Generalised Latent Slice Sampling

Slice sampling is a family of auxiliary-variable Monte Carlo algorithms that convert the problem of sampling from a target distribution to one of sampling from the region bounded by the graph of its density function. The main challenge in implementing slice samplers is performing constrained resampling from the region where the density exceeds a threshold, which typically involves selecting a search region -- by a stepping-out or probabilistic procedure -- and then applying a shrinkage algorithm until a point within the slice is found. Here, we generalise a probabilistic method for selecting the search region to select ellipsoids instead of hyperrectangles and introduce efficient shrinkage and adaptation procedures. We also show for the first time that slice sampling can be combined with parallel tempering to improve performance on multi-modal targets. All new algorithms are implemented efficiently in vectorised form and benchmarked on some target distributions, where the proposed methods show improvement in sample-based metrics as a function of the number of target evaluations compared to prior methods.