# Taylor decomposition importance factors¶

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

Let us denote by the input random vector. Assume that the marginals of are independent. Suppose that is a real function of the input, i.e. . Assume that the order 1 Taylor expansion of the function $h$ at the point is exact, i.e.

where:

is the mean of the input random vector,

is the partial derivative of the model with respect to the i-th input variable, evaluated at the point .

Therefore the expectation of is:

The independence of the marginals implies:

where:

is the variance of the output variable,

is the variance of the i-th input variable.

Let be the importance factor of the i-th input variable, defined by:

Therefore, the importance factors sum to one:

These are also called importance factors derived from perturbation methods.

API:

Examples: