eldo_user

Monte Carlo Analysis
Importance Sampling Monte Carlo
The two forms of the MCPROB function can be combined to calculate yield, that is, the
probability π L, U that a given response is between bounds y L and y U (with y L ≤ y U ). To calculate
such a probability:
use the following commands:
.EXTRACT MC LABEL=PROB_L MCPROB(OUTPUT, LE, BOUND_L)
.EXTRACT MC LABEL=PROB_U MCPROB(OUTPUT, GE, BOUND_U)
.EXTRACT MC LABEL=PROB_LU '1-(PROB_L+PROB_U)'
where OUTPUT is the name of the output response H(X), and where BOUND_L and
BOUND_U are y L and y U respectively.
Quantile Computation using MCBOUND
The MCBOUND function computes the quantile y π associated with a given probability π.
Formally, the computed value is the solution to the following optimization problem. For 0 < π <
1, the quantity F Y −1 (π) = inf{y | F Y (y) ≥ π} is called the π-quantile of the random variable Y.
The MCBOUND function is inverse to the MCPROB(…, LE, …) function. To calculate a
quantile y π satisfying:
use the following command:
.EXTRACT MC LABEL=BOUND MCBOUND(OUTPUT, PROB)
where OUTPUT is the name of the output response H(X), and where PROB is π.
To determine a yield interval, defined as the interval (y L , y U ) such that the associated coverage
probability π L, U has a given value, use the following commands:
.EXTRACT MC LABEL=BOUND_L MCBOUND(OUTPUT, PROB_L)
.EXTRACT MC LABEL=BOUND_U MCBOUND(OUTPUT, PROB_U)
where OUTPUT is the name of the output response H(X), and where PROB_L and PROB_U
are probability values satisfying PROB_U - PROB_L = π L, U .
Eldo® User's Manual, 15.3 455