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Monte Carlo Analysis
Introduction to Uncertainty Analysis
This is, in some sense, the best estimate possible of the expectation. The sample variance, which
estimates the variance of the probability distribution of Y, is given by:
This estimate of the variance and its square root (called the experimental standard deviation)
characterizes the variability of the observed values Y i , or their dispersion about their mean.
Figure 11-1. Central Tendency and Dispersion
A Monte Carlo experiment (with 1,000 runs, for example) provides one single realization of the
random variables (sample mean, variance, and so on). However, this realization is not useful if
the result does not come with a reliable confidence interval. Figure 11-1 shows an interval
that encloses the mean . This interval characterizes the precision obtained by
the Monte Carlo estimator of the mean.
In practice, the coefficient of variation and the relative standard error of mean
are often used to quantify the relative variability (or obtained precision) of one
given estimator . The Eldo Monte Carlo flow uses the following definition of the RSEM if the
mean is non-zero:
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Eldo® User's Manual, 15.3