# Blog Archives

## another riddle

March 28, 2016
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A very nice puzzle on The Riddler last week that kept me busy on train and plane rides, runs and even in between over the weekend. The core of the puzzle is about finding the optimal procedure to select k guesses about the value of a uniformly random integer x in {a,a+1,…,b}, given that each

## Le Monde puzzle [#954]

March 24, 2016
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A square Le Monde mathematical puzzle: Given a triplet (a,b,c) of integers, with a<b<c, it satisfies the S property when a+b, a+c, b+c, a+b+c are perfect squares such that a+c, b+c, and a+b+c are consecutive squares. For a given a, is it always possible to find a pair (b,c) such (a,b,c) satisfies S? Can you

## Le Monde puzzle [#952]

March 18, 2016
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A quite simple Le Monde mathematical puzzle again with Alice and Bob: In a multiple choice questionnaire with 50 questions, Alice gets a score s such that Bob can guess how many correct (+5 points), incorrect (-1 point) and missing (0 point) Alice got when adding that Alice could not have gotten s-2 or s+2.

## preserving frequencies without resampling

March 8, 2016
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An interesting question came up on X validated a few days ago: given a probability vector p=(p¹,…,p⁷), is there a way to pick 5 values in {1,…,7} without replacement and still preserve the probability repartition in the resulting sample? In other words, is there a sampling without replacement strategy that leads to for i=1,…,7..? Unless

## Amazonish warning

March 1, 2016
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As in previous years, I want to repost a warning to ‘Og readers that all http links to Amazon.com products found on this ‘Og are actually susceptible to reward me with an advertising percentage if a purchase is made by the reader in the 24 hours following the entry

## twilight zone [of statistics]

February 25, 2016
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“I have decided that mixtures, like tequila, are inherently evil and should be avoided at all costs.” L. Wasserman Larry Wasserman once remarked that finite mixtures were like the twilight zone of statistics, thanks to the numerous idiosyncrasies associated with such models. And George Casella had similar strong reservations about mixture estimation. Avi Feller and

## more e’s [and R’s]

February 21, 2016
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Alex Thiéry suggested debiasing the biased estimate of e by Rhee and Glynn truncated series method, so I tried the method to see how much of an improvement (if any!) this would bring. I first attempted to naïvely implement the raw formula of Rhee and Glynn with a (large) Poisson distribution on the stopping rule

## R colours

February 17, 2016
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As I am always fishing for colour names in R, I looked for an easy summary of those names and found this table on New Energy Research blog, which I reproduce here for future access.  Filed under: pictures, R Tagged: colors(), colours(), R

## Гнеде́нко and Forsythe [and e]

February 15, 2016
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In the wake of my earlier post on the Monte Carlo estimation of e and e⁻¹, after a discussion with my colleague Murray Pollock (Warwick) Gnedenko’s solution, he pointed out another (early) Monte Carlo approximation called Forsythe’s method. That is detailed quite neatly in Luc Devroye’s bible, Non-uniform random variate generation (a free bible!). The

## new version of abcrf

February 12, 2016
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Version 1.1 of our R library abcrf version 1.1  is now available on CRAN.  Improvements against the earlier version are numerous and substantial. In particular,  calculations of the random forests have been parallelised and, for machines with multiple cores, the computing gain can be enormous.Filed under: R, Statistics, University life Tagged: ABC model choice, CRAN,