10 - Monte Carlo

Summary

The name ‘Monte Carlo’ dates from about 1944 and the Los Alamos project in the US that produced the atomic bomb. The work involved simulating the random diffusion of neutrons. Von Neumann, Ulam and others worked on the bomb project and later disseminated the idea of Monte Carlo methods to solve both deterministic and stochastic problems.

Ulam (1976) related how the idea for Monte Carlo arose while he was in hospital after a bout of meningitis. While playing solitaire, it occurred to him that one could get an idea of the probability of an event such as a successful outcome in a game of cards, simply by recording the proportion of successful attempts. At the time, people were trying to estimate probabilities by following all chains of possibilities, a difficult task for all but the simplest cases.

This idea formed the foundation of what came to be known as Monte Carlo analysis (alluding to uncertainty in gambling). The methods originally focused on analytical solutions, but computers gave rapid solutions to complex problems by simulation.

Some of the earliest applications of Monte Carlo were to environmental problems. Hammersley and Handscomb (1964) noted a report in The Times of London from 1957 in which Monte Carlo methods were used to design controls of floodwater and the construction of dams on the Nile. The problem was inherently probabilistic because rainfall is unpredictable. The data consisted of weather, rainfall and water levels over 48 years.