Efficiency and Convergence Properties of Slice Samplers

Antonietta Mira and Luke Tierney

Scandinavian Journal of Statistics, 2002, vol. 29, issue 1, 1-12

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.

Date: 2002
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