eldo_user

Monte Carlo Analysis
Sensitivity Analysis
Sensitivity Analysis
There are two different methods that can post-process the Monte Carlo simulations for
computing the sensitivities. The first method, the Global Approach, is a variance-based method
that does not rely on model assumptions. The second method, Large Scale Variable Screening,
specifically builds a regression function which attempts to capture the main variations of the
response variables of interest.
As a rule of thumb, the global approach should be used when the context enables a large number
of Monte Carlo simulations, say a few thousand. This sensitivity analysis is independent of the
problem dimension (the number of circuit parameters with statistical variations). On the other
hand, when you can afford only a few tens of simulations and the number of variables is much
larger, the approach must be based on the assumption that the problem dimension (or the
effective dimension) is very small, say ten variables are really important. This assumption is
important for efficiency and the interpretability of the approach.
Global Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
Large Scale Variable Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
Global Sensitivity Analysis
Use global sensitivity analysis to identify the parameters in the circuit that, left free to vary over
their range of uncertainty, make no significant contribution to the variability of the output. The
identified factors can then be fixed at any given value without affecting the output variance.
A variance-based method is used with the capacity to capture the influence of the full range of
variation of each input factor. The method is based on the decomposition of the response:
into a set of functions of increasing dimensionality:
This expansion, also named ANOVA decomposition, is not unique. In Eldo, an approximation
is made of the first terms that form a sum of univariate functions in the representation:
The univariate terms are called the first-order ‘main effects’, and the bivariate terms f ij (X i ,X j )
the interactions of second-order.
In particular, it can be proved that under some assumptions:
520
Eldo® User's Manual, 15.3