Question regarding the Kriging variance Initial Value and Bounds


Dear UQ-community,

I was wondering about altering the options for the kriging variance (SigmaSQ). Does the preset initial value for SigmaSQ (0.5var(y)) take into account the mean/trend function, especially when using the ‘simple’ functionalty and the mean function will not be optimized and stays constant throughout the computation?
In my opinion, when having a really good mean function, the residuals to to be fit by the GP should be of way smaller magnitude than (0.5
var(y)) where y are the observations. Or does UQLab account for this and I’m not aware of it?

The confusion stems from my observation, that my optimized SigmaSQ will undershoot the default bounds.

Best, Robert

Hi @Rob

Just to clarify a few things:

Are you trying to create a Kriging regression model with a known noise variance (note the terminology in UQLab, regression means a Kriging model with noisy output/response)?
Because, as far as I know, the GP variance (SigmaSQ) will only be separately optimized in that particular case (see Eq. 1.51 in the Kriging User Manual).

For the other cases, i.e., noise-free and and unknown homogeneous noise, SigmaSQ in UQLab is strictly a function of theta (correlation function hyper-parameters; see, for instance, Eq. 1.43-1.45 in the User Manual for the noise-free case).
Therefore, the optimization bounds and initial value for SigmaSQ are irrelevant in these cases and only the initial value and bounds for the correlation hyper-parameters are considered.

I hope this helps!

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Oh right, that’s indeed explicated in the theory part of the manual. And that’s also a major difference towards the procedures implemented in Matlab, that I was not aware of. Thank you!