Articles by xi'an

an elegant sampler

January 14, 2020 | xi'an

Following an X validated question on how to simulate a multinomial with fixed average, W. Huber produced a highly elegant and efficient resolution with the compact R code tabulate(sample.int((k-1)*n, s-n) %% n + 1, n) + 1 where k is the number of classes, n the number of draws, and s ...
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Le Monde puzzle [#1120]

January 13, 2020 | xi'an

A board game as Le weekly Monde current mathematical puzzle: 11 players in a circle and 365 tokens first owned by a single player. Players with at least two tokens can either remove one token and give another one left or move two right and one left. How quickly does the game ...
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postdoc at Warwick on robust SMC [call]

January 11, 2020 | xi'an

Here is a call for a research fellow at the University of Warwick to work with Adam Johansen and Théo Damoulas on the EPSRC and Lloyds Register Foundaton funded project “Robust Scalable Sequential Monte Carlo with application to Urban Air Quality”. To quote The position will be based primarily ...
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Metropolis in 95 characters

January 1, 2020 | xi'an

Here is an R function that produces a Metropolis-Hastings sample for the univariate log-target f when the later is defined outside as another function. And when using a Gaussian random walk with scale one as proposal. (Inspired from a X validated question.) m1,T), c(y*{f({z
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Le Monde puzzle [#1124]

December 28, 2019 | xi'an

A prime number challenge [or rather two!] as Le weekly Monde current mathematical puzzle: When considering the first two integers, 1 and 2, their sum is 3, a prime number. For the first four integers, 1,2,3,4, it is again possible to sum them pairwise to obtain two prime numbers, eg 3 and 7. Up to […]
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postdoc in Bayesian machine learning in Berlin [reposted]

December 23, 2019 | xi'an

The working group of Statistics at Humboldt University of Berlin invites applications for one Postdoctoral research fellow (full-time employment, 3 years with extension possible) to contribute to the research on mathematical and statistical aspects of (Bayesian) learning approaches. The research positions are associated with the Emmy Noether group Regression Models beyond ...
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riddle on a circle

December 21, 2019 | xi'an

The Riddler’s riddle this week provides another opportunity to resort to brute-force simulated annealing! Given a Markov chain defined on the torus {1,2,…,100} with only moves a drift to the right (modulo 100) and a uniformely random jump, find the optimal transition matrix to reach 42 in a minimum (average) number of ... [Read more...]

an arithmetic mean identity

December 18, 2019 | xi'an

A 2017 paper by Ana Pajor published in Bayesian Analysis addresses my favourite problem [of computing the marginal likelihood] and which I discussed on the ‘Og, linking with another paper by Lenk published in 2012 in JCGS. That I already discussed here last year. Lenk’s (2009) paper is actually using a technique ...
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sampling the mean

December 11, 2019 | xi'an

A challenge found on the board of the coffee room at CEREMADE, Université Paris Dauphine: When sampling with replacement three numbers in {0,1,…,N}, what is the probability that their average is (at least) one of the three? With a (code-golfed!) brute force solution of mean(!apply((a
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Le Monde puzzle [#1119]

December 7, 2019 | xi'an

A digit puzzle as Le weekly Monde current mathematical puzzle that sounds close to some earlier versions: Perfect squares are pairs (a²,b²) with the same number of digits such that a²b² is itself a square. What is the pair providing a²b² less than 10⁶? Is there a solution ...
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riddle by attrition

December 1, 2019 | xi'an

The weekend riddle from The Riddler is rather straightforward [my wording and simplification]: Construct a decimal number X between 0 and 1 by drawing the first digit a¹ uniformly over {0,1,…,9}, the second digit a² uniformly over {0,1,…,9}, &tc., until 0 is attained. What is the expectation of this random variable X? Since each new […]
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Froebenius coin problem

November 28, 2019 | xi'an

A challenge from The Riddler last weekend came out as the classical Frobenius coin problem, namely to find the largest amount that cannot be obtained using only n coins of specified coprime denominations (i.e., with gcd equal to one). There is always such a largest value. For the units ...
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BayesComp 20 [schedule]

November 19, 2019 | xi'an

The schedule for the program is now available on the conference webpage of BayesComp 20, for the days of 7-10 Jan 2020. There are twelve invited sessions, including one j-ISBA session, and a further thirteen contributed sessions were selected by the scientific committee. And three tutorials on the first day. Looking forward ...
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Galton’s board all askew

November 19, 2019 | xi'an

Since Galton’s quincunx has fascinated me since the (early) days when I saw a model of it as a teenager in an industry museum near Birmingham, I jumped on the challenge to build an uneven nail version where the probabilities to end up in one of the boxes were ...
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Le Monde puzzle [#1115]

October 27, 2019 | xi'an

A two-person game as Le weekly Monde current mathematical puzzle: Two players Amaruq and Atiqtalik are in a game with n tokens where Amaruq chooses a number 1
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three birthdays and a numeral

October 17, 2019 | xi'an

The riddle of the week on The Riddler was to find the size n of an audience for at least a 50% chance of observing at least one triplet of people sharing a birthday, as is the case in the present U.S. Senate. The question is much harder to solve ...
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Le Monde puzzle [#1114]

October 15, 2019 | xi'an

Another very low-key arithmetic problem as Le Monde current mathematical puzzle: 32761 is 181² and the difference of two cubes, which ones? And 181=9²+10², the sum of two consecutive integers. Is this a general rule, i.e. the root z of a perfect square that is the difference of two cubes is always ...
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Le Monde puzzle [#1112]

October 2, 2019 | xi'an

Another low-key arithmetic problem as Le Monde current mathematical puzzle: Find the 16 integers x¹,x²,x³,x⁴,y¹,y²,y³,y⁴,z¹,z²,z³,z⁴,w¹,w²,w³,w⁴ such that the groups x¹,y¹,z¹,w¹, &tc., are made of distinct positive integers, the sum of the x’s ...
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poor statistics

September 23, 2019 | xi'an

I came over the weekend across this graph and the associated news that the county of Saint-Nazaire, on the southern border of Brittany, had a significantly higher rate of cancers than the Loire countries. The complete study written by Solenne Delacour, Anne Cowppli-Bony, amd Florence Molinié, is quite cautious about ...
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Le Monde puzzle [#1111]

September 17, 2019 | xi'an

Another low-key arithmetic problem as Le Monde current mathematical puzzle: Notice that there are 10 numbers less than, and prime with 11, 100 less than and prime with 101, 1000 less than, and prime with 1111? What is the smallest integer N such that the cardinal of the set of M
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