What is the Monte Carlo Method?—A Simulation with Random Numbers

Abstract

The Monte Carlo method is a general term for computational methods that utilize random numbers (see e.g., [1]). Usually, it specifically means a class of algorithms that are guaranteed to give the right answer if we continue the simulation long time. Let us first see a few simple examples of Monte Carlo algorithms that are different from the “Markov Chain” Monte Carlo [2, 3]. (More nontrivial applications of “naive” Monte Carlo algorithms than those mentioned in this chapter can be found, e.g., in Ref. [4].) These algorithms are very easy, but there are significant limitations. By knowing the limitations of such “naive” Monte Carlo algorithms, we can understand the advantage of the Markov Chain Monte Carlo algorithms.