Unbounded Slice Sampling

TL;DR

This paper introduces a change-of-variable approach to improve slice sampling for unbounded variables, enabling more uniform exploration in Markov Chain Monte Carlo methods.

Contribution

It proposes a simple change-of-variable technique that allows slice sampling of unbounded variables from [0,1), overcoming local limitations of the stepping-out heuristic.

Findings

Enhanced uniform exploration of unbounded variables

Maintains acceptance ratio of 1 in slice sampling

Simplifies slice sampling for unbounded distributions

Abstract

Slice sampling is an efficient Markov Chain Monte Carlo algorithm to sample from an unnormalized density with acceptance ratio always $1$. However, when the variable to sample is unbounded, its "stepping-out" heuristic works only locally, making it difficult to uniformly explore possible candidates. This paper proposes a simple change-of-variable method to slice sample an unbounded variable equivalently from [0,1).