ordered observed values for its quantiles. To check that the standardized residuals are distributed as required, we therefore plot the $N$ ordered residuals of our fit against the $N$-th quantiles of the normal distribution. If the covariance function has been well-specified we expect them to be evenly scattered along the diagonal. We also require that the residuals are small, and hence calculate the *mean squared predicted error* (also *leave-one-out cross-validation score*), $$R := \frac{1}{N} \sum_{i = 1}^{N} (y(\bm{a}_i) - \hat{y}_{-i}(\bm{a}_i))^2,
    \label{eq:cv_score}$$ which tends to zero in the infinite-training data limit, as well as plot the predicted values against the true values. Furthermore, we require that the residuals exhibit no trend, and hence plot the standardized predicted errors against the associated predicted values for $y$. Finally, we require that there are no significant outliers (greater than three sigma, or $e_{-i} > 3$, say), which would indicate that the estimator is underperforming is certain regions of parameter space.

We expect poor accuracy in our estimator when neighbouring points are poorly correlated, i.e. when the scale of features in our function is approximately equal to or less than the point separation. We also expect the accuracy to be poor at the boundary of 