How do you typically choose ϵ and L in practice, based on your data or modeling goals? Any tips or references would be super helpful!
Def take a look at the paper Bob posted. The short answer is that how you set those parameters is entirely up to your discretion. This is the part where PC priors are not uninformative. You’ll have to understand your problem, know what \alpha is doing, do some prior predictive simulation and then set L and \epsilon accordingly. All the PC priors work this way.