Ambiguities in fit-evaluation for selector models

The use of the direct evaluation of the Gaussian Process, using the square exponential function kernel prediction at the given data points is often misleading towards evaluation of the fit, given by the coefficient of determination. The predicted value at the data points when using the Gaussian Process, is almost at all cases equal to the original value. As such, interpretation problems arise when coefficient of determination suggest the model to be a good fit, but visual representations suggest otherwise. We illustrate the difficulties in presenting the coefficient of determination for the Gaussian Process and recommend the use of alternative methods for the evaluation of the predicted value, thus realizing the true function of the coefficient of determination.