Publications by xi'an

Le Monde puzzle [#1147]

09.06.2020

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 5 (6) the product of the digits is not a multiple of 6 (7) the digits are between 0 and ...

1414 sym R (1085 sym/2 pcs) 2 img

overlap, overstreched

14.06.2020

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 rep!): qro=function(n,T=1e3){ quo=functio...

865 sym R (175 sym/1 pcs) 2 img

sans sérif & sans chevron

16.06.2020

{\sf df=function(x)2*pi*x-4*(x>1)*acos(1/(x+(1-x)*(x<1)))} As I was LaTeXing a remote exam for next week, including some R code questions, I came across the apparent impossibility to use < and > 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 ...

1145 sym R (58 sym/1 pcs)

one bridge further

29.06.2020

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 bi...

2342 sym R (187 sym/1 pcs) 4 img

Le Monde puzzle [#1149]

30.06.2020

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 buckets. However, a fraction 1/k is lost with each...

1087 sym R (224 sym/2 pcs) 2 img

deterministic moves in Metropolis-Hastings

09.07.2020

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, -μ+(μ-x)/α and -ν+(ν-x)/α for… rever...

1404 sym R (345 sym/1 pcs) 4 img

Riddle of the lanes

12.07.2020

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 lanes and E(n) is the expected number of swimmers, E(n) satisfies a recurre...

886 sym R (159 sym/1 pcs) 2 img

Le Monde puzzle [#1152]

19.07.2020

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, the other teams have won at least one games. What is the minimum number of teams? Show an inst...

1191 sym R (970 sym/2 pcs) 2 img

le compte est bon

21.07.2020

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. Unsurprisingly there is an online solver for this g...

1313 sym 4 img

[The Art of] Regression and other stories

22.07.2020

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 take with a spoonful of salt. The “other stories’ in the title is a very nice...

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