Articles by xi'an

Le Monde puzzle [#1149]

June 30, 2020 | xi'an

The weekly puzzle from Le Monde is a leaking variant on an old puzzle: Three buckets have capacities of 8, 5 and 3 litres, respectively. At the start of the game, the 8 litre bucket is full and both others are empty. Aiming at reaching exactly 4 litres in one bucket, water is transferred between […]
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one bridge further

June 29, 2020 | xi'an

Jackie Wong, Jon Forster (Warwick) and Peter Smith have just published a paper in Statistics & Computing on bridge sampling bias and improvement by splitting. “… known to be asymptotically unbiased, bridge sampling technique produces biased estimates in practical usage for small to moderate sample sizes (…) the estimator yields positive bias that ...
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sans sérif & sans chevron

June 16, 2020 | xi'an

{\sf df=function(x)2*pi*x-4*(x__1)*acos(1/(x+(1-x)*(x symbols in the sans-sérif “\sf” font… Which is a surprise, given the ubiquity of the symbols in R and my LaTeXing books over the years. Must have […] [Read more...]

overlap, overstreched

June 14, 2020 | xi'an

An interesting challenge on The Riddler on the probability to see a random interval X’ing with all other random intervals when generating n intervals from Dirichlet D(1,1,1). As it happens the probability is always 2/3, whatever n__1, as shown by the R code below (where replicate cannot be replaced by ...
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Le Monde puzzle [#1147]

June 9, 2020 | xi'an

The weekly puzzle from Le Monde is not much, again: A number A is such that (1) the difference between two digits is never 1 (2) two digits are equal to 2 (3) it only involves 3 different digits (4) it is a multiple of 4 (5)  the sum of two of the digits is […]
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the strange occurrence of the one bump

June 7, 2020 | xi'an

When answering an X validated question on running an accept-reject algorithm for the Gamma distribution by using a mixture of Beta and drifted (bt 1) Exponential distributions, I came across the above glitch in the fit of my 10⁷ simulated sample to the target, apparently displaying a wrong proportion of simulations above (...
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Le Monde puzzle [#1146]

June 4, 2020 | xi'an

The weekly puzzle from Le Monde is once more disappointing. Everyday of the month, take 0, 1 or 2 units. If one unit taken past day, next day none can be taken. If two units taken two day ago, none can be taken the current day. What is the strategy maximising the number ...
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minimax, maximin or plain

May 31, 2020 | xi'an

A simple riddle from The Riddler on choosing between the maximum between two minima of two throws of an N-face dice, the minimum between two maxima of two throws of an N-face dice, and a single throw. Since maximin is always less than maximin, second choice is always worse than ...
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a new Monty Hall riddle

May 21, 2020 | xi'an

The Riddler was sort of feeling the rising boredom of being under lockdown when proposing the following variant to the Monty Hall puzzle: There are zero to three goats, with a probability ¼ each, and they are allocated to different doors uniformly among the three doors of the show. After the ...
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not a Bernoulli factory

May 19, 2020 | xi'an

A Riddler riddle I possibly misunderstood: Four isolated persons are given four fair coins, which can be either flipped once or returned without being flipped. If all flipped coins come up heads, the team wins! Else, if any comes up tails, or if no flip at all is done, it ...
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another Bernoulli factory

May 17, 2020 | xi'an

A question that came out on X validated is asking for help in figuring out the UMVUE (uniformly minimal variance unbiased estimator) of (1-θ)½ when observing iid Bernoulli B(θ). As it happens, there is no unbiased estimator of this quantity and hence not UMVUE. But there exists a Bernoulli factory ...
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more games of life

May 4, 2020 | xi'an

Another puzzle in memoriam of John Conway in The Guardian: Find the ten digit number, abcdefghij. Each of the digits is different, and a is divisible by 1 ab is divisible by 2 abc is divisible by 3 abcd is divisible by 4 abcde is divisible by 5 abcdef is divisible by 6 abcdefg is […] [Read more...]

Le Monde puzzle [#1141]

May 3, 2020 | xi'an

The weekly puzzle from Le Monde is in honour of John Conway, who just passed away, ending up his own game of life: On an 8×8 checker-board, Alice picks n squares as “infected”. She then propagates the disease by having each square with least two infected neighbours to become infected as ...
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another surmortaliy graph

April 27, 2020 | xi'an

Another graph showing the recent peak in daily deaths throughout France as recorded by INSEE and plotted by Baptiste Coulmont from Paris 8 Sociology Department. And further discussed by Arthur Charpentier on Freakonometrics. With a few days off due to reporting, this brings an objective perspective on the impact of the ...
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Le Monde puzzle [#1139]

April 23, 2020 | xi'an

A weekly Monde current mathematical puzzle that reminded me of an earlier one (but was too lazy to check): The integer n=36 enjoys the property that all the differences between its ordered divisors are also divisors of 36. Find the only 18≤m≤100 that enjoys this property such that all its prime ...
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random generators produce ties

April 20, 2020 | xi'an

“…an essential part of understanding how many ties these RNGs produce is to understand how many ties one expects in 32-bit integer arithmetic.” A sort of a birthday-problem paper for random generators by Markus Hofert on arXiv as to why they produce ties. As shown for instance in the R ... [Read more...]

wrapped Normal distribution

April 13, 2020 | xi'an

One version of the wrapped Normal distribution on (0,1) is expressed as a sum of Normal distributions with means shifted by all relative integers which, while a parameterised density, has imho no particular statistical appeal over the use of other series. It was nonetheless the centre of a series of questions ...
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Le Monde puzzle [#1133]

March 27, 2020 | xi'an

A weekly Monde current mathematical puzzle that reminded me of an earlier one (but was too lazy to check): If ADULE-ELUDE=POINT, was is the largest possible value of POINT? With the convention that all letters correspond to different digits and no digit can start with 0. Same question when ADULE+...
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Probability and Bayesian modeling [book review]

March 25, 2020 | xi'an

Probability and Bayesian modeling is a textbook by Jim Albert and Jingchen Hu that CRC Press sent me for review in CHANCE. (The book is also freely available in bookdown format.) The level of the textbook is definitely most introductory as it dedicates its first half on probability concepts (with ...
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