Blog Archives

Bayes factors and martingales

August 10, 2011
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Bayes factors and martingales

A surprising paper came out in the last issue of Statistical Science, linking martingales and Bayes factors. In the historical part, the authors (Shafer, Shen, Vereshchagin and Vovk) recall that martingales were popularised by Martin-Löf, who is also influential in the theory of algorithmic randomness. A property of test martingales (i.e., martingales that are non

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Number of components in a mixture

August 5, 2011
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Number of components in a mixture

I got a paper (unavailable online) to referee about testing for the order (i.e. the number of components) of a normal mixture. Although this is an easily spelled problem, namely estimate k in I came to the conclusion that it is a kind of ill-posed problem. Without a clear definition of what a component is,

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JSM 2011 [3]

August 2, 2011
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JSM 2011 [3]

Monday August 01 was the first full day of JSM 2011 and full is the appropriate word to describe the day! It started for me at 7am with a round table run by Marc Suchard on parallel computing (or at 3am if I am considering the time I woke up!). I was rather out of

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Le Monde puzzle [#29]

July 28, 2011
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Le Monde puzzle [#29]

This week, the puzzle from the weekend edition of Le Monde was easy to state: in the sequence (8+17n), is there a 6th power? a 7th? an 8th? If so, give the first occurrence. So I first wrote an R code for a function testing whether an integer is any power: (The function returns the

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Core not in CiRM

July 27, 2011
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Core not in CiRM

Despite not enjoying this year the optimal environment of CiRM, we are still making good progress on the revision (or the R vision) of Bayesian Core. In the past two days, we went over Chapters 1 (Introduction), 2 (Normal Models), 5 (Capture-Recapture Experiments), and 6 (Mixture Models), with Chapters 3 (Regression), 4 (Generalised Linear Models)

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A slice of infinity

July 27, 2011
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A slice of infinity

Peng Yu sent me an email about the conditions for convergence of a Gibbs sampler: The following statement mentions convergence. But I’m not familiar what the regularity condition is. “But it is necessary to have a finite probability of moving away from the current state at all times in order to satisfy the regularity conditions on which

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Bayesian Core and loose logs

July 26, 2011
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Bayesian Core and loose logs

Jean-Michel (aka Jean-Claude!) Marin came for a few days so that we could make late progress on the revision of our book Bayesian Core towards an Use R! version. In one of the R programs in the mixture chapter, we were getting improbable answers, until we found an R mistake in the shape of which

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Ternary sorting

July 24, 2011
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Ternary sorting

The last Le Monde puzzle made me wonder about the ternary version of the sorting algorithms, which all seem to be binary (compare x and y, then…). The problem is, given (only) a blackbox procedure that returns the relative order of three arbitrary numbers, how many steps are necessary to sort a series of n

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Le Monde puzzle [#28]

July 22, 2011
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Le Monde puzzle [#28]

The puzzle of last weekend in Le Monde was about finding the absolute rank of x9 when given the relative ranks of x1,….,x8 and the possibility to ask for relative ranks of three numbers at a time. In R terms, this means being able to use or yet being able to sort the first 8

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The foundations of Statistics [reply]

July 18, 2011
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The foundations of Statistics [reply]

Shravan Vasishth has written a response to my review both published on the Statistics Forum. His response is quite straightforward and honest. In particular, he acknowledges not being a statistician and that he “should spend more time studying statistics”. I also understand the authors’ frustration at trying “to recruit several statisticians (at different points) to

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