function such that $$d_{\mathbf{w}}(s(\mathbf{x_1}),s(\mathbf{x_2})) = \sum_{i=1}^{\kappa} w_i (s_{1 i} - s_{2 i})^2,$$ where $s(\mathbf{x}) = (s_1, \ldots, s_{\kappa}) \in \mathbb{R}^{\kappa}$ is a vector of summary statistics and the sum over $i$ is taken over all the summary statistics considered. This distance function is a reasonable and flexible choice commonly used in the literature [@mckinley2009inference]. It is these distance weights, $w_i$, that control how the summary statistics are combined in this case. Given simulated pairs of parameter samples and datasets, we find weights, $\mathbf{w} = (w_1, \ldots, w_\kappa) \in E \subset \mathbb{R}^{\kappa}$, that maximize a distance between the prior and the posterior that represents the maximum possible gain in information about the parameters from the given data. Constructing the weights in this way allows us to account for the scale of the summary statistics, as well as their relative contribution to a posterior.

Adaption of weights {#Adaption_method}
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We seek to optimize the weights, $\mathbf{w}$, so that we can place less emphasis on summary statistics that are not informative for the posterior, but also scale summary statistics appropriately so that we do not neglect to obtain information about certain parameters. We do this within the ABC-SMC framework [@del2006sequential; @sisson2007sequential; @toni2009approximate] given 