Random Number Generation and Monte Carlo Methods

The role of Monte Carlo methods and simulation in all of the sciences has in- creased in importance during the past several years. These methods are at the heart of the rapidly developing subdisciplines of computational physics, compu- tational chemistry, and the other computational sciences. The growing power of computers and the evolving simulation methodology have led to the recog- nition of computation as a third approach for advancing the natural sciences, together with theory and traditional experimentation. Monte Carlo is also a fundamental tool of computational statistics. At the kernel of a Monte Carlo or simulation method is random number generation. Generation of random numbers is also at the heart of many standard statis- tical methods. The random sampling required in most analyses is usually done by the computer. The computations required in Bayesian analysis have become viable because of Monte Carlo methods. This has led to much wider applications of Bayesian statistics, which, in turn, has led to development of new Monte Carlo methods and to refinement of existing procedures for random number generation.