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Monte Carlo Analysis
Large Scale Variable Screening
Except for the relative inaccuracy at the border, the non-parametric model, which fits the
conditional expectation, is a good approximation of the first-order terms.
The numerical procedure for computing the sensitivity indices gives S 1 = 0.2096 and
S 2 = 0.3990 with sample size N = 1024. The non-zero difference 1 − S 1 − S 2 < 1 is a clear
indication that the interaction term f 12 (X 1 , X 2 ) cannot be neglected in the output.
Related Topics
Post-Analysis of Monte Carlo Simulations
Sensitivity Analysis
Monte Carlo Analysis Examples
Large Scale Variable Screening
As already mentioned, this second approach to sensitivity analysis is a model-based method. It
means that a (meta-) model is specified for the regression function f(x) = E[Y|X=x], with the
assumption that this function f(x) is approximately linear in its arguments:
At this step, it is clear that each individual component of the vector β gives a certain amount of
information about the relative importance of the parameters (the main effects).
Classically, the parameters β are found by Ordinary Least Squares regression based on the set of
training data (x i ,y i ) from the Monte Carlo simulation. This estimation method finds the β by
minimizing the residual sum of squares:
In the context of large scale screening the dimension of the vector of variables x is much larger
than the number of simulations, and it is assumed that there is only a small set of important
variables. This means we are willing to determine a small subset of variables that give the main
effects and neglect the small effects. We perform this task by using the well known method
LASSO which is stable and exhibits good properties for subset selection. The LASSO method
find a continuous path of solutions by minimizing the residual sum of squares and a L 1
penalization of the vector β:
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