I read on this thread the following:
If you can use both the gibbs sampler and slice sampling to sample from a posterior I would use the Gibbs sampler as the slice sampler seems unnecessary to me <...> If you cannot use the gibbs but you can use the slice then your question seems irrelevant.
But then, when on these slides from M. Jordan's lecture he says that:
Slice sampling is a special case of Gibbs sampling (in a product space).
What does he mean by that?
Also, when would one not be able to do Gibbs sampling but still do slice sampling?