Index: Sensitivity Analysis

Sensitivity Analysis

Routing Summary

This folder covers global sensitivity analysis (GSA) for ABM parameter spaces — variance-based Sobol indices, Morris screening, and Saltelli/FAST estimation. Source: Sadeghi & Matwin (2024). Contains 5 notes.

• Need the big picture, the four GSA families, and screen-vs-quantify guidance? → Global Sensitivity Analysis - Overview
• Need the ANOVA variance decomposition and first-order / total-effect index formulas? → Variance-Based Sensitivity and Sobol Indices
• Need cheap factor screening with ${\mu }^{\ast }$ and $\sigma$? → Morris Elementary Effects Screening
• Need the Saltelli sampling scheme, run-count cost, FAST, or SALib? → Sampling and Estimation for Sobol Indices
• Need to know why OAT/local SA is misleading for high-dim interacting ABMs? → Local vs Global Sensitivity Analysis

Concept Map

Concept	Note	Type	Depends On	Key Result
GSA overview & method families	Global Sensitivity Analysis - Overview	overview	Local vs Global Sensitivity Analysis	Sample-then-analyze; variance/derivative/distribution families; screen then quantify
Sobol indices & ANOVA decomposition	Variance-Based Sensitivity and Sobol Indices	definition	Global Sensitivity Analysis - Overview	$S_i=V_i/V(Y)$, $S_{Ti}={\sum }_{k\in \#i}{S}_k$; $S_{Ti}-S_i$ = interactions
Morris elementary-effects screening	Morris Elementary Effects Screening	definition	Global Sensitivity Analysis - Overview	${\mu }^{\ast },\sigma$ at $O(r(p+1))$ runs; ${\mu }^{\ast }$ ranks like $S_{Ti}$
Saltelli/FAST estimation & cost	Sampling and Estimation for Sobol Indices	concept	Variance-Based Sensitivity and Sobol Indices	Saltelli $N(p+2)$ runs; FAST spectral; SALib
Local vs global SA	Local vs Global Sensitivity Analysis	concept	Global Sensitivity Analysis - Overview	OAT misses interactions & high-dim coverage; global captures both

Notes

• Global Sensitivity Analysis - Overview — CONTAINS: two-phase sample/analyze paradigm, four GSA families (variance/derivative/distribution/feature-additive), screening vs quantification, factor prioritization/fixing/interaction questions, cost overview, MNIST case-study findings
• Variance-Based Sensitivity and Sobol Indices — CONTAINS: ANOVA/Sobol-Hoeffding variance decomposition $V(Y)=\sum V_i+\sum V_{ij}+\dots$, $V_i=V(E(Y|X_i))$, first-order $S_i$, second-order $S_{ij}$, total-effect $S_{Ti}$, additivity identity $\sum S_i\le 1$, interaction detection
• Morris Elementary Effects Screening — CONTAINS: elementary effect $E{E}_i$, mean ${\mu }_i$, std ${\sigma }_i$, Campolongo ${\mu }_i^{\ast }$ (absolute), $({\mu }^{\ast },\sigma )$ plane interpretation, DGSM generalization, screening cost
• Sampling and Estimation for Sobol Indices — CONTAINS: Saltelli A/B/$A_B^{(i)}$ design and $N(p+2)$ cost, FAST Fourier/Parseval spectral estimation, RBD/FAST_RBD, Table 1 sample budgets, SALib usage
• Local vs Global Sensitivity Analysis — CONTAINS: OAT definition, assumptions of linearity/independence, OAT pitfalls (no interactions, baseline dependence, vanishing high-dim coverage, non-monotonicity), pure-interaction $Y=ab$ counterexample

Sources

• Review of Global Sensitivity Analysis Methods 2024.pdf — Sadeghi & Matwin (2024), “A Review of Global Sensitivity Analysis Methods and a Comparative Case Study on Digit Classification”