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Monte Carlo Analysis
Quasi-Monte Carlo Method
Quasi-Monte Carlo Method
Quasi-Monte Carlo is an empirical sampling method based on Monte Carlo, but using low
discrepancy point sets (such as the Faure, Sobol, or Niederreiter sequences) instead of
pseudorandom numbers.
This improved (and deterministic) sampling scheme roughly ‘fill the space’ in a better way as
shown in Figure 11-11. The left plot shows an example of LDS in (0,1) 2 compared to a
pseudorandom sequence calculated with a classical generator.
Figure 11-11. Comparison Between Low Discrepancy and Pseudorandom
Point Sets
The Monte Carlo integration error depends on the discrepancy of the sequence used:
where V Τ is the total variation function. The discrepancy is defined as the deviation to the
perfect uniformity as follows:
where λ(I) is the Lebesgue’s measure of the interval and n I the number of points in the interval.
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Eldo® User's Manual, 15.3