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Monte Carlo Analysis
Importance Sampling Monte Carlo Examples
follows a binomial law with parameters (n, π y ). Since S n is the sum of independent Bernouilli
random variables with parameter π y (such that
), the central limit theorem
gives:
where
At a confidence level α, the precision ε can be related to the sample size via 2Φ(-t) ≤ α. The
number of Monte Carlo simulations is:
In terms of the relative precision (the IS_RTOL parameter in the .MC statement) τ > 0, the
number of Monte Carlo simulations is:
because ε = τπ y .
The reported speedup can be calculated by replacing τ by the effective relative precision
obtained for the estimator. This value is given in the CV(%) column of the results. The ratio
n MC / n ISMC then gives the speedup, where n ISMC is the effective number of runs.
Table 11-1 displays the results of an experiment that can be carried out using this example. The
value of IS_MAXITER is 50 to limit the total number of Monte Carlo runs. The ISMC method
only failed to reach the desired precision within 50 iterations in the last experiment (1% RTOL).
Eldo® User's Manual, 15.3 529