Uncertainty ranking: SRC¶
This method deals with analyzing the influence the random vector
has on a random
variable
which is being studied for uncertainty. Here we
attempt to measure linear relationships that exist between
and the different components
.
The principle of the multiple linear regression model consists in
attempting to find the function that links the
variable to the
variables
by means of a linear model:
where describes a random variable with zero mean
and standard deviation
independent of the
input variables
. If the random variables
are independent and with finite variance
, the variance of
can be
estimated as follows:
The estimators for the regression coefficients
, and the standard deviation
are obtained from a sample of
. Uncertainty ranking by linear
regression ranks the
variables
in terms of the estimated contribution of each
to the
variance of
:
which is estimated by:
where describes the empirical standard
deviation of the sample of the input variables. This estimated
contribution is by definition between 0 and 1. The closer it is to 1,
the greater the impact the variable
has on the dispersion of
.
The contribution to the variance is sometimes described in
the literature as the “importance factor”, because of the similarity
between this approach to linear regression and the method of cumulative
variance quadratic which uses the term importance factor.
API:
Examples:
References:
Saltelli, A., Chan, K., Scott, M. (2000). “Sensitivity Analysis”, John Wiley & Sons publishers, Probability and Statistics series
J.C. Helton, F.J. Davis (2003). “Latin Hypercube sampling and the propagation of uncertainty analyses of complex systems”. Reliability Engineering and System Safety 81, p.23-69
J.P.C. Kleijnen, J.C. Helton (1999). “Statistical analyses of scatterplots to identify factors in large-scale simulations, part 1 : review and comparison of techniques”. Reliability Engineering and System Safety 65, p.147-185