Hi

Still quite new to Stan here. I have been practicing doing simulations of the data generating process to see what priors are sensible, i.e. when parameters are drawn from the priors I get qualitatively similar data to my dataset.

I try to give wiggle that’s a bit beyond realistic appeareance to make sure the priors are not too stringent. But it seems that the priors that make my simulations look good are often too stringent to include as actual priors in my model.

For example, I found \sigma\sim\textrm{Exp}(1) is a good prior for the scale parameter in many situations, hierarchical, using ODEs, etc, but it is often very inappropriate in prior predictive checks. I get good looking simulations with \textrm{Exp}(5) or \textrm{Exp}(10) , but those always yield a poorer posterior sample.

I could try to come up with a small reprex so that people may have a chance to give a better answer, I will if required, but I perused the forums and I feel this question must have been addressed or someone has already encountered this and thought of an answer.

I have heard about Stan from McElreath’s awesome Rethinking course, where he advocates for and goes through many prior predictive checks in his lectures. He always uses \sigma\sim\textrm{Exp}(1) but doesn’t actually justify that one from a prior predictive check perspective I believe. I am working with data where the scale of the numbers are very small indeed, for example, bacterial growth curves measured by a spectrophotometer yield values between 0-1 with resolution of 0.01 and sigma values for various models around these growth curves are typically 0.05-0.1. If I sample from the aforementioned prior I get a complete mess in the vast majority of simulations.

Thank you for any precious insight