Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

翻译：极坐标切片采样（Roberts & Rosenthal, 2002）是一种用于分布近似采样的马尔可夫链方法，虽然高效实现困难甚至不可能，但已在维度上被证明具有良好性质。通过分别更新链迭代的方向分量与径向分量，我们获得了一族模拟极坐标切片采样行为、同时可高效实现的采样器。多组数值实验表明，我们提出的算法优于两个最相关的方法——椭圆切片采样（Murray等人，2010）与随机游走均匀切片采样（MacKay，2003）。在目标分布满足适当假设的条件下，我们证明了方法的良定义性与收敛性。