[This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

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 $exp{-G(x)}$ when $0le G(x)le 1$ (the extension to any upper bound is straightforward). The idea is to avoid computing the exponential function by simulating uniforms $u_i$ until $G(x) ge u_1 ldots ge u_{n-1} le u_n$

since the probability of this event is $dfrac{G(x)^{n-1}}{(n-1)!} - dfrac{G(x)^{n}}{n!}$

its expectation is $exp{G(x)}$ and the probability that n is even is $exp{-G(x)}$. This turns into a generation method if the support of G is bounded. In relation with the Bernoulli factory problem, I think this has potential applications in that, when the function G(x) is replaced with an unbiased estimator the subsequent steps remain valid. This approach would indeed involve computing one single value of G(x), but this is also the case with Latuszyński et al.’s and our solutions… So I am uncertain as to whether or not this has practical implications. (Brent mentions normal simulation but this is more history than methodology.)

Filed under: R, Statistics Tagged: Bernoulli factory, George Forsythe, John von Neumann, Monte Carlo methods, normal distribution, series expansion, simulation      To leave a comment for the author, please follow the link and comment on their blog: Xi'an's Og » R.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

# Never miss an update! Subscribe to R-bloggers to receive e-mails with the latest R posts.(You will not see this message again.)

Click here to close (This popup will not appear again)