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Monte Carlo Analysis
Large Scale Variable Screening
and by varying the penalty parameter λ. Typically, only a small subset of the β j will be non-zero
for a fixed value of λ.
Tip
For an introduction to Subset Selection and Shrinkage methods, see Hastie, Tibshirani and
Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction,
2009, 2nd Edition, New York: Springer Verlag.
Using the Large Scale Variable Screening Method
The Large Scale Variable Screening method should be used when the number of variables is
much larger than the number of simulations that can be afforded. However, the method can only
perform well if the number of simulations is around five times greater than the number
significant variables. In most cases, only a few dozens of variables are important. Thus, one
hundred simulations should be sufficient. For computational efficiency, the Large Scale
Variable Screening method only uses the first 500 Monte Carlo simulations. The sensitivity
indices computed by the Large Scale Variable Screening method have the same meaning as
those of the “Global Sensitivity Analysis” on page 520.
The Large Scale Variable Screening method is applied to a simple circuit composed of 500
serial resistors whose nominal value is 10kΩ. Ten resistors have their standard deviation equal
to 1kΩ while the standard deviation of the others is set to 1Ω. A Monte Carlo analysis with 100
runs is performed. The results of the sensitivity analysis are shown below:
Estimation of Sensitivity Indices for Output Measure : V(1,0)
List of Important Parameters :
Index(I) Histo S(I) (percent / cumulative) Variable
Value
Name
494 |-------------------- 8.6% 8.6% PE(DEV_1000,R7,R)
498 |------------------- 8.3% 16.9% PE(DEV_1000,R3,R)
491 |------------------- 8.2% 25.2% PE(DEV_1000,R10,R)
495 |------------------- 8.2% 33.4% PE(DEV_1000,R6,R)
497 |------------------ 8.0% 41.4% PE(DEV_1000,R4,R)
492 |------------------ 8.0% 49.4% PE(DEV_1000,R9,R)
493 |------------------ 8.0% 57.4% PE(DEV_1000,R8,R)
499 |------------------ 7.8% 65.2% PE(DEV_1000,R2,R)
496 |------------------ 7.8% 73.0% PE(DEV_1000,R5,R)
500 |----------------- 7.6% 80.6% PE(DEV_1000,R1,R)
174 | 0.0% 80.6% PE(DEV_1,R327,R)
133 | 0.0% 80.6% PE(DEV_1,R368,R)
337 | 0.0% 80.6% PE(DEV_1,R164,R)
190 | 0.0% 80.6% PE(DEV_1,R311,R)
524
Eldo® User's Manual, 15.3