Efficiency and Convergence Properties of Slice Samplers

Abstract

The slice sampler (SS) is a method of constructing a reversible Markov chain with a specified invariant distribution. Given an independence Metropolis–Hastings algorithm (IMHA) it is always possible to construct a SS that dominates it in the Peskun sense. This means that the resulting SS produces estimates with a smaller asymptotic variance than the IMHA. Furthermore the SS has a smaller second‐largest eigenvalue. This ensures faster convergence to the target distribution. A sufficient condition for uniform ergodicity of the SS is given and an upper bound for the rate of convergence to stationarity is provided.