Global Sensitivity Analysis — Sobol, Morris, and FAST
Global Sensitivity Analysis (Sobol, Morris, FAST) · Also known as: variance decomposition, Sobol indices, Morris screening, FAST method, Global Duyarlılık Analizi (Sobol, Morris, FAST)
Global sensitivity analysis (GSA) is a family of techniques that decompose the variance of a model's output across its input parameters, quantifying how much each input — and each combination of inputs — contributes to the total uncertainty in the result. Sobol's variance-based indices (2001), Morris's one-at-a-time (OAT) screening (1991), and the Fourier Amplitude Sensitivity Test (FAST, first proposed by Cukier et al. in 1973) are the three most widely used approaches. Together they serve as the standard toolkit for identifying which parameters drive model behaviour and which can be safely fixed.
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When to use it
Global sensitivity analysis is appropriate whenever you need to understand which inputs drive the uncertainty in a computational model, or when you want to simplify a model by identifying non-influential parameters that can be fixed. It applies to any deterministic or stochastic model where inputs can be described by distributions or plausible ranges. Sobol indices are the most informative choice when the number of model runs is affordable (typically hundreds to thousands per parameter). Morris screening is preferred for initial exploration when the model is expensive and there are many candidate parameters to rank quickly. FAST is a good middle ground when Sobol's sample cost is prohibitive but full variance decomposition is desired. The method does not require normally distributed inputs; continuous input types are expected. It is not suitable when inputs cannot be assigned probability distributions or plausible ranges, or when the model is purely data-driven without a forward simulation structure.
Strengths & limitations
- Explores the entire input space simultaneously rather than making local linearisation assumptions, capturing nonlinear behaviour and parameter interactions.
- Sobol total-effect indices (ST) directly identify non-influential parameters that can be fixed, enabling principled model simplification.
- The Morris method is extremely cheap relative to full variance decomposition, making it practical for high-dimensional or computationally expensive models.
- FAST achieves full variance decomposition with fewer runs than Saltelli-Sobol sampling, offering an efficient compromise.
- Results are interpretable: sensitivity indices are normalised fractions of total variance, enabling straightforward ranking and communication.
- Sobol indices require N×(2k+2) model runs, which can be prohibitive for expensive simulators with many parameters.
- Morris screening reveals the ranking of parameter importance but does not decompose variance into quantified fractions; it cannot replace Sobol indices when precise apportionment is needed.
- All methods assume that input uncertainty can be characterised by probability distributions or bounded ranges; if this prior knowledge is unavailable or unreliable, the resulting indices reflect assumed rather than true uncertainty.
- For models with discrete or categorical inputs, the standard variance-based framework does not apply directly and extensions or alternative approaches are required.
Frequently asked
Should I use Sobol, Morris, or FAST?
The choice depends on your budget of model runs and your goal. Start with Morris if the model is expensive and you have many parameters to screen — it ranks them cheaply. If you can afford N×(2k+2) runs (where k is the number of parameters), Sobol indices give the most complete picture by quantifying first-order and interaction effects as fractions of total variance. FAST is a good option when you want full variance decomposition but Sobol's sample size is too large; it achieves similar information with fewer runs.
What do first-order (S1) and total-effect (ST) indices actually mean?
S1 for a parameter is the fraction of the total output variance explained by that parameter alone, ignoring interactions. ST is the fraction explained by that parameter and all its interactions with other parameters. If S1 ≈ ST for all parameters, interactions are negligible. A large gap between S1 and ST signals important interaction effects. Parameters with ST near zero can be fixed without meaningfully changing the output uncertainty.
How many model runs do I need?
The standard Saltelli scheme for Sobol indices requires N×(2k+2) runs, where N is a base sample size (often 512–2048) and k is the number of input parameters. For example, with k=10 parameters and N=1024, that is 22 528 runs. Morris typically needs r×(k+1) runs, where r is the number of trajectories (often 10–50), giving a much smaller total. FAST requirements vary by implementation but are generally between those of Morris and Sobol.
Can I use global sensitivity analysis on a model that is not a simulation?
GSA applies to any model that maps a set of inputs to outputs and can be evaluated repeatedly at different input values. This includes statistical models, machine-learning models, and analytical equations, not only physics-based simulations. The requirement is that inputs can be assigned plausible distributions or ranges and the model can be run enough times to populate the sample matrix.
Sources
- Sobol, I.M. (2001). Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates. Mathematics and Computers in Simulation, 55(1–3), 271–280. DOI: 10.1016/S0378-4754(00)00270-6 ↗
- Saltelli, A. et al. (2008). Global Sensitivity Analysis: The Primer. Wiley. DOI: 10.1002/9780470725184 ↗
How to cite this page
ScholarGate. (2026, June 1). Global Sensitivity Analysis (Sobol, Morris, FAST). ScholarGate. https://scholargate.app/en/simulation/global-sensitivity-analysis
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Design of experimentsExperimental design↔ compare
- Latin Hypercube SamplingSimulation↔ compare
- MONTE-CARLO-SIMULATIONDecision-making↔ compare
- Uncertainty QuantificationSimulation↔ compare