We describe two slice sampling methods for taking multivariate steps using the crumb framework. These methods use the gradients at rejected proposals to adapt to the local curvature of the log-density surface, a technique that can produce much better proposals when parameters are highly correlated. We evaluate our methods on four distributions and compare their performance to that of a non-adaptive slice sampling method and a Metropolis method. The adaptive methods perform favorably on low-dimensional target distributions with highly-correlated parameters.
Technical Report No. 1002, Dept. of Statistics, University of Toronto (March 2010), 17 pages: postscript, pdf.
The R programs accompanying this paper are here.