It would be good to have the option to use a hierarchy of embedded spaces in the hierarchy of models, as described in the section "1.5 Different Fine and Coarse States" in the MLDA paper. This idea is also explained in detail in the MLMCMC paper
The idea is that a coarse model would only sample from a subspace of the next-finer model, and the additional modes for the next-finer model would be drawn from a separate proposal distribution. This would allow coarser models only to use a subset of the full parameter set, reflecting their limited expressiveness.
It would be good to have the option to use a hierarchy of embedded spaces in the hierarchy of models, as described in the section "1.5 Different Fine and Coarse States" in the MLDA paper. This idea is also explained in detail in the MLMCMC paper
The idea is that a coarse model would only sample from a subspace of the next-finer model, and the additional modes for the next-finer model would be drawn from a separate proposal distribution. This would allow coarser models only to use a subset of the full parameter set, reflecting their limited expressiveness.