  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.
