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Concept# VEGAS algorithm

Summary

The VEGAS algorithm, due to G. Peter Lepage, is a method for reducing error in Monte Carlo simulations by using a known or approximate probability distribution function to concentrate the search in those areas of the integrand that make the greatest contribution to the final integral.
The VEGAS algorithm is based on importance sampling. It samples points from the probability distribution described by the function |f|, so that the points are concentrated in the regions that make the largest contribution to the integral. The GNU Scientific Library (GSL) provides a VEGAS routine.
Sampling method
In general, if the Monte Carlo integral of f over a volume \Omega is sampled with points distributed according to a probability distribution described by the function g, we obtain an estimate \mathrm{E}_g(f; N),
:\mathrm{E}_g(f; N) = {1 \over N } \sum_i^N { f(x_i)} / g(x_i) .
The variance of the new estima

Official source

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