The slice sampler and centrally symmetric distributions

We point out that the simple slice sampler generates chains that are correlation-free when the target distribution is centrally symmetric. This property explains several results in the literature about the relative performance of the simple and product slice samplers. We exploit it to improve two algorithms often used to circumvent the slice inversion problem, namely stepping out and multivariate sampling with hyperrectangles. In the general asymmetric case, we argue that symmetrizing the target distribution before simulating greatly enhances the efficiency of the simple slice sampler. To achieve symmetry we focus on the Box-Cox transformation with parameters chosen to minimize a measure of skewness. This strategy is illustrated with several sampling problems.