Articles by xi'an

on arithmetic derivations of square roots

November 12, 2020 | xi'an

An intriguing question made a short-lived appearance on the CodeGolf section of Stack Exchange, before being removed, namely the (most concise possible) coding of an arithmetic derivation of the square root of an integer, S, with a 30 digit precision and using only arithmetic operators. I was not aware of the ...
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Le Monde puzzle [#1158]

November 9, 2020 | xi'an

A weekly puzzle from Le Monde on umbrella sharing: Four friends, Antsa, Cyprien, Domoina and Fy, are leaving school to return to their common housing. It is raining and they only have one umbrella with only room for two. Given walking times, x¹, x², x³ and x⁴, find the fastest ...
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asymmetric information

November 3, 2020 | xi'an

The Riddler of 16 October had the following puzzle: Take a real number θ uniformly distributed over (0,100). Among three players, the winner is whoever guessed the closest price without going over θ. In the event all guesses exceeded θ, the contestant with the lowest (and therefore closest) guess is declared the winner. The second […]
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sampling w/o replacement except when replacing

November 2, 2020 | xi'an

Another Riddle(r), considering a box with M myrtle balls and D dandelion balls. Drawing balls without replacement while they stay of the same color as the initial draw, else put back the last ball and repeat the process until all balls are drawn. The funny thing is that, unless ...
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inverse Gaussian trick [or treat?]

October 28, 2020 | xi'an

When preparing my mid-term exam for my undergrad mathematical statistics course, I wanted to use the inverse Gaussian distribution IG(μ,λ) as an example of exponential family and include a random generator question. As shown above by a Fortran computer code from Michael, Schucany and Haas, a simple version can be ...
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artificial EM

October 27, 2020 | xi'an

When addressing an X validated question on the use of the EM algorithm when estimating a Normal mean, my first comment was that it was inappropriate since there is no missing data structure to anchor by (right preposition?). However I then reflected upon the infinite number of ways to demarginalise ... [Read more...]

parking riddle

October 22, 2020 | xi'an

The Riddler of this week had a quick riddle: if one does want to avoid parallel parking a car over a six spot street, either the first spot is available or two consecutive spots are free. What is the probability this happens with 4 other cars already parked (at random)? While ...
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Fermat’s Riddle

October 15, 2020 | xi'an

·A Fermat-like riddle from the Riddler (with enough room to code on the margin) An  arbitrary positive integer N is to be written as a difference of two distinct positive integers. What are the impossible cases and else can you provide a list of all distinct representations? Since the problem ...
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understanding elections through statistics [book review]

October 11, 2020 | xi'an

A book to read most urgently if hoping to take an informed decision by 03 November! Written by a political scientist cum statistician, Ole Forsberg. (If you were thinking of another political scientist cum statistician, he wrote red state blue state a while ago! And is currently forecasting the outcome of ...
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Le Monde puzzle [#1159]

October 5, 2020 | xi'an

The weekly puzzle from Le Monde is quite similar to #1157: Is it possible to break the ten first integers, 1,…,10, into two groups such that the sum over the first group is equal to the product over the second? Is it possible that the second group is of cardinal 4? of cardinal 3? ...
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Le Monde puzzle [#1157]

September 30, 2020 | xi'an

The weekly puzzle from Le Monde is an empty (?) challenge: Kimmernaq and Aputsiaq play a game where Kimmernaq picks ten different integers between 1 and 100, and Aputsiaq must find a partition of these integers into two groups with identical sums. Who is winning? Indeed, if the sums are equal, then the ...
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Le Monde puzzle [#1155]

September 25, 2020 | xi'an

The weekly puzzle from Le Monde is another Sudoku challenge: Anahera and Wiremu play a game for T rounds. They successively pick a digit between 1 and 3, never repeating the previous one, and sum these digits. The last to play wins if the sum is a multiple of 3. Who is the ...
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the limits of R

August 10, 2020 | xi'an

It has been repeated many times on many platforms, the R (or R⁰) number is not a great summary about the COVID-19 pandemic, see eg Rossman’s warning in The Conversation, but Nature chose to stress it one more time (in its 16 Jul edition). Or twice when considering a similar ...
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MCqMC 2020 live and free and online

July 26, 2020 | xi'an

The MCqMC 20202 conference that was supposed to take place in Oxford next 9-14 August has been turned into an on-line free conference since travelling remains a challenge for most of us. Tutorials and plenaries will be live with questions  on Zoom, with live-streaming and recorded copies on YouTube. They will ...
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[The Art of] Regression and other stories

July 22, 2020 | xi'an

CoI: Andrew sent me this new book [scheduled for 23 July on amazon] of his with Jennifer Hill and Aki Vehtari. Which I read in my garden over a few sunny morns. And as Andrew and Aki are good friends on mine, this review is definitely subjective and biased! Hence to ...
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le compte est bon

July 21, 2020 | xi'an

The Riddler asks how to derive 24 from (1,2,3,8), with each number appearing once and all operations (x,+,/,-,^) allowed. This reminded me of a very old TV show on French TV, called Le compte est bon!, where players were given 5 or 6 numbers and supposed to find a given total within 60 ,seconds. ...
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Le Monde puzzle [#1152]

July 19, 2020 | xi'an

The weekly puzzle from Le Monde is a tournament classic: An even number of teams play one another once a week with no tie allowed and have played all other teams. Four weeks into the tournament, A has won all its games, B,C, and D have won three games, ...
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Riddle of the lanes

July 12, 2020 | xi'an

An express riddle from the Riddler about reopening pools, where lanes are allowed provided there is no swimmer in the lane or in any of the adjacent lanes. If swimmers pick their lane at random (while they can), what is the average number of occupied lanes? If there are n ...
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deterministic moves in Metropolis-Hastings

July 9, 2020 | xi'an

A curio on X validated where an hybrid Metropolis-Hastings scheme involves a deterministic transform, once in a while. The idea is to flip the sample from one mode, ν, towards the other mode, μ, with a symmetry of the kind μ-α(x+μ) and ν-α(x+ν) with α a positive coefficient. Or the reciprocal, ...
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