ABSTRACT
This chapter introduces the concept of Monte Carlo integration and reviews some basic concepts in probability theory. The term “Monte Carlo” was coined in the 1940s, at the advent of electronic computing, to describe mathematical techniques that use statistical sampling to simulate phenomena or evaluate values of functions. In this chapter, we briefly review important concepts from probability theory. A Monte Carlo process is a sequence of random events. Often, a numerical outcome can be associated with each possible event. Monte Carlo integration techniques can be roughly subdivided into two categories: those that have no information about the function to be integrated (sometimes called blind Monte Carlo), and those that do have some kind of information (sometimes called informed Monte Carlo). Intuitively, one expects that informed Monte Carlo methods are able to produce more accurate results as compared to blind Monte Carlo methods.
