Quantile Slice Sampling

Music City Center 

We propose and demonstrate a novel, 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 a factorization used in importance sampling, 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 pseudo-target specification and interpretable diagnostics. 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 to multivariate slice samplers and demonstrate with a constrained state-space model. R package qslice is available on CRAN.

Markov chain Monte Carlo

Hybrid slice sampling

Bayesian computation 

Section on Bayesian Statistical Science