Probably shouls unify this with the already existing LogDensityProblems interface impl for DynamicHMC below. With this PR, it seems now we have to different definitions of the log joint with LogDensityProblems. This seems a bit unnecessarily complicated.
_Originally posted by @devmotion in https://github.com/JuliaGaussianProcesses/AbstractGPs.jl/pull/349#discussion_r1058387681_