Elementary effects method: Difference between revisions

Revision as of 19:12, 17 November 2020

Latest revision as of 12:20, 20 January 2024

(6 intermediate revisions by 5 users not shown)

Line 1:

{{Short description|Screening method}}

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

Published in 1991 by Max Morris<ref>https://www.stat.iastate.edu/people/max-morris Home Page of Max D. Morris at [[Iowa State University]]</ref> the '''elementary effects (EE) method'''<ref name="Morris"/> is one of the most used<ref>Borgonovo, Emanuele, and Elmar Plischke. 2016. “Sensitivity Analysis: A Review of Recent Advances.” European Journal of Operational Research 248 (3): 869–87. https://doi.org/10.1016/J.EJOR.2015.06.032. </ref><ref>Iooss, Bertrand, and Paul Lemaître. 2015. “A Review on Global Sensitivity Analysis Methods.” In Uncertainty Management in Simulation-Optimization of Complex Systems, edited by G. Dellino and C. Meloni, 101–22. Boston, MA: Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7547-8_5. </ref><ref>Norton, J.P. 2015. “An Introduction to Sensitivity Assessment of Simulation Models.” Environmental Modelling & Software 69 (C): 166–74. https://doi.org/10.1016/j.envsoft.2015.03.020. </ref><ref>Wei, Pengfei, Zhenzhou Lu, and Jingwen Song. 2015. “Variable Importance Analysis: A Comprehensive Review.” Reliability Engineering & System Safety 142: 399–432. https://doi.org/10.1016/j.ress.2015.05.018.</ref> screening methods in [[sensitivity analysis]].

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.

Line 11:

: <math> Y = f(X_1, X_2, ... X_k).</math>

The original EE method of Morris <ref name="Morris">Morris, M. D. (1991). Factorial sampling plans for preliminary computational experiments. ''Technometrics'', '''33''', 161–174.</ref> provides two sensitivity measures for each input factor:

* the measure <math> \mu </math>, assessing the overall importance of an input factor on the model output;

Line 27:

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.

Line 50:

{{reflist}}

[[Category:ScientificMathematical modeling]]

[[Category:Sensitivity analysis]]