Currently when trying to specify prior mean functions for H(z) and rho(z) the GP learns sigma_f approx 0 for the signal variance hyperparameter and a much larger length scale than when not using prior mean functions. This kinda makes sense because prior mean functions tend to zero the data and so would result in longer length scales. However optimised values of the signal variance are so small that the variance in the resulting samples is negligible. This should be addressed because without prior mean functions the GP priors tend to introduce edge effects, skewing the distributions of T_1 and T_2 towards negative values, especially at the far end.
Currently when trying to specify prior mean functions for H(z) and rho(z) the GP learns sigma_f approx 0 for the signal variance hyperparameter and a much larger length scale than when not using prior mean functions. This kinda makes sense because prior mean functions tend to zero the data and so would result in longer length scales. However optimised values of the signal variance are so small that the variance in the resulting samples is negligible. This should be addressed because without prior mean functions the GP priors tend to introduce edge effects, skewing the distributions of T_1 and T_2 towards negative values, especially at the far end.