Global Sensitivity Analysis - Overview

Summary

Global sensitivity analysis (GSA) apportions the uncertainty in a model’s output across its uncertain inputs, with all inputs varied simultaneously across their full ranges. Sadeghi & Matwin (2024) organize GSA into four families: variance-based (Sobol, FAST/RBD), derivative-based (Morris elementary effects, DGSM), distribution/moment-independent (Delta), and feature-additive methods. The general workflow is two phases — sample the input space, then analyze how output variance/behavior attributes back to each factor. For ABMs this answers “which parameters actually drive the behavior, and which can be fixed?” while accounting for interactions that local one-at-a-time methods miss.

Overview

For a model $Y=f(X_1,\dots ,X_p)$ with $p$ uncertain inputs, GSA quantifies the contribution of each $X_i$ (and combinations of inputs) to the variability of $Y$. The paper frames GSA as the global counterpart to local explainability: global methods “explain the overall behavior of a model by varying the entire range of input factors and examining the joint effect and interaction between them,” whereas local methods “study the effect of a parameter by exploring its local vicinity while holding all other parameters fixed at their baseline values.” Local methods implicitly assume linearity and input independence; when factors interact, they “may produce misleading or inaccurate results.” See Local vs Global Sensitivity Analysis.

The general GSA paradigm has two phases:

1. Sampling — generate samples of the inputs $X_i$ over their distributions/ranges.
2. Analysis — run the model to produce $Y$, then assess each factor’s impact.

The four families of GSA methods ^gsa-families

The review (Sec. 1) groups GSA methods into four categories:

• Variance-based — assume output variance fully characterizes output uncertainty (Saltelli et al.); decompose $V(Y)$ across factors. Includes Sobol, FAST, RBD/FAST_RBD. See Variance-Based Sensitivity and Sobol Indices.
• Derivative-based — sensitivity from (averaged) partial derivatives $\left|\frac{\partial f}{\partial x_i}\right|$. Includes Morris elementary effects and DGSM. See Morris Elementary Effects Screening.
• Distribution / moment-independent — examine the whole output PDF, not just its moments. Includes the Delta (${\delta }_i$) index.
• Feature-additive methods.

Screening vs. quantification ^screen-vs-quantify

Two distinct goals drive method choice:

• Screening (factor fixing): cheaply rank factors and identify the non-influential ones that can be frozen. Best served by Morris (${\mu }^{\ast }$, $\sigma$) at $O(r(p+1))$ runs.
• Quantification: produce accurate, decomposed importance shares (first-order $S_i$, total-effect $S_{Ti}$, interactions). Served by Sobol/FAST, which cost more model evaluations. Typical practice: screen first with Morris, then quantify the survivors with Sobol. See Sampling and Estimation for Sobol Indices.

Main Content

What a GSA answers ^gsa-questions

• Factor prioritization: which inputs, if better determined, would most reduce output variance? → first-order $S_i$.
• Factor fixing: which inputs can be fixed anywhere in their range without affecting $Y$? → total-effect $S_{Ti}\approx 0$.
• Interaction detection: do factors act jointly rather than additively? → $S_{Ti}>S_i$, or Morris $\sigma$ large.

The paper’s empirical takeaway (MNIST case study, Sec. Results): the $S_T$ index of Sobol and the $\sigma$ and ${\mu }^{\ast }$ indices of Morris “present superior results” in identifying the critical regions/factors, while DGSM’s $v$ and FAST’s $S_T$ showed “substantial inconsistency.” Different global methods can yield “somewhat different rankings of feature importance” on the same model, so the authors stress careful, problem-specific method selection.

Cost scales with method and dimension ^cost-overview

Per the case-study sampling budgets (Table 1), relative cost ranking is roughly Morris (cheapest screening) < FAST < Sobol < Delta ≈ DGSM. For Sobol, the standard Saltelli estimator costs $N(p+2)$ model runs for first + total order indices (see Sampling and Estimation for Sobol Indices), so cost grows with both the base sample size $N$ and the number of factors $p$ — the central practical constraint for expensive ABMs.

Examples

A modeler has an epidemiological ABM with 12 parameters and a budget of a few thousand runs. Workflow:

1. Screen with Morris ($r\approx 20$ trajectories $\Rightarrow 20\times 13=260$ runs). Three parameters have large ${\mu }^{\ast }$; two more have small ${\mu }^{\ast }$ but large $\sigma$ (interaction/nonlinearity); the rest have ${\mu }^{\ast }\approx 0$ and are fixed.
2. Quantify the 5 survivors with Sobol via Saltelli sampling ($N=1024\Rightarrow 1024\times 7\approx 7000$ runs) to get $S_i$ and $S_{Ti}$.
3. Interpret: transmission rate has $S_i=0.55$ (drives most variance alone); contact-network parameter has $S_i=0.05$ but $S_{Ti}=0.30$ — its influence is almost entirely through interactions.

Connections

• Local vs Global Sensitivity Analysis — why OAT fails for interacting, high-dimensional ABM parameter spaces.
• Variance-Based Sensitivity and Sobol Indices — the ANOVA/HDMR decomposition and $S_i$, $S_{Ti}$.
• Morris Elementary Effects Screening — the cheap screening method (${\mu }^{\ast }$, $\sigma$).
• Sampling and Estimation for Sobol Indices — Saltelli scheme, FAST, costs, SALib.
• Population Initialization and Parameter Sensitivity — local OAT sensitivity already in the vault; GSA generalizes it.
• Uncertainty Quantification for ABM Calibration — GSA reduces parameter dimension before/alongside UQ.
• ABM Validation Challenges — sensitivity analysis as part of model credibility assessment.

See Also

• Approximate Bayesian Computation for ABMs — GSA-screened parameters reduce ABC dimensionality.
• History Matching for ABMs — sensitivity guides which inputs to refine when ruling out implausible space.
• Saltelli et al., Sensitivity Analysis in Practice (2004); Sobol (2001).