\alpha)
    \label{eq:likelihood_confidence}$$ where $\chi_D^2$ is the quantile function (i.e. the inverse of the cumulative distribution function) for the chi-squared distribution for $D$ degrees of freedom and $\alpha$ is the critical value, i.e. the value such that $C$ traps $\bm{a}_0$ with probability $\alpha$. The Fisher information quantifies the curvature of the likelihood function at its maximum value and hence the breadth of the distribution’s peak. A narrow peak (i.e. large curvature and large Fisher information) indicates that the maximum is well constrained. A broad peak (i.e. small curvature and small Fisher information) indicates that the maximum is poorly constrained.

Once we have the MLE of the parameters and the observed Fisher information matrix, we may compute the distribution of the MLE of any function of the parameters using the delta method [@wasserman_all_2007]. This states that any real-valued function of the parameters, $g: \bm{A} \longrightarrow
\bm{R}$, is distributed normally with mean $g(\hat{\bm{a}})$ and variance $$\begin{aligned}
    \dfrac{\partial g(\hat{\bm{a}})}{\partial \bm{a}^\mathrm{t}}
    \bm{J}^{-1}(\hat{\bm{a}}) \dfrac{\partial g(\hat{\bm{a}})}{\partial
      \bm{a}}.
    \label{eq:delta_method}\end{aligned}$$ For us $g$ will be some function of the phase-space DF (for example the galactic dark-matter profile, or Binney’s anisotropy parameter).

The likelihood (equation \[eq:likelihood\]) will not usually be expressible in closed form. Both the likelihood and its derivative 