must compute these maximum-likelihood estimates and then *check* that the assumption of normality is met by inspecting a histogram of the transformed values. In general the condition is not met, i.e. there exists no power transformation such that $G'_{1}, \ldots, G'_{N} \sim N(\mu_\mathrm{t}, \sigma_\mathrm{t}^2)$. However we may still use the power transformation to *regularize* $G$, i.e. to bring its distribution closer to normal [@draper_distributions_1969].

When using the zero regression function the residuals $\bm{y} - \bm{r}$ (equation \[eq:gpe\_mean\]) may be poorly behaved. They may all have the same sign, or may contain outliers. The use of a transformation overcomes these problems, and avoids the need to specify a regression function, of which we have very little prior knowledge.

Having stabilized the variance of the data, we must also ensure the autocovariance is approximately constant. We do this by transforming the parameter space (i.e. by reparameterizing the random process). This is an altogether more difficult problem [see, for example @sampson_nonparametric_1992] as the length scale $l_i$ (and hence sensitivity $m_i$) is a function of the parameter $a_i$. We will assume that for positive parameters the sensitivity $m_i$ is monotonically decreasing in $a_i$ and converges on zero, i.e. we will assume that the model 