Are exponential GP kernels easier to fit than exp_quad?

I am finding that while exp_quad kernel GP models require careful prior specification (see e.g. @betanalpha’s GP tutorial) of the length scale \rho, my exponential kernel GP models seem to fit fine with very basic constraints. For example, simply declaring

real<lower=L, upper=U> rho;

where L and U are the smallest and largest pairwise distance between observation locations works for me (meaning I recover parameters in fake data simulation and inference). Assuming that the locations were chosen well to capture the phenomenon of interest, this is a very weak prior.

I am happy to share some code but just wanted to check whether this conforms to anyone else’s experience and, if it is true, whether someone has an intuition as to why?


What is the prior that you are using for ρ? Also, did you check how the posterior of ρ looks like?