Quantile Slice Sampling

TL;DR

This paper introduces a universal, efficient slice sampling method using probability integral transforms and pseudo-targets, improving sampling efficiency and adaptability for complex distributions.

Contribution

It generalizes Neal's shrinkage algorithm with an automatic, universal approach and extends it to multivariate cases, enhancing slice sampling techniques.

Findings

Improved sampler efficiency with fewer rejections.

Effective in high-dimensional and constrained models.

Automatic tuning via pseudo-targets enhances usability.

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.