Guest Editors' Introduction: Monte Carlo Methods

The term Monte Carlo method stands for any member of a very large class of computational methods that use randomness to generate "typical" instances of a problem under investigation. Typical instances are generated because it's impractical or even impossible to generate all instances. A set of typical instances is supposed to help us learn something about a problem of interest. Most of the time, Monte Carlo works amazingly well, but when used blindly, with no firm basis in theory, it can yield some very strange results or run for many, many hours and yield nothing. One of the triumphs of the modern period in Monte Carlo methods has been a dramatic improvement in our understanding of how to speed up the computation and how to know when the method will work.