One way to sample from a distribution is to sample uniformly from the region under the plot of its density function. A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal `slice' defined by the current vertical position. Variations on such `slice sampling' methods can easily be implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn. This approach is often easier to implement than Gibbs sampling, and may be more efficient than easily-constructed versions of the Metropolis algorithm. Slice sampling is therefore attractive in routine Markov chain Monte Carlo applications, and for use by software that automatically generates a Markov chain sampler from a model specification. One can also easily devise overrelaxed versions of slice sampling, which sometimes greatly improve sampling efficiency by suppressing random walk behaviour. Random walks can also be avoided in some slice sampling schemes that simultaneously update all variables.
Technical Report No. 9722, Dept. of Statistics (November 1997), 27 pages: postscript, pdf.
Neal, R. M. (2000) ``Slice sampling'', Technical Report No. 2005, Dept. of Statistics, University of Toronto, 40 pages: abstract, postscript, pdf, associated references, associated software, more associated software.This in turn became the following paper:
Neal, R. M. (2003) ``Slice sampling'' (with discussion), Annals of Statistics, vol. 31, pp. 705-767: abstract, text from online journal site, associated references, associated software, more associated software.