Are exponential GP kernels easier to fit than exp_quad?

Modeling
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1

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?

2

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