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Importance Sampling

With this change of variables we can express the integral of Eq. (20) as I=bap(y)F(y)p(y)dy=˜b˜aF(y(x))p(y(x))dx, meaning that a Monte Carlo evaluation of the above integral gives ˜b˜aF(y(x))p(y(x))dx=1NNi=1F(y(xi))p(y(xi)).