\[eq:gpe\_mean\]) is distributed normally with variance equal to the MSE (equation \[eq:mse\]), and expect that for a well-specified covariance this distribution will be observed in our estimator. Ideally we would evaluate our dynamical model at a large number of test points, and compare the distribution of the residuals of our predictions with that of the MSE. This, of course, imposes an impractical computational burden. Instead, we omit the $i$-th pair, $(\bm{a}_i, y(\bm{a}_i))$, from our training data to give the reduced data, $(\bm{a}_i, y(\bm{a}_i))_{i \neq i}$. Using these data we then compute an estimate for $y$ at the omitted point, $\bm{a}_i$, finding that (see equation \[eq:gpe\_conditional\]) $Y(\bm{a}_i) | (\bm{Y}_{-i} = \bm{y}_{-i}) \sim N(\hat{y}_{-i}(\bm{a}_i), \hat{\sigma}_{-i}^2(\bm{a}_i))$. This gives us $N$ residuals, which we may compare with the MSE. We expect that the *standardized predicted error* [@wasserman_all_2007], $$e_{-i}(\bm{a}_i) := \frac{y(\bm{a}_i) - \hat{r}_{-i}(\bm{a}_i)}{\hat{\sigma}_{-i}(\bm{a}_i)},
    \label{eq:predicted_error}$$ is normally distributed with zero mean and unit variance.[^5]

One way to compare two distributions is by means of a *quantile-quantile plot*, in which we plot the quantiles of one distribution against the quantiles of the other. If the two distributions are the same, then the points will lie on the diagonal. If either distribution is empirical we may substitute its 