How to match obs_noise in Gaussian likelihood with simulated obs noise?

[jakeyeung]

Hi all,

I am wondering what kind of simulation would allow me to verify that the obs_noise from the Gaussian likelihood is correct?

To try to get the ground truth obs_noise, I drew samples from a Gaussian distribution with mean mean1 and variance var1.

I then fit the data to a constant kernel, hoping that the GP would estimate the obs_noise would correspond to sqrt(var1), but I can't quite get the numbers to match. Perhaps I am thinking about this obs_noise incorrectly? Or maybe the model isn't fitting properly?

I attach a jupyterhub notebook (in markdown format) of example code that simulates the data and fits the constant kernel to try to estimate this obs_noise.

https://gist.github.com/jakeyeung/d0e0daad0ea10ebf674976df329085f4

Jake