A Brief History
1930ís: Enrico Fermi uses Monte Carlo in the calculation of neutron diffusion.
1940ís: Stan Ulam while playing solitaire tries to calculate the likelihood of winning based on the initial layout of the cards. After exhaustive combinatorial calculations, he decided to go for a more practical approach of trying out many different layouts and observing the number of successful games. He realised that computers could be used to solve such problems.
Stan Ulam worked with John Von Neumann to develop algorithms including importance sampling and rejection sampling.
|The Monte Carlo Casino, Monaco
Ulam and Von Neumann suggested that aspects of research into nuclear fission at Los Alamos could be aided by use of computer experiments based on chance. The project was top secret so Von Neumann chose the name Monte Carlo in reference to the Casino in Monaco.
Nick Metropolis designed new controls for a state of the art computer and fascinated by Monte Carlo methods he developed computing devices to handle such calculations. Collaboration with the likes of Fermi, Ulam and Von Neumann led to the publishing of a paper with Ulam in 1949 which formed the basis for modern sequential Monte Carlo methods such as bootstrap filters.
1950ís: Many papers on Monte Carlo simulation appeared in physics literature. The first major MCMC paper was published by Metropolis et al in 1953.
1970: Generalisation of the Metropolis algorithm by Hastings which led to development of MCMC
1980ís: Important MCMC papers appeared in the fields of computer vision and artificial intelligence but there were few significant publications in the field of statistics
1990: MCMC made the first significant impact in statistics in the work of Gelfand and Smith.
In the last 20 years MCMC has become a widely used tool in several fields and much research progress has been made. Thanks to the development of MCMC, Bayesian statistics is more widely used since MCMC provides a platform for solving multi-parameter Bayesian problems.
Monte Carlo Methods are now used to solve problems in numerous fields including applied statistics, engineering, finance and business, design and visuals, computing, telecommunications, and the physical sciences.