CompoundStep MH Sampling - Separate scaling factors?

[junpenglao]

There is a bit more detail here: Compounds steps

@nmrobert

Is this a component-wise MH algorithm, where each continuous variable has a separate and independent univariate proposal distribution, and the overall proposal vector is updated component-wise, with each element being accepted or rejected in a loop sequentially?

Yes, it is essentially a metropolis within Gibbs sampler.

As for the scaling, I think they are also updated/tuned during tuning independently.