To assess how sensitive the risk scores are to the choice of weighting parameters,
this function explores many alternative combinations of weights and (optionally)
a power-mean parameter, and examines how resulting risk scores vary.
When risk_form = "additive", uncertainty is induced by sampling weight triplets
\((\alpha, \beta, \gamma)\) under the constraint \(\alpha + \beta + \gamma = 1\),
representing different plausible balances between complexity, connectivity and centrality.
When risk_form = "power_mean", uncertainty is induced by sampling both the weights
\((\alpha, \beta, \gamma)\) (renormalized to sum to 1) and a power parameter \(p\)
used in the node-risk definition:
$$r =
\left(\alpha\,\tilde{C}^{p} + \beta\,(\tilde{d}^{\mathrm{in}})^{p} + \gamma\,\tilde{b}^{p}\right)^{1/p}\,.$$
For each node, risk scores are repeatedly recalculated using the sampled parameter
combinations, producing a distribution of possible outcomes. This distribution is
then used to quantify uncertainty in the risk scores and compute Sobol' sensitivity
indices for each sampled parameter.
Path-level uncertainty is obtained by propagating node-level uncertainty draws through
the path aggregation function:
$$P_k = 1 - \prod_{i=1}^{n_k} (1 - r_{k(v_i)})\,,$$
where \(r_{k(v_i)}\) are node risks along path \(k\).
All uncertainty metrics are computed from the first N
Sobol draws (matrix A), while sensitivity indices use the full Sobol' design.
For more information about the uncertainty and sensitivity analysis and the output of
this function, see the sensobol package (Puy et al. 2022).
The returned node table includes the following columns:
The returned paths table includes:
path_id: path identifier.
path_str: sequence of function calls for each path.
hops: number of edges.
uncertainty_analysis: numeric vector giving the uncertainty draws in the path risk score.
gini_index: numeric vector giving the uncertainty draws in the gini index.
risk_trend: numeric vector giving the uncertainty draws in the risk trend.