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First-order and total Sobol indices
Definition
Let on a finite product probability law and let denote for the components of Independent product inputs have an orthogonal Hoeffding decomposition. Write . Only when define the first-order Sobol index and total Sobol index of coordinate by For , these normalized indices are undefined. The unnormalized numerators remain well-defined and equal zero for a constant output.
Depends on
Used by
- Pick-freeze Monte Carlo estimators for Sobol indices Algorithm
- A constant output has no normalized Sobol indices Example
- A pick-freeze ratio can be biased at finite sample size Example
- Noisy simulator output separates intrinsic noise from input variance Example
- Polynomial-chaos coefficients group by variable support Example
- The Ishigami function's only possible interaction is X1-X3 Example
- Complete orthonormal tensor expansions group into Sobol components Theorem
- Coordinate Poincare inequalities bound total Sobol effects Theorem
- Pick-freeze covariances recover first and total Sobol numerators Theorem
Dependency tree · two levels
9 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Thierry Klein, Introduction to Sensitivity Analysis: The Statistical Study of Sobol Indices, complete lecture notes, Definition 2.1 (standard reference, not scraped)