Blog Archives

puzzled by harmony [not!]

December 12, 2016
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puzzled by harmony [not!]

In answering yet another question on X validated about the numerical approximation of the marginal likelihood, I suggested using an harmonic mean estimate as a simple but worthless solution based on an MCMC posterior sample. This was on a toy example with a uniform prior on (0,π) and a “likelihood” equal to sin(θ)

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ratio-of-uniforms [-1]

December 11, 2016
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ratio-of-uniforms [-1]

Luca Martino pointed out to me my own and forgotten review of a 2012 paper of his, “On the Generalized Ratio of Uniforms as a Combination of Transformed Rejection and Extended Inverse of Density Sampling” that obviously discusses a generalised version of Kinderman and Monahan’s (1977) ratio-of-uniform method. And further points out the earlier 1991 paper

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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 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]

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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