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
[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 ... [Read more...]
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 ...
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 ...
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) ... [Read more...]
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 ... [Read more...]
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:... [Read more...]
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 ... [Read more...]
A rather obscure question on Metropolis-Hastings algorithms on X Validated ended up being about our first illustration in Introducing Monte Carlo methods with R. And exposing some inconsistencies in the following example… Example 7.2 is based on a [toy] joint Beta x Binomial target, which leads to a basic Gibbs sampler. ...
This afternoon, one of my Monte Carlo students at ENSAE came to me with an exercise from Monte Carlo Statistical Methods that I did not remember having written. And I thus “charged” George Casella with authorship for that exercise! Exercise 3.3 starts with the usual question (a) about the (Binomial) precision ...
Being still puzzled (!) by the ratio-of-uniform approach, mostly failing to catch its relevance for either standard distributions in a era when computing a cosine or an exponential is negligible, or non-standard distributions for which computing bounds and boundaries is out-of-reach, I kept searching for solutions that would include unbounded densities ...
Next summer of 2017, the biennial International Conference on Monte Carlo Methods and Applications (MCM) will take place in Montréal, Québec, Canada, on July 3-7. This is a mathematically-oriented meeting that works in alternance with MCqMC and that is “devoted to the study of stochastic simulation and Monte Carlo ... [Read more...]
Following a question on X Validated, I became aware of the following descriptions of the pros and cons of Bayesian analysis, as perceived by whoever (Tim Arnold?) wrote SAS/STAT(R) 9.2 User’s Guide, Second Edition. I replied more specifically on the point It [Bayesian inference] provides inferences that are ...
Following my earlier post on Kinderman’s and Monahan’s (1977) ratio-of-uniform method, I must confess I remain quite puzzled by the approach. Or rather by its consequences. When looking at the set A of (u,v)’s in R⁺×X such that 0≤u²≤ƒ(v/u), as discussed in the previous ...
As discussed in the previous entry, there are two interpretations to this question from The Riddler: “…how long is the longest path a knight can travel on a standard 8-by-8 board without letting the path intersect itself?” as to what constitutes a path. As a (terrible) chess player, I would ...
One approach to random number generation that had always intrigued me is Kinderman and Monahan’s (1977) ratio-of-uniform method. The method is based on the result that the uniform distribution on the set A of (u,v)’s in R⁺xX such that 0≤u²≤ƒ(v/u) induces the distribution with density ...
Following a request from one of the reviewers of our chapter Likelihood-free model choice, I tried to run EP-ABC on a toy problem and to compare it with the outcome of a random forest ABC. Literally starting from scratch, namely from the description found in Simon and Nicolas’ JASA paper. ... [Read more...]
David Rossell and Francisco Rubio (both from Warwick) arXived a month ago a paper on non-normal variable selection. They use two-piece error models that preserve manageable inference and allow for simple computational algorithms, but also characterise the behaviour of the resulting variable selection process under model misspecification. Interestingly, they show ...
The Riddler of this week had a riddle that is a variation of the knight tour problem, namely “…how long is the longest path a knight can travel on a standard 8-by-8 chessboard without letting the path intersect itself?” the riddle being then one of a self-avoiding random walk [kind]… ...
Following my earlier post on Delyon and Portier’s proposal to replacing the true importance distribution ƒ with a leave-one-out (!) kernel estimate in the importance sampling estimator, I ran a simple one-dimensional experiment to compare the performances of the traditional method with this alternative. The true distribution is a N(0,½) with ...