Articles by xi'an

Using MCMC output to efficiently estimate Bayes factors

May 18, 2016 | xi'an

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 ...
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reversible chain[saw] massacre

May 15, 2016 | xi'an

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 ...
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AISTATS 2016 [#1]

May 10, 2016 | xi'an

Travelling through Seville, I arrived in Càdiz on Sunday night, along with a massive depression [weather-speaking!]. Walking through the city from the station was nonetheless pleasant as this is an town full of small streets and nice houses. If with less churches than Seville! Richard Samworth gave the first ...
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a Simpson paradox of sorts

May 5, 2016 | xi'an

The riddle from The Riddler this week is about finding an undirected graph with N nodes and no isolated node such that the number of nodes with more connections than the average of their neighbours is maximal. A representation of a connected graph is through a matrix X of zeros ... [Read more...]

gap frequencies [& e]

April 28, 2016 | xi'an

A riddle from The Riddler where brute-force simulation does not pay: For a given integer N, pick at random without replacement integers between 1 and N by prohibiting consecutive integers until all possible entries are exhausted. What is the frequency of selected integers as N grows to infinity? A simple implementation ...
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Le Monde puzzle [#960]

April 27, 2016 | xi'an

An arithmetic Le Monde mathematical puzzle: Given an integer k__1, consider the sequence defined by F(1)=1+1 mod k, F²(1)=F(1)+2 mod k, F³(1)=F²(1)+3 mod k, &tc. [With this notation, F is not necessarily a function.] For which value of k is the sequence the entire {0,1,…,k-1} set? This leads ...
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an integer programming riddle

April 20, 2016 | xi'an

A puzzle on The Riddler this week that ends up as a standard integer programming problem. Removing the little story around the question, it boils down to optimise 200a+100b+50c+25d under the constraints 400a+400b+150c+50d≤1000, b≤a, a≤1, c≤8, d≤4, and (a,b,c,d) all ... [Read more...]

Le Monde puzzle [#959]

April 19, 2016 | xi'an

Another of those arithmetic Le Monde mathematical puzzle: Find an integer A such that A is the sum of the squares of its four smallest dividers (including1) and an integer B such that B is the sum of the third poser of its four smallest factors. Are there such integers ...
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Le Monde puzzle [#958]

April 10, 2016 | xi'an

A knapsack Le Monde mathematical puzzle: Given n packages weighting each at most 5.8kg for a total weight of 300kg, is it always possible to allocate these packages  to 12 separate boxes weighting at most 30kg each? weighting at most 29kg each? This can be checked by brute force using the ...
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Statistical rethinking [book review]

April 5, 2016 | xi'an

Statistical Rethinking: A Bayesian Course with Examples in R and Stan is a new book by Richard McElreath that CRC Press sent me for review in CHANCE. While the book was already discussed on Andrew’s blog three months ago, and [rightly so!] enthusiastically recommended by Rasmus Bååth on ...
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Le Monde puzzle [#956]

April 4, 2016 | xi'an

A Le Monde mathematical puzzle with little need of R programming: Does there exist a function f from N to N such that (i) f is (strictly) increasing, (ii) f(n)≥n, and (iii) f²(n)=f(f(n))=3n? Indeed, the constraints imply (i) f²(0)=0, hence that that f(0)=0, (...
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another riddle

March 28, 2016 | xi'an

A very nice puzzle on The Riddler last week that kept me busy on train and plane rides, runs and even in between over the weekend. The core of the puzzle is about finding the optimal procedure to select k guesses about the value of a uniformly random integer x ... [Read more...]

Le Monde puzzle [#952]

March 18, 2016 | xi'an

A quite simple Le Monde mathematical puzzle again with Alice and Bob: In a multiple choice questionnaire with 50 questions, Alice gets a score s such that Bob can guess how many correct (+5 points), incorrect (-1 point) and missing (0 point) Alice got when adding that Alice could not have gotten s-2 ...
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preserving frequencies without resampling

March 8, 2016 | xi'an

An interesting question came up on X validated a few days ago: given a probability vector p=(p¹,…,p⁷), is there a way to pick 5 values in {1,…,7} without replacement and still preserve the probability repartition in the resulting sample? In other words, is there a sampling without replacement strategy that ...
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Amazonish warning

March 1, 2016 | xi'an

As in previous years, I want to repost a warning to ‘Og readers that all http links to Amazon.com [and much more rarely to Amazon.fr] products found on this ‘Og are actually susceptible to reward me with an advertising percentage if a purchase is made by the reader ... [Read more...]

twilight zone [of statistics]

February 25, 2016 | xi'an

“I have decided that mixtures, like tequila, are inherently evil and should be avoided at all costs.” L. Wasserman Larry Wasserman once remarked that finite mixtures were like the twilight zone of statistics, thanks to the numerous idiosyncrasies associated with such models. And George Casella had similar strong reservations about ...
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more e’s [and R’s]

February 21, 2016 | xi'an

Alex Thiéry suggested debiasing the biased estimate of e by Rhee and Glynn truncated series method, so I tried the method to see how much of an improvement (if any!) this would bring. I first attempted to naïvely implement the raw formula of Rhee and Glynn with a (...
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R colours

February 17, 2016 | xi'an

As I am always fishing for colour names in R, I looked for an easy summary of those names and found this table on New Energy Research blog, which I reproduce here for [my] future access.  Filed under: pictures, R Tagged: colors(), colours(), R [Read more...]

Гнеде́нко and Forsythe [and e]

February 15, 2016 | xi'an

In the wake of my earlier post on the Monte Carlo estimation of e and e⁻¹, after a discussion with my colleague Murray Pollock (Warwick) Gnedenko’s solution, he pointed out another (early) Monte Carlo approximation called Forsythe’s method. That is detailed quite neatly in Luc Devroye’s bible, ...
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