Computes a vector of node-level risk scores under a Sobol' sampling design and returns both the uncertainty-analysis draws and Sobol sensitivity indices.
risk_ua_sa_fun(
cyclo_sc,
indeg_sc,
btw_sc,
sample_matrix,
N,
params,
order,
risk_form = c("additive", "power_mean"),
eps = 1e-12
)For risk_form = "additive", the node risk score is
$$r = \alpha\,\tilde{C} + \beta\,\tilde{d}^{\mathrm{in}} + \gamma\,\tilde{b}\,,$$
where \(\tilde{C}\), \(\tilde{d}^{\mathrm{in}}\), and \(\tilde{b}\) are scaled
inputs and \(\alpha + \beta + \gamma = 1\).
For risk_form = "power_mean", the node risk score is computed as a (weighted) power mean
with exponent \(p\):
$$r =
\left(\alpha\,\tilde{C}^{p} + \beta\,(\tilde{d}^{\mathrm{in}})^{p} + \gamma\,\tilde{b}^{p}\right)^{1/p}\,.$$
In the limit \(p \to 0\), this reduces to a weighted geometric mean, implemented with a small constant \(\epsilon\) to avoid \(\log(0)\): $$r = \exp\left(\alpha\log(\max(\tilde{C},\epsilon)) + \beta\log(\max(\tilde{d}^{\mathrm{in}},\epsilon)) + \gamma\log(\max(\tilde{b},\epsilon))\right)\,.$$