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Le Monde puzzle [#939bis]

December 17, 2015
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Le Monde puzzle [#939bis]

If you remember the previous post, I had two interpretations about Le Monde mathematical puzzle #639: Find all integers with less than 11 digits that are perfect squares and can be written as a(a+6), a being an integer. and: Find all integers with less than 11 digits that are perfect squares and can be written

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Le Monde puzzle [#939]

December 10, 2015
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Le Monde puzzle [#939]

A Le Monde mathematical puzzle about special integers: Find all integers with less than 11 digits that are perfect squares and can be written as a(a+6), a being an integer. Eleven digits being too much for a brute force exploration of the form `for (t in 1:1e11)`…, some preliminary  analysis is needed, but I could

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a programming bug with weird consequences

November 24, 2015
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a programming bug with weird consequences

One student of mine coded by mistake an independent Metropolis-Hastings algorithm with too small a variance in the proposal when compared with the target variance. Here is the R code of this implementation: It produces outputs of the following shape which is quite amazing because of the small variance. The reason for the lengthy freezes

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Sunday morning puzzle

November 21, 2015
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Sunday morning puzzle

A question from X validated that took me quite a while to fathom and then the solution suddenly became quite obvious: If a sample taken from an arbitrary distribution on {0,1}⁶ is censored from its (0,0,0,0,0,0) elements, and if the marginal probabilities are know for all six components of the random vector, what is an

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Paret’oothed importance sampling and infinite variance [guest post]

November 16, 2015
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Paret’oothed importance sampling and infinite variance [guest post]

The following is mostly based on our arXived paper with Andrew Gelman and the references mentioned  there. Koopman, Shephard, and Creal (2009) proposed to make a sample based estimate of the existence of the moments using generalized Pareto

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importance sampling with infinite variance

November 12, 2015
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importance sampling with infinite variance

“In this article it is shown that in a fairly general setting, a sample of size approximately exp(D(μ|ν)) is necessary and sufficient for accurate estimation by importance sampling.” Sourav Chatterjee and Persi Diaconis arXived yesterday an exciting paper where they study the proper sample size in an importance sampling setting with no variance. That’s right,

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Le Monde puzzle [#937]

November 10, 2015
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Le Monde puzzle [#937]

A combinatoric Le Monde mathematical puzzle that resembles many earlier ones: Given a pool of 30 interns allocated to three person night-shifts, is it possible to see 31 consecutive nights such that (a) all the shifts differ and (b) there are no pair of shifts with a single common intern? In fact, the constraint there

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Think Bayes: Bayesian Statistics Made Simple

October 26, 2015
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Think Bayes: Bayesian Statistics Made Simple

By some piece of luck, I came upon the book Think Bayes: Bayesian Statistics Made Simple, written by Allen B. Downey and published by Green Tea Press which usually publishes programming books with

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Think Bayes: Bayesian Statistics Made Simple

October 26, 2015
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Think Bayes: Bayesian Statistics Made Simple

By some piece of luck, I came upon the book Think Bayes: Bayesian Statistics Made Simple, written by Allen B. Downey and published by Green Tea Press which usually publishes programming books with

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Le Monde puzzle [#929]

September 28, 2015
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Le Monde puzzle [#929]

A combinatorics Le Monde mathematical puzzle: In the set {1,…,12}, numbers adjacent to i are called friends of i. How many distinct subsets of size 5 can be chosen under the constraint that each number in the subset has at least a friend with him? In a brute force approach, I tried a quintuple loop

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