🤖 AI Summary
Slice sampling suffers from low efficiency and heavy reliance on manual tuning when applied to complex target distributions—such as highly skewed or constrained spaces. To address this, we propose Quantile Slice Sampling (QSS), a novel framework that (1) integrates probability integral transformation with quantile mapping to enable automatic initialization and unit-interval standardization; (2) introduces an evaluable pseudo-target importance reweighting mechanism, coupled with dual-metric quality assessment and adaptive parameter optimization; and (3) extends slice sampling to multivariate and constrained state spaces by incorporating elliptical slicing, Neal’s shrinkage, and Gibbs-like coordinate updates. Experiments on benchmark distributions and Bayesian modeling tasks demonstrate that QSS significantly outperforms conventional slice sampling and Metropolis–Hastings: in highly skewed and constrained settings, it reduces rejection rates by over 30%, while delivering enhanced robustness, full automation, and practical usability.
📝 Abstract
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.