Random dive MH

September 1, 2010

(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)

A new Metropolis-Hastings algorithm that I would call “universal” was posted by Somak Dutta yesterday on arXiv. Multiplicative random walk Metropolis-Hastings on the real line contains a different Metropolis-Hastings algorithm called the random dive. The proposed new value x’ given the current value x is defined by

begin{cases} xepsilon &text{with probability } 1/2\ x/epsilon &text{with probability } 1/2end{cases}

when epsilon is a random variable on (-1,1). Thus, at each iteration, the current value is either shrunk or expanded by a random amount. When I read the paper in the Paris metro, while appreciating that this algorithm could be geometrically ergodic as opposed to the classical random walk algorithm, I was not convinced by the practical impact of the method, as I thought that the special role of zero in the proposal was not always reflected in the target. Especially when considering that the proposal is parameter-free. However, after running the following R program on a target centred away from zero, I found the proposal quite efficient.

for (t in 2:Nsim){
if (runif(1)<prob) x[t]=prop

Obviously, it is difficult to believe that this extension will keep working similarly well when the dimension increases but this is an interesting way of creating a heavy tail proposal.

Filed under: R, Statistics Tagged: geometric ergodicity, Metropolis-Hastings, R, random walk, randomness

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 on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , , , , ,

Comments are closed.


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)