## Slice Sampling

**Radford M. Neal,
Dept. of Statistics and Dept. of Computer Science,
University of Toronto**
Markov chain sampling methods that adapt to characteristics of the
distribution being sampled can be constructed using the principle that
one can sample from a distribution by sampling 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, or more generally, with some update that leaves the uniform
distribution over this slice invariant. Such `slice sampling' methods
are easily 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 more efficient than simple Metropolis updates, due to
the ability of slice sampling to adaptively choose the magnitude of
changes made. It is therefore attractive for routine and automated
use. Slice sampling methods that update all variables simultaneously
are also possible. These methods can adaptively choose the magnitudes
of changes made to each variable, based on the local properties of the
density function. More ambitiously, such methods could potentially
adapt to the dependencies between variables by constructing local
quadratic approximations. Another approach is to improve sampling
efficiency by suppressing random walks. This can be done for
univariate slice sampling by `overrelaxation', and for multivariate
slice sampling by `reflection' from the edges of the slice.

Published (with discussion) in *Annals of Statistics*,
vol. 31, pp. 705-767:
text from online journal site.

Software implementing methods described in this paper is available
here and here.

**Associated references:**
Earlier versions of this work appeared as the following technical
reports:
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.
Neal, R. M. (1997) ``Markov chain Monte Carlo methods based on
`slicing' the density function'', Technical Report
No. 9722, Dept. of Statistics, University of Toronto, 27 pages:
abstract,
postscript,
pdf,
associated references.