Daniel Rudolf (Friedrich Schiller University Jena): On the hybrid slice sampler

It is known that the simple slice sampler has very robust convergence properties. In contrast, we consider hybrid slice samplers where another Markov chain approximately samples the uniform distribution on each slice. Under appropriate assumptions of the Markov chain on the slice we show a lower bound and upper bound of the spectral gap of the hybrid slice sampler in terms of the spectral gap of the simple slice sampler.
Keywords: hybrid Markov chains, slice sampler, spectral gap