## Markov chain Monte Carlo methods based on
`slicing' the density function

**Radford M. Neal,
Dept. of Statistics and Dept. of Computer Science,
University of Toronto**

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.

**Associated references:**
A revised and substantially extended version of this paper was
issued as the following technical report:
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.