Editing VEGAS algorithm (section)

==Approximation of probability distribution==
The VEGAS algorithm approximates the exact distribution by making a number of passes over the integration region while [[histogram]]ming the function f. Each histogram is used to define a sampling distribution for the next pass. Asymptotically this procedure converges to the desired distribution. In order to avoid the number of histogram bins growing like <math>K^d</math> with dimension ''d'' the probability distribution is approximated by a separable function: <math>g(x_1, x_2, \ldots) = g_1(x_1) g_2(x_2) \cdots</math> so that the number of bins required is only ''Kd''. This is equivalent to locating the peaks of the function from the [[projection (mathematics)|projection]]s of the integrand onto the coordinate axes. The efficiency of VEGAS depends on the validity of this assumption. It is most efficient when the peaks of the integrand are well-localized. If an integrand can be rewritten in a form which is approximately separable this will increase the efficiency of integration with VEGAS.