Elementary effects method: Difference between revisions

Revision as of 19:12, 17 November 2020

Revision as of 18:50, 27 December 2020

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{{Multiple issues|{{Primary sources|date=January 2010}}}}

The '''elementary effects (EE) method''' is the most used{{Citation needed|date=January 2010}} screening method in [[sensitivity analysis]].

EE is applied to identify non-influential inputs for a computationally costly [[mathematical model]] or for a model with a large number of inputs, where the costs of estimating other sensitivity analysis measures such as the [[variance]]-based measures is not affordable. Like all screening, the EE method provides qualitative sensitivity analysis measures, i.e. measures which allow the identification of non-influential inputs or which allow to rank the input factors in order of importance, but do not quantify exactly the relative importance of the inputs.

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where <math> \mathbf{X} = (X_1, X_2, ... X_k)</math> is any selected value in <math> \Omega </math> such that the transformed point is still in <math> \Omega </math> for each index <math> i=1,\ldots, k. </math>

<math> r </math> elementary effects are estimated for each input <math> d_i\left(X^{(1)} \right), d_i\left( X^{(2)} \right), \ldots, d_i\left( X^{(r)} \right) </math> by [[Random sampling|randomly sampling]] <math> r </math> points <math> X^{(1)}, X^{(2)}, \ldots , X^{(r)}</math>.

Usually <math> r </math> ~ 4-10, depending on the number of input factors, on the [[computational cost]] of the model and on the choice of the number of levels <math> p </math>, since a high number of levels to be explored needs to be balanced by a high number of trajectories, in order to obtain an exploratory sample. It is demonstrated that a convenient choice for the [[Parameter|parametersparameter]]s <math> p </math> and <math> \Delta </math> is <math> p </math> even and <math> \Delta </math> equal to <math>

p/[2(p-1)]</math>, as this ensures equal probability of sampling in the input space.