Posts Tagged ‘ University life ’

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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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 [or rather exchange of emails] 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 [as shown in the above] 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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MCMskv, Lenzerheide, Jan. 5-7, 2016

March 30, 2015
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MCMskv, Lenzerheide, Jan. 5-7, 2016

Following the highly successful [authorised opinion!, from objective sources] MCMski IV, in Chamonix last year, the BayesComp section of ISBA has decided in favour of a two-year period, which means the great item of news that next year we will meet again for MCMski V [or MCMskv for short], this time on the snowy slopes […]

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intuition beyond a Beta property

March 29, 2015
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intuition beyond a Beta property

A self-study question on X validated exposed an interesting property of the Beta distribution: If x is B(n,m) and y is B(n+½,m) then √xy is B(2n,2m) While this can presumably be established by a mere change of variables, I could not carry the derivation till the end and used instead the moment generating function E[(XY)s/2] […]

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Le Monde puzzle [#904.5]

March 25, 2015
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Le Monde puzzle [#904.5]

About this #904 arithmetics Le Monde mathematical puzzle: Find all plural integers, namely positive integers such that (a) none of their digits is zero and (b) removing their leftmost digit produces a dividing plural integer (with the convention that one digit integers are all plural). a slight modification in the R code allows for a […]

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