Articles by xi'an

one or two?

March 11, 2020 | xi'an

A superposition of two random walks from The Riddler: Starting from zero, a random walk is produced by choosing moves between ±1 and ±2 at each step. If the choice between both is made towards maximising the probability of ending up positive after 100 steps, what is this probability? Although the optimal path ... [Read more...]

!ABC%in%Grenoble

March 9, 2020 | xi'an

Most regrettably, the incoming ABC in Grenoble, planned on 19-20 March 2020 is now postponed till a yet unspecified date, like next Summer or next Fall. Due to travel disruptions all over the World and to gathering restrictions in France, courtesy of the Covid-19 virus. Not particularly surprising given the avalanche ...
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chain of lynx and drove of hares

February 26, 2020 | xi'an

A paper (and an introduction to the paper) in Nature this week seems to have made progress on the existence of indefinite predator-prey cyles. As in the lynx/hare dataset available on R. The paper is focusing on another pair, an invertebrate and its prey, an algae. For which the ...
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multiplying the bars

February 24, 2020 | xi'an

The latest Riddler makes the remark that the expression |-1|-2|-3| has no unique meaning (and hence value) since it could be | -1x|-2|-3 | = 5   or   |-1| – 2x|-3| = -5 depending on the position of the multiplication sign and asks for all the possible values of |-1|-2|…|... [Read more...]

Le Monde puzzle [#1132]

February 23, 2020 | xi'an

A vaguely arithmetic challenge as Le weekly Monde current mathematical puzzle: Given two boxes containing x and 2N+1-x balls respectively. If one proceeds by repeatedly transferring half the balls from the even box to the odd box, what is the largest value of N for which the resulting sequence ...
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SMC on the 2019-2020 nCoV outbreak

February 18, 2020 | xi'an

Two weeks ago, Kurcharski et al., from the CMMID nCoV working group at the London School of Hygiene and Tropical Medicine, published on medrXiv a statistical analysis via a stochastic SEIR model of the evolution of the 2019-2020 nCoV epidemics, with prediction of a peak outbreak by late February in ...
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Le Monde puzzle [#1129]

February 9, 2020 | xi'an

A number challenge as Le weekly Monde current mathematical puzzle: When the three consecutive numbers 110, 111 and 112, they all are multiples of the sum of their digits. Are there 4 consecutive numbers with three digits like this? A contrario, does there exist 17 consecutive numbers with three digits such that they cannot be […]
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Le Monde puzzle [#1130]

February 6, 2020 | xi'an

A two-player game as Le weekly Monde current mathematical puzzle: Abishag and Caleb fill in alternance a row of N boxes in a row by picking one then two then three &tc. consecutive boxes. When a player is unable to find enough consecutive boxes, the player has lost. Who is ...
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another easy Riddler

January 30, 2020 | xi'an

A quick riddle from the Riddler In a two-person game, Abigail and Zian both choose between a and z. Abigail win one point with probability .9 if they choose (a,a) and with probability 1 if they choose (a,z), and two points with probability .4 if they choose (z,z) and with ...
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MCMC, with common misunderstandings

January 26, 2020 | xi'an

As I was asked to write a chapter on MCMC methods for an incoming Handbook of Computational Statistics and Data Science, published by Wiley, rather than cautiously declining!, I decided to recycle the answers I wrote on X validated to what I considered to be the most characteristic misunderstandings about ...
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a very quick Riddle

January 21, 2020 | xi'an

A very quick Riddler’s riddle last week with the question Find the (integer) fraction with the smallest (integer) denominator strictly located between 1/2020 and 1/2019. and the brute force resolution for (t in (2020*2019):2021){ a=ceiling(t/2020) if (a*2019
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Le Monde puzzle [#1127]

January 16, 2020 | xi'an

A permutation challenge as Le weekly Monde current mathematical puzzle: When considering all games between 20 teams, of which 3 games have not yet been played, wins bring 3 points, losses 0 points, and draws 1 point (each). If the sum of all points over all teams and all games is 516, was is the […]
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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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