The Monte Carlo Method of Evaluating Integrals

Abstract : This monograph is a tutorial presentation of the Monte Carlo method of numerically estimating definite integrals. Intended primarily for scientists and engineers, and assuming very little background in probability theory, the monograph attempts to convey a clear understanding of what the Monte Carlo method is, why it works, and how it can be used to evaluate complicated (and often otherwise intractable) multidimensional integrals. General methods are developed for generating sets of random points having prescribed biases; procedures are outlined for using such random points to obtain an estimate of the value of a given integral and the uncertainty associated with this estimate; and techniques are described for reducing the uncertainty without significantly increasing the computation time.