Slices and crumbs [arXiv:1011.4722]

November 29, 2010

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

An interesting note was arXived a few days ago by Madeleine Thompson and Radford Neal. Beside the nice touch of mixing crumbs and slices, the neat idea is to have multiple-try proposals for simulating within a slice and to decrease the dimension of the simulation space at each try. This dimension diminution is achieved via the construction of an orthogonal basis based on the gradient of the log densities at previously-rejected proposals.

mathbf{J}=(nablalog f(x_1),ldots,nablalog f(x_k))

until all dimensions are exhausted, in which case the scale of the Gaussian proposal is reduced. (The paper comes with R and C codes.) Provided the gradient can be computed (or at least approximated), this is a fairly general method (even though I have not tested it so cannot say how much calibration it requires). An interesting point is that, contrariwise to the delayed-rejection method of Antonietta Mira and co-authors,  the repeated proposals do not induce a complexification in the slice acceptance probability. I am less convinced by the authors’ conclusion that the method compares with adaptive Metropolis techniques, in the sense the “shrinking rank” method forgets about past experiences as it starts from scratch at each iteration: it is thus not really learning… (Now, in terms of performances, this may be the case!)

Filed under: Books, R, Statistics Tagged: adaptive MCMC methods, crumbs, Gaussian random walk, MCMC, Monte Carlo Statistical Methods, R, slice sampling, smilation

To leave a comment for the author, please follow the link and comment on their blog: Xi'an's Og » R. 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.


Mango solutions

RStudio homepage

Zero Inflated Models and Generalized Linear Mixed Models with R

Quantide: statistical consulting and training


CRC R books series

Contact us if you wish to help support R-bloggers, and place your banner here.

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)