  We propose and demonstrate an alternate, effective approach to simple slice
sampling. Using the probability integral transform, we first generalize Neal's
shrinkage algorithm, standardizing the procedure to an automatic and universal
starting point: the unit interval. This enables the introduction of approximate
(pseudo-) targets through importance reweighting, a technique that has
popularized elliptical slice sampling. Reasonably accurate pseudo-targets can
boost sampler efficiency by requiring fewer rejections and by reducing target
skewness. This strategy is effective when a natural, possibly crude,
approximation to the target exists. Alternatively, obtaining a marginal
pseudo-target from initial samples provides an intuitive and automatic tuning
procedure. We consider two metrics for evaluating the quality of approximation;
each can be used as a criterion to find an optimal pseudo-target or as an
interpretable diagnostic. We examine performance of the proposed sampler
relative to other popular, easily implemented MCMC samplers on standard targets
in isolation, and as steps within a Gibbs sampler in a Bayesian modeling
context. We extend the transformation method to multivariate slice samplers and
demonstrate with a constrained state-space model for which a readily available
forward-backward algorithm provides the target approximation.
