In order to integrate a function over a complicated Domain , Monte Carlo integration picks random points over some simple Domain which is a superset of , checks whether each point is within , and estimates the Area of (Volume, -D Content, etc.) as the Area of multiplied by the fraction of points falling within .
An estimate of the uncertainty produced by this technique is given by
See also Monte Carlo Method
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Simple Monte Carlo Integration'' and
``Adaptive and Recursive Monte Carlo Methods.'' §7.6 and 7.8 in
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge
University Press, pp. 295-299 and 306-319, 1992.