Quantile Slice Sampling

Abstract

We propose and demonstrate a novel, effective approach to 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 the factorization used in importance sampling, a technique that popularized elliptical slice sampling, while still sampling from the correct target distribution. Accurate pseudo-targets can boost sampler efficiency by requiring fewer rejections and by reducing skewness in the transformed target. 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. Supplemental materials and accompanying R package qslice are available online.