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• LATIN HYPERCUBE SAMPLING SIMULATION CODE

This knowledge is also required in comparing the accuracy of other probability estimation techniques to Monte Carlo results.

In order to devise an algorithm for autonomously terminating Monte Carlo sampling when sufficiently small and reliable confidence intervals (CI) are achieved on calculated probabilities, the behavior of CI estimators must be characterized. Conditions on h, general enough to include this setting, are given under which LHS produces more efficient estimates than = , Function h is not monotonic in a common case it is not monotonic if success occurs when X is near the true value, and failure occurs when X departs sufficiently from this value in any direction.

For example, suppose X is a vector of a mission's sensor measurements, and Y = h(X) is one when the mission is successful and zero otherwise. This monotonicity restriction on h excludes some interesting response functions. The referenced paper proves that, when h is monotonic in each of its arguments, some common summary statistics on Y are more efficient under LHS than under SRS.

LATIN HYPERCUBE SAMPLING SIMULATION CODE

For each realization of random input vector X, suppose that a computer code produces a scalar output Y = h(X). The Latin Hypercube Sampling, LHS, plan was presented by McKay, Beckman and Conover (Technometrics, 21, 239 - 245(May 1979)) as an alternative to simple random sampling, SRS, in Monte Carlo studies.