2017
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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 […]

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Le Monde puzzle [#1020]

September 14, 2017
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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 […]

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Le Monde puzzle [#1018]

August 28, 2017
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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 […]

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Le Monde puzzle [#1707]

July 27, 2017
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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 […]

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On the Origin of "Frequentist" Statistics

July 23, 2017
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Efron and Hastie note that the "frequentist" term "seems to have been suggested by Neyman as a statistical analogue of Richard von Mises' frequentist theory of probability, the connection being made explicit in his 1977 paper, 'Frequentist Probabi...

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RNG impact on MCMC [or lack thereof]

July 12, 2017
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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 <- […]

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easy riddle

July 11, 2017
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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 […]

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[un]solved riddles

July 3, 2017
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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))}} ave/M returning a value of 0.0183, but which combinatoric resolution I […]

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Bayes, Jeffreys, MCMC, Statistics, and Econometrics

July 3, 2017
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In Ch. 3 of their brilliant book, Efron and Tibshirani (ET) assert that:Jeffreys’ brand of Bayesianism [i.e., "uninformative" Jeffreys priors] had a dubious reputation among Bayesians in the period 1950-1990, with preference going to subjective analy...

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thinning a Markov chain, statistically

June 12, 2017
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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. […]

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