Guesstimate is napkin math. It makes no sense to spend an inordinate amount of time fine-tuning the distribution when both the distribution and its parameters a

Guesstimate is napkin math. It makes no sense to spend an inordinate amount of time fine-tuning the distribution when both the distribution and its parameters are just best guesses. The important part is the propagation of uncertainty across many dependent variables, and the normal distribution is often good enough for that purpose. Whenever it isn't, for me that'd be a sign to use a proper statistical model instead. MCMC was invented to do inference on models of arbitrary complexity, with however much or little data you might have.