Publications by xi'an
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 it involves a qu...
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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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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 perfect for the sma...
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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 bell rings, up to six decimal pl...
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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 ear...
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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) [really a toy problem!]. ...
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a Galton-Watson riddle
The Riddler of this week has an extinction riddle which summarises as follows: One observes a population of N individuals, each with a probability of 10⁻⁴ to kill the observer each day. From one day to the next, the population decreases by one individual with probability K√N 10⁻⁴ What is the value of K that leaves the observer alive w...
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truncated normal algorithms
Nicolas Chopin (CREST) just posted an entry on Statisfaction about the comparison of truncated Normal algorithms run by Alan Rogers, from the University of Utah. Nicolas wrote a paper in Statistics and Computing about a simulation method, which proposes a Ziggurat type of algorithm for this purpose, and which I do not remember reading, thanks to ...
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weakly informative reparameterisations for location-scale mixtures
We have been working towards a revision of our reparameterisation paper for quite a while now and too advantage of Kate Lee visiting Paris this fortnight to make a final round: we have now arXived (and submitted) the new version. The major change against the earlier version is the extension of the approach to a large class of models that include ...
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an express riddle
A quick puzzle on The Riddler this week that enjoys a quick solution once one writes it out. The core of the puzzle is about finding the average number of draws one need to empty a population of size T if each draw is uniform over the remaining number of individuals between one and the number that remain. It is indeed easy to see that this averag...
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