models themselves. In particular, there is no assumption that the line-of-sight velocity distributions are Gaussian, as is sometimes assumed in the dynamical modelling of dSphs ([@battaglia_kinematic_2008], [@strigari_common_2008], and [@wolf_accurate_2010]).

Our principal interest is in what observed data can tell us about the distribution of dark matter in a dSph. Which dark-matter morphologies do the data rule out? Which best account for the observations? We therefore adopt the maximum-likelihood approach, which allows us to draw robust confidence regions within parameter space. We outline this procedure in section \[sec:likelihood\]. In section \[sec:gpe\] we discuss the use of GPE to estimate the likelihood when it too expensive to for us to perform a parameter sweep. In section \[sec:plummer\] we illustrate the method using our toy model. In section \[sec:conclusion\] we summarize our conclusions.

Likelihood {#sec:likelihood}
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In this paper, our representation of a stellar system (in this case a dSph) consists of a parameterized set of functions (i.e. the dynamical model) representing the phase-space probability density function (also called the distribution function). We treat the positions, $\bm{X}$, and the velocities, $\bm{V}$, as random vectors, meaning that the state of a star is represented by the random vector, $\bm{W} := (\bm{X}, \bm{V})$. The distribution 