Reparameterizable vs non-reparameterizable latent variables

Tutorials
1

In the Deep Markov Model Tutorial (an in many other place) we refer to reparameterizable vs non-reparameterizable latent variables.
It is stated that:

  1. reparameterizable latent variables have low variance and therefore the Trace_ELBO suffice
  2. non-reparameterizable latent variables have higher variance and TraceGraph_ELBO should be used.

My question is:
How do I figure out if my latent variables are reparameterizable?
Is it the same as checking whether I have DISCRETE latent variables?

2

In Pyro, yes, it happens that all built-in continuous distributions are reparameterized. Discrete distributions are non-reparameterized, and sometimes it is easier to implement a non-reparameterized version of a custom continuous distribution (e.g. via rejection sampling or mcmc).