Interpolation error of Gaussian process regression for misspecified case
An interpolation error is an integral of the squared error of a regression model over a domain of interest. We consider the interpolation error for the case of misspecified Gaussian process regression: a used covariance function differs from a true one. We derive the interpolation error for a grid design of experiments for an arbitrary covariance function. Then we consider particular types of covariance functions from theoretical and practical points of view. For $\textitMatern_1/2$ covariance function poor estimation of parameters only slightly affects the quality of interpolation. For the most common covariance functions including $\textitMatern_3/2$ and squared exponential covariance functions poor choose of parameters of covariance functions leads to a bad quality of interpolation.