It is common to use minimum ESS/time (effective sample size) across all parameters as a summary for MCMC sampler efficiency. Suppose two similar models M_1 and M_2 both use parameters \alpha, but differ in others i.e. only M_i uses \beta_i. Is it sensible to compare min ESS/time where the minimum is taken over all parameters? Or is it more sensible to only take the minimum over \alpha only? Or is any comparison fundamentally flawed since the models are different?
Two specific examples in my case:
- My models all involve multiple dependent Gaussian processes, but the dependency structure is different across models. Suppose that the parameters specifying the dependency structure are called GP hyperparameters. All models use the same GP variables, but the GP hyperparameters are different.
- The GPs are used to generated latent discrete variables, which then generate observed discrete variables. One approach marginalises out the latent discrete variables, another approach instead samples the latent discrete variables during MCMC. This is the case I care more about: is it okay if I compare minimum ESS rates where the minimum is taken over GP variables only, since that is what is shared between the two approaches?