  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.
