I am trying to make predictions for two different outputs (independent) using two separate models. I am normalising the input and output data using relevant factors from the physics of my problem. But the uncertainty (standard deviation) in the mean value predictions changes upon using different scaling schemes, while the mean values themselves are predicted with high accuracy for two different schemes.
How do I make sense of the uncertainty (the standard deviation of the prediction of the GPy model) independent of the scaling scheme I use? How do I figure out if an appropriate transformation is required to obtain the standard deviation which is in the order of the magnitude of the output.
My apologies in advance for any lack of clarity.