Blog Archives

Le Monde puzzle [#909]

April 30, 2015
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Le Monde puzzle [#909]

Another of those “drop-a-digit” Le Monde mathematical puzzle: Find all integers n with 3 or 4 digits an single interior zero digit, such that removing that zero digit produces a divider of x. As in puzzle #904, I made use of the digin R function: and simply checked all integers up to 10⁶: which leads

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the most patronizing start to an answer I have ever received

April 29, 2015
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the most patronizing start to an answer I have ever received

Another occurrence of a question on X validated where the originator (primitivus petitor) was trying to get an explanation without the proper background. On either Bayesian statistics or simulation. The introductory sentence to the question was about “trying to understand how the choice of priors affects a Bayesian model estimated using MCMC”

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scale acceleration

April 23, 2015
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scale acceleration

Kate Lee pointed me to a rather surprising inefficiency in matlab, exploited in Sylvia Früwirth-Schnatter’s bayesf package: running a gamma simulation by rgamma(n,a,b) takes longer and sometimes much longer than rgamma(n,a,1)/b, the latter taking advantage of the scale nature of b. I wanted to check on my own whether or not R faced the same

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simulating correlated Binomials [another Bernoulli factory]

April 20, 2015
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simulating correlated Binomials [another Bernoulli factory]

This early morning, just before going out for my daily run around The Parc, I checked X validated for new questions and came upon that one. Namely, how to simulate X a Bin(8,2/3) variate and Y a Bin(18,2/3) such that corr(X,Y)=0.5. (No reason or motivation provided for this constraint.) And I thought the following (presumably

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Bernouilli, Montmort and Waldegrave

April 14, 2015
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Bernouilli, Montmort and Waldegrave

In the last issue of Statistical Science, David Belhouse   and Nicolas Fillion published an accounting of a discussion between Pierre Rémond de Montmort, Nicolaus Bernoulli—”the” Bernoulli associated with the St. Petersburg paradox—, and Francis Waldegrave, about the card game of Le Her (or Hère, for wretch). Here is the abridged

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failures and uses of Jaynes’ principle of transformation groups

April 13, 2015
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failures and uses of Jaynes’ principle of transformation groups

This paper by Alon Drory was arXived last week when I was at Columbia. It reassesses Jaynes’ resolution of Bertrand’s paradox, which finds three different probabilities for a given geometric event depending on the underlying σ-algebra (or definition of randomness!). Both Poincaré and Jaynes argued against Bertrand that there was only one acceptable solution under

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a vignette on Metropolis

April 12, 2015
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a vignette on Metropolis

Over the past week, I wrote a short introduction to the Metropolis-Hastings algorithm, mostly in the style of our Introduction to Monte Carlo with R book, that is, with very little theory and worked-out illustrations on simple examples. (And partly over the Atlantic on my flight to New York and Columbia.) This vignette is intended

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an email exchange about integral representations

April 7, 2015
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an email exchange about integral representations

I had an interesting email exchange with a (German) reader of Introducing Monte Carlo Methods with R in the past days, as he had difficulties with the validation of the accept-reject algorithm via the integral in that it took me several iterations to realise the

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scalable Bayesian inference for the inverse temperature of a hidden Potts model

April 6, 2015
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scalable Bayesian inference for the inverse temperature of a hidden Potts model

Matt Moores, Tony Pettitt, and Kerrie Mengersen arXived a paper yesterday comparing different computational approaches to the processing of hidden Potts models and of the intractable normalising constant in the Potts model. This is a very interesting paper, first because it provides a comprehensive survey of the main methods used in handling this annoying normalising

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Le Monde puzzle [#905]

March 31, 2015
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Le Monde puzzle [#905]

A recursive programming  Le Monde mathematical puzzle: Given n tokens with 10≤n≤25, Alice and Bob play the following game: the first player draws an integer1≤m≤6 at random. This player can then take 1≤r≤min(2m,n) tokens. The next player is then free to take 1≤s≤min(2r,n-r) tokens. The player taking the last tokens is the winner. There is

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