Did you read on to part 3 of that case study? I tried @betanalpha’s prescription for estimating the parameters of an informative inverse gamma prior for a similar situation of having a reasonable idea of the minimum and maximum length scales. It works at least in the sense of not producing obvious pathologies. The only implementation issue I ran into is that algebra_solver seems to need a good starting guess or it fails with a cryptic error message.
Here’s a sample pairs plot of the parameters related to the GP. I don’t know what the “true” values should be (this is from real data, not a simulation), but ρ should be somewhere in the range (0.2, 1) in the adopted distance units. Curvature in the posterior is supposed to be a problem, but all convergence diagnostics were fine in this case.
