Blog Archives

flea circus

December 7, 2016
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flea circus

An old riddle found on X validated asking for Monte Carlo resolution  but originally given on Project Euler: A 30×30 grid of squares contains 30² fleas, initially one flea per square. When a bell is rung, each flea jumps to an adjacent square at random. What is the expected number of unoccupied squares after 50 […]

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the incredible accuracy of Stirling’s approximation

December 6, 2016
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the incredible accuracy of Stirling’s approximation

The last riddle from the Riddler [last before The Election] summed up to find the probability of a Binomial B(2N,½) draw ending up at the very middle, N. Which is If one uses the standard Stirling approximation to the factorial function, log(N!)≈Nlog(N) – N + ½log(2πN) the approximation to ℘ is 1/√πN, which is not […]

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ratio-of-uniforms [#4]

December 1, 2016
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ratio-of-uniforms [#4]

Possibly the last post on random number generation by Kinderman and Monahan’s (1977) ratio-of-uniform method. After fiddling with the Gamma(a,1) distribution when a<1 for a while, I indeed figured out a way to produce a bounded set with this method: considering an arbitrary cdf Φ with corresponding pdf φ, the uniform distribution on the set […]

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asymptotically exact inference in likelihood-free models [a reply from the authors]

November 30, 2016
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asymptotically exact inference in likelihood-free models [a reply from the authors]

[Following my post of lastTuesday, Matt Graham commented on the paper with force détails. Here are those comments. A nicer HTML version of the Markdown reply below is also available on Github.] Thanks for the comments on the paper! A few additional replies to augment what Amos wrote: This however sounds somewhat intense in that […]

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sampling by exhaustion

November 24, 2016
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sampling by exhaustion

The riddle set by The Riddler of last week sums up as follows: Within a population of size N, each individual in the population independently selects another individual. All individuals selected at least once are removed and the process iterates until one or zero individual is left. What is the probability that there is zero […]

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Monty Python generator

November 22, 2016
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Monty Python generator

By some piece of luck I came across a paper by the late George Marsaglia, genial contributor to the field of simulation, and Wai Wan Tang, entitled The Monty Python method for generating random variables. As shown by the below illustration, the concept is to flip the piece H outside the rectangle back inside the […]

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postdoc on missing data at École Polytechnique

November 17, 2016
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postdoc on missing data at École Polytechnique

Julie Josse contacted me for advertising a postdoc position at École Polytechnique, in Palaiseau, south of Paris. “The fellowship is focusing on missing data. Interested graduates should apply as early as possible since the position will be filled when a suitable candidate is found. The Centre for Applied Mathematics (CMAP) is  looking for highly motivated […]

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simulation under zero measure constraints

November 16, 2016
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simulation under zero measure constraints

A theme that comes up fairly regularly on X validated is the production of a sample with given moments, either for calibration motives or from a misunderstanding of the difference between a distribution mean and a sample average. Here are some entries on that topic: How to sample from a distribution so that mean of […]

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analysing the US election result, from Oxford, England

November 14, 2016
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analysing the US election result, from Oxford, England

Seth Flaxman (Oxford), Dougal J. Sutherland (UCL), Yu-Xiang Wang (CMU), and Yee Whye Teh (Oxford), published on arXiv this morning an analysis of the US election, in what they called most appropriately a post-mortem. Using ecological inference already employed after Obama’s re-election. And producing graphs like the following one:Filed under: pictures, R, Statistics, Travel, University […]

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copy code at your own peril

November 13, 2016
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copy code at your own peril

I have come several times upon cases of scientists [I mean, real, recognised, publishing, senior scientists!] from other fields blindly copying MCMC code from a paper or website, and expecting the program to operate on their own problem… One illustration is from last week, when I read a X Validated question [from 2013] about an […]

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