Space Augmented and Double Slice Sampling

We present a generalisation of the standard well known and widely used Metropolis-Hastings algorithm which, unlike the Metropolis-Hastings sampler, can mix well over a target distribution which has separated and possibly narrow modes. The idea arose via a consideration of a space augmented slice sampler where the uniform space required to be sampled for the slice sampler, say I , is augmented with an additional space, say O. In I , our sampler behaves approximately as a slice sampler, while in O it behaves as a standard Metropolis-Hastings sampler. In O, we can propose large moves which allow jumps between modes, while in I we can take small steps which allow good exploration within each mode. Via an alternative perspective on this sampler, we then propose what we call the double slice sampler, which also exhibits good mixing properties.