Blog Archives

Le Monde puzzle [#965]

June 13, 2016
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Le Monde puzzle [#965]

A game-related Le Monde mathematical puzzle: Starting with a pile of 10⁴ tokens, Bob plays the following game: at each round, he picks one of the existing piles with at least 3 tokens, takes away one of the tokens in this pile, and separates the remaining ones into two non-empty piles of arbitrary size. Bob

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data challenge in Sardinia

June 9, 2016
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data challenge in Sardinia

In what I hope is the first occurrence of a new part of ISBA conferences, Booking.com is launching a data challenge at ISBA 2016 next week. The prize being a trip to take part in their monthly hackathon. In Amsterdam. It would be terrific if our Bayesian conferences, including BayesComp, could gather enough data and

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the new version of abcrf

June 6, 2016
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the new version of abcrf

A new version of the R package abcrf has been posted on Friday by Jean-Michel Marin, in conjunction with the recent arXival of our paper on point estimation via ABC and random forests. The new R functions come to supplement the existing ones towards implementing ABC point estimation: covRegAbcrf, which predicts the posterior covariance between

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Le Monde puzzle [#964]

June 1, 2016
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Le Monde puzzle [#964]

A not so enticing Le Monde mathematical puzzle: Find the minimal value of a five digit number divided by the sum of its digits. This can formalised as finding the minimum of N/(a+b+c+d+e) when N writes abcde. And solved by brute force. Using a rough approach to finding the digits of a five-digit number, the

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the random variable that was always less than its mean…

May 29, 2016
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the random variable that was always less than its mean…

Although this is far from a paradox when realising why the phenomenon occurred, it took me a few lines to understand why the empirical average of a log-normal sample is apparently a biased estimator of its mean. And why the biased plug-in estimator does not appear to present a bias. The picture below compares two

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another riddle with a stopping rule

May 26, 2016
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another riddle with a stopping rule

A puzzle on The Riddler last week that is rather similar to an earlier one. Given the probability (1/2,1/3,1/6) on {1,2,3}, what is the mean of the number N of draws to see all possible outcomes and what is the average number of 1’s in those draws? The second question is straightforward, as the proportions

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occupancy rules

May 22, 2016
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occupancy rules

While the last riddle on The Riddler was rather anticlimactic, namely to find the mean of the number Y of empty bins in a uniform multinomial with n bins and m draws, with solution , this led

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ABC random forests for Bayesian parameter inference

May 19, 2016
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ABC random forests for Bayesian parameter inference

Before leaving Helsinki, we arXived the paper Jean-Michel presented on Monday at ABCruise in Helsinki. This paper summarises the experiments Louis conducted over the past months to assess the great performances of a random forest regression approach to ABC parameter inference. Thus validating in this experimental sense the use of

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Using MCMC output to efficiently estimate Bayes factors

May 18, 2016
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Using MCMC output to efficiently estimate Bayes factors

As I was checking for software to answer a query on X validated about generic Bayes factor derivation, I came across an R software called BayesFactor, which only applies in regression settings and relies on the Savage-Dickey representation of the Bayes factor when the null hypothesis writes as θ=θ⁰ (and possibly additional nuisance parameters with

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reversible chain[saw] massacre

May 15, 2016
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reversible chain[saw] massacre

A paper in Nature this week that uses reversible-jump MCMC, phylogenetic trees, and Bayes factors. And that looks at institutionalised or ritual murders in Austronesian cultures. How better can it get?! “by applying Bayesian phylogenetic methods (…) we find strong support for models in which human sacrifice stabilizes social stratification once stratification has arisen, and

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