Markov Chain Monte Carlo Methods Based On`slicing ' the Density Function

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 horizontaìslice' deened 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 eecient 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 specii-cation. One can also easily devise overrelaxed versions of slice sampling, which sometimes greatly improve sampling eeciency by suppressing random walk behaviour. Random walks can also be avoided in some slice sampling schemes that simultaneously update all variables.