does changing those values (in this case, 0.5 and 0.2) change anything about the way inference is performed?
Posterior distributions are only defined via Bayes’ theorem with reference to a prior distribution. sd = pyro.sample('sd_test', Normal(0.5, 0.2)) means there is a random variable sd_test in your model with prior (or likelihood, if sd_test is observed) distribution Normal(0.5, 0.2).
If you’re asking how to compute the posterior distributions over sd_mu and sd_scale in addition to the posterior distribution over sd_test, you’ll need to put priors on them as well. If you just want maximum likelihood estimates of these values, you can use pyro.param to mark them as free model parameters. See the model and inference introductory tutorials for more background.