eldo_user

Monte Carlo Analysis
Model-Based Monte Carlo Simulation
When SSD_COMPLEXITY=0, a model is optimized to capture the shape of the output
measures, and is defined as an affine combination of univariate random variables, as
follows:
In the chosen non-linear extension with SSD_COMPLEXITY=1, we assume that the
surrogate function s(.) is represented as a linear combination of basis functions ϕ k (x),
k=0, …, K:
Notes
and the coefficients α 0 , α 1 , …, α K are estimated with a dedicated optimization algorithm.
• After running the Monte Carlo analysis with the SSD method, statistical plots are
available in EZwave. The SSD method tries to provide the same post-analysis features
as standard Monte Carlo. View the outputs in the .mcm file and the additional .mch, .mci,
and .mco files.
The following notes aim at expressing some important facts you have to understand before
using this model-based approach. Some rules that may help you are provided.
• The SSD approach suffers from an issue that is common to many model-based Monte
Carlo Analyses. It is difficult to quantify the error committed on the Statistics obtained
from the variability analysis. The fundamental problem is that we cannot relate the error
estimated during the model-based Monte Carlo analysis to the true uncertainty that
could be obtained by running the Monte Carlo based on SPICE simulations. A specific
methodology has been implemented and tested.
If we translate the popular adage “There's no such thing as a free lunch” to our
variability settings, we want to express the idea that despite the potential CPU speedup
we may obtain, it is impossible to get something for nothing. Using the statistical
concepts of bias and variance, model-based approaches potentially reduce variance of
estimators to zero, but the bias may be large and not controllable. The reason is that the
cost of model evaluation becomes almost negligible with respect to true simulation.
Hence, a very large number of model evaluation is allowed and implies almost zero
variance estimators.
Eldo® User's Manual, 15.3 461