It is known that the simple slice sampler has robust convergence properties, however the class of problems where it can be implemented is limited. In contrast, we consider hybrid slice samplers which are easily implementable and where another Markov chain approximately samples the uniform distribution on each slice. Under appropriate assumptions on the Markov chain on the slice we show a lower bound and an upper bound of the spectral gap of the hybrid slice sampler in terms of the spectral gap of the simple slice sampler. An immediate consequence of this is that spectral gap and geometric ergodicity of the hybrid slice sampler can be concluded from spectral gap and geometric ergodicity of its simple version which is very well understood. These results indicate that robustness properties of the simple slice sampler are inherited by (appropriately designed) easily implementable hybrid versions. We apply the developed theory and analyse a number of specific algorithms such as the stepping-out shrinkage slice sampling, hit-and-run slice sampling on a class of multivariate targets and an easily implementable combination of both procedures on multidimensional bimodal densities.

翻译：已知简单切片抽样具有稳健的收敛性质，但其可应用的问题类别有限。与此相对，本文研究易于实现的混合切片抽样，其中另一个马尔可夫链近似地在每个切片上均匀分布采样。在适当的切片马尔可夫链假设下，我们通过简单切片抽样的谱间隙给出了混合切片抽样谱间隙的下界和上界。这一结果直接表明：从简单版本（其性质已被充分理解）的谱间隙和几何遍历性可推导出混合切片抽样的谱间隙和几何遍历性。这些结论显示简单切片抽样的稳健性可被（适当设计的）易于实现的混合版本继承。我们应用所发展的理论，分析了多种具体算法，包括步进收缩型切片抽样、针对多变量目标分布的跑停式切片抽样，以及将两者结合用于多维双峰密度分布的易于实现的混合程序。