Articles by xi'an

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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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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