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.

翻译：利用弱庞加莱不等式框架，我们从狄利克雷形式角度对混合切片抽样与理想切片抽样马尔可夫链进行了一般性比较。特别地，在适当假设下，混合切片抽样将从理想切片抽样继承快速收敛性，反之亦然。我们将所得结果应用于分析独立Metropolis-Hastings算法、带步进与收缩的切片抽样算法，以及切片内击跑算法的收敛性。