Tuning the hyperparameters

When changing the hyperparameters for my gaussian process length scale say from this l = pm.InverseGamma(“l”, alpha=1, beta=5) to l = pm.InverseGamma(“l”, alpha=1, beta=40) the trace it produces and the value the find_MAP function used remain fairly constant. The error from cross validation changes slightly showing the second performs slightly better. I have limited it to beta=40 as beyond this it gives weight to length scales which go beyond that of the data so would underfit the data.

I’m not suggesting there is anything wrong with this as both produce good gaussian process plots using trace and find_MAP but could someone explain why they both end up using very similar parameters even though they have quite different hyperparameters. For reference I’m not varying the prior function as this was selected from research, but is that why I don’t get much variation?

It doesn’t matter if not varying much is expected as its just a learning point in my report but I just want to know there is nothing wrong with this result.