Publications by xi'an
simulating signed mixtures
While simulating from a mixture of standard densities is relatively straightforward, when the component densities are easily simulated, to the point that many simulation methods exploit an intermediary mixture construction to speed up the production of pseudo-random samples from more challenging distributions (see Devroye, 1986), things get surpris...
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simulating Gumbel’s bivariate exponential distribution
A challenge interesting enough for a sunny New Year morn, found on X validated, namely the simulation of a bivariate exponential distribution proposed by Gumbel in 1960, with density over the positive quadrant in IR² Although there exists a direct approach based on the fact that the marginals are Exponential distributions and the conditionals sig...
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max spacing between mass shootings [data graphics]
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making the next meeting more productive
One of the students’ requests I almost invariably reject is code debugging (and they are warned about it from the start). Here is an illustration why, with an R code sent by a student working this summer on the standard estimators of a Cauchy location parameter, asking for debugging help in order “to make the next meeting more productive”. Wh...
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uniform spacings
A riddle on uniform spacings!, namely when considering eight iid Uniform (0,1) variates as visiting times and three further iid Uniform (0,1) variates as server availability times, with unit service time, the question being the probability a server is available for a ninth visiting time, T⁹. Which can be decomposed into four cases: at least one ...
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Galton and Watson voluntarily skipping some generations
A riddle on a form of a Galton-Watson process, starting from a single unit, where no one dies but rather, at each of 100 generations, Dog either opts for a Uniform number υ of additional units or increments a counter γ by this number υ, its goal being to optimise γ. The solution proposed by the Riddler does not establish his solution’s is the...
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operation precisely impossible
Since the solution to the previous riddle from The Riddler on the maximum of different terms in the composed operation a∅b∅c∅d∅e∅f depending on the bracketing ordering and the meaning of each ∅ among one of the six elementary operations got posted today as 974,860, I got back to my R code to understand why it differed from my figures ...
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operation impossible
A riddle from The Riddler on how many different numbers one could at most produce from six initial values and the four basic operations. In other words, how many values could the terms in a∅(b∅{c∅[d∅(e∅f)]}) could take? (With each ∅ being one of the four operations and a,…,f the initial values or a permutation of these.) A very crude ...
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simulated annealing and logistic regression to the max
A Riddler puzzle on the three binary and sequential questions one should ask three players hiding their respective U(0,1) realisation, U, V, and W, to best guess which player holds the largest number, max{U,V,W}. Assuming questions of the type Is U, &tc., the challenge boils down to selecting seven bounds (one for U, two for V, and four for W) in o...
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powering a probability [a Bernoulli factory tale]
Starting from an X validated question on finding an unbiased estimator of an integral raised to a non-integer power, I came across a somewhat interesting Bernoulli factory solution! Thanks to Peter Occil’s encyclopedic record of cases, pointing out to Mendo’s (2019) solution for functions of ρ that can be expressed as power series. Like ργ s...
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