Monte Carlo theory and practice

The Monte Carlo method has long been recognised as a powerful technique for performing certain calculations, generally those too complicated for a more classical approach. Since the use of high-speed computers became widespread in the 1950s, a great deal of theoretical investigation has been undertaken and practical experience has been gained in the Monte Carlo approach. The aim of this review is, first, to lay a theoretical basis for both the 'traditional' Monte Carlo and quasi-Monte Carlo methods, and, secondly, to present some practical aspects of when and how to use them. An important theme of this review will be the comparison of Monte Carlo, quasi-Monte Carlo and numerical quadrature for the integration of functions, especially in many dimensions.