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Monte Carlo Analysis
Global Sensitivity Analysis
where
is the conditional expectation.
This conditional expectation is approximated. In this way, if the scatter plot (X i , Y) has a pattern,
the conditional expectation has a large variation across X i values, and parameter X i is
revealed to be important. In fact, the variance of the terms in the decomposition above is the
measure of importance being sought. We then compute
and when this is divided
by the unconditional variance Var(Y), the first-order sensitivity index is obtained:
Tip
For further reading on Global Sensitivity methods, see: Saltelli, A. et. al., Global Sensitivity
Analysis. The Primer, John Wiley & Sons, 2008.
Different sensitivity computation modes are available in Eldo, specified by the SENS parameter
of the .MC command.
Interpreting a Global Sensitivity Analysis
Global sensitivity analysis results are written to the .chi and .mcm files.
Some properties used in the interpretation of sensitivity indices are:
• The index S i is a number always between 0 and 1. A large value indicates an important
parameter X i .
• The sum of the sensitivity indices is less than 1 (in theory). In other words, the sum of
the conditional variances
cannot be greater than the total variance.
• The sum of all S i is equal to 1 for additive output Y, such that:
and less than 1 for non-additive models. The difference:
Eldo® User's Manual, 15.3 521