# Taylor importance factorsΒΆ

The importance factors derived from a Taylor expansion are defined to rank the sensitivity of the output to the inputs for central dispersion analysis.

We consider the Taylor expansion of a function. We use the notations introduced in Taylor Expansion. Let be the input random vector. We assume that the marginals of are independent. Let with be a function with a scalar output.

Refer to Taylor Expansion for details on the expressions of the first-order and second-order Taylor expansions and to Taylor Expansion Moments for details on the approximations of the mean and the variance of .

The importance factor of is defined by:

If the model is linear (i.e. if the model is equal to its first-order Taylor expansion), then the importance factors sum to one:

These importance factors are also called *importance factors derived from perturbation methods*.