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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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

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 ...

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 ...