Monte Carlo methods

another X’idated question

February 23, 2012 | xi'an

An X’idated reader of Monte Carlo Statistical Methods had trouble with our Example 3.13, the very one our academic book reviewer disliked so much as to “diverse [sic] a 2 star”. The issue is with computing the integral when f is the Student’s t(5) distribution density. In our book, we ... [Read more...]

ultimate R recursion

January 31, 2012 | xi'an

One of my students wrote the following code for his R exam, trying to do accept-reject simulation (of a Rayleigh distribution) and constant approximation at the same time: which I find remarkable if alas doomed to fail! I wonder if there exists a (real as opposed to fantasy) computer language ... [Read more...]

Hammersley and Handscomb 1964 on line

May 26, 2011 | xi'an

Through the webpage of the Advanced Monte Carlo Methods I & II, given a few years ago by Michael Mascagni at ETH Zürich, I found a link to the scanned version of the 1964 book Monte Carlo Methods by Hammersley and Handscomb. This is a short book, with less than 150 pages, ... [Read more...]

A survey of the [60′s] Monte Carlo methods [2]

May 17, 2011 | xi'an

The 24 questions asked by John Halton in the conclusion of his 1970 survey are Can we obtain a theory of convergence for random variables taking values in Fréchet spaces? Can the study of Monte Carlo estimates in separable Fréchet spaces give a theory of global approximation? When sampling functions, ... [Read more...]

A survey of [the 60’s] Monte Carlo methods

May 16, 2011 | xi'an

“The only good Monte Carlos are the dead Monte Carlos” (Trotter and Tukey, quoted by Halton) When I presented my [partial] history of MCM methods in Bristol two months ago, at the Julian Besag memorial, Christophe Andrieu mentioned a 1970 SIAM survey by John Halton on A retrospective and prospective survey ... [Read more...]

ABC lectures [finale]

October 31, 2010 | xi'an

The latest version of my ABC slides is on slideshare. To conclude with a pun, I took advantage of the newspaper clipping generator once pointed out by Andrew. (Note that nothing written in the above should be taken seriously.) On the serious side, I managed to cover most of the 300 ...
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Random generators for parallel processing

October 28, 2010 | xi'an

Given the growing interest in parallel processing through GPUs or multiple processors, there is a clear need for a proper use of (uniform) random number generators in this environment. We were discussing the issue yesterday with Jean-Michel Marin and briefly looked at a few solutions: given p parallel streams/threads/...
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NIPS 2010: Monte Carlo workshop

September 3, 2010 | xi'an

In the wake of the main machine learning NIPS 2010 meeting in Vancouver, Dec. 6-9 2010, there will be a very interesting workshop organised by Ryan Adams, Mark Girolami, and Iain Murray on Monte Carlo Methods for Bayesian Inference in Modern Day Applications, on Dec. 10. (And in Whistler, not Vancouver!) I wish ...
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Stratified sampling

June 9, 2010 | xi'an

The recently arXived paper of Goldstein, Rinott and Scarsini studies the impact of refining a partition on the precision of a stratified maximising/integration Monte Carlo approach. Quite naturally, if the partition gets improved, simulating points in each set of the partition can only improve the quality of the approximation, ... [Read more...]

Forsythe’s algorithm

May 8, 2010 | xi'an

In connection with the Bernoulli factory post of last week, Richard Brent arXived a short historical note recalling George Forsythe’s algorithm for simulating variables with density when (the extension to any upper bound is straightforward). The idea is to avoid computing the exponential function by simulating uniforms until since ... [Read more...]

The Bernoulli factory

April 22, 2010 | xi'an

A few months ago, Latuszyński, Kosmidis, Papaspiliopoulos and Roberts arXived a paper I should have noticed earlier as its topic is very much related to our paper with Randal Douc on the vanilla Rao-Blackwellisation scheme. It is motivated by the Bernoulli factory problem, which aims at (unbiasedly) estimating f(... [Read more...]

t-walk on the banana side

March 14, 2010 | xi'an

Following my remarks on the t-walk algorithm in the recent A General Purpose Sampling Algorithm for Continuous Distributions, published by Christen and Fox in Bayesian Analysis that acts like a general purpose MCMC algorithm, Darren Wraith tested it on the generic (10 dimension) banana target we used in the cosmology paper. ...
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t-walk on the wild side

March 11, 2010 | xi'an

When I read in the abstract of the recent A General Purpose Sampling Algorithm for Continuous Distributions, published by Christen and Fox in Bayesian Analysis that We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning. I am slightly bemused. The proposal of the ... [Read more...]

Congruential generators all are RANDUs!

January 30, 2010 | xi'an

In case you did not read all the slides of Regis Lebrun’s talk on pseudo-random generators I posted yesterday, one result from Marsaglia’s (in a 1968 PNAS paper) exhibited my ignorance during Regis’ Big’ MC seminar on Thursday. Marsaglia indeed showed that all multiplicative congruential generators lie on a ... [Read more...]

Big’MC seminar

January 29, 2010 | xi'an

Two very interesting talks at the Big’ MC seminar on Thursday: – Phylogenetic models and MCMC methods for the reconstruction of language history by Robin Ryder – Uniform and non-uniform random generators by Régis Lebrun which are both on topics close to my interest, evolution of languages (I’ll be a ... [Read more...]

Typos in Chapter 8

January 16, 2010 | xi'an

Phew!, we are now done with the solution manual in the sense that we have compiled solutions for all odd-numberedd exercises (but one!) and solved a fair number of even-numbered exercises. As it stands, the manual is 120 pages long and I am exhausted by the run to produce it over ...
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Typos in Chapters 6-7

January 14, 2010 | xi'an

Over the weekend and during the R exams, I managed to complete the solution set for Chapters 6 and 7 of “Introducing Monte Carlo Methods with R”. Chapter 6 only exhibited a few typos, despite me covering most exercises in Chapter 6, hence the merging of both chapters. – in Exercise 6.13, both and [...]
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