  Using the framework of weak Poincar{\'e} inequalities, we provide a general
comparison between the Hybrid and Ideal Slice Sampling Markov chains in terms
of their Dirichlet forms. In particular, under suitable assumptions Hybrid
Slice Sampling will inherit fast convergence from Ideal Slice Sampling and
conversely. We apply our results to analyse the convergence of the Independent
Metropolis--Hastings, Slice Sampling with Stepping-Out and Shrinkage, and
Hit-and-Run-within-Slice Sampling algorithms.
