In the late 1940s, Stanislaw Ulam invented the modern version of the Markov Chain
Monte Carlo method while he was working on nuclear weapons projects at the Los Alamos National Laboratory. In 1946, nuclear weapons physicists at Los Alamos were investigating neutron diffusion in the core of a nuclear weapon.
Despite having most of the necessary data, such as the average distance a neutron would travel in a substance before it collided with an atomic nucleus and how much energy the neutron was likely to give off following a collision, the Los Alamos physicists
were unable to solve the problem using conventional, deterministic mathematical methods. Ulam proposed
using random experiments. He recounts his inspiration as follows:
The first thoughts and attempts I made to practice [the Monte Carlo Method] were suggested by a question which occurred to me in 1946 as I was convalescing from an illness and playing solitaires. The question was what are the chances that a Canfield solitaire laid out with 52 cards will come out successfully? After spending a lot of time trying to estimate them by pure combinatorial calculations, I wondered whether a more practical method than "abstract thinking" might not be to lay it out say one hundred times and simply observe and count the number of successful plays. This was already possible to envisage with the beginning of the new era of fast computers, and I immediately thought of problems of neutron diffusion and other questions of mathematical physics, and more generally how to change processes described by certain differential equations into an equivalent form interpretable as a succession of random operations. Later [in 1946], I described the idea to John von Neumann, and we began to plan actual calculations.
...Monte Carlo methods were central to the
simulations required for the Manhattan Project, though severely limited by the computational tools at the time. Von Neumann, Nicholas Metropolis and others programmed the ENIAC computer to perform the first fully automated Monte Carlo calculations, of a fission weapon core, in the spring of 1948.[20] In the 1950s Monte Carlo methods were used at Los Alamos for the
development of the hydrogen bomb, and became popularized in the fields of physics, physical chemistry, and operations research. The Rand Corporation and the U.S. Air Force were two of the major organizations responsible for funding and disseminating information on Monte Carlo methods during this time, and they
began to find a wide application in many different fields.
...
- Monte Carlo simulation: Drawing a large number of pseudo-random uniform variables from the interval [0,1] at one time, or once at many different times, and assigning values less than or equal to 0.50 as heads and greater than 0.50 as tails, is a Monte Carlo simulation of the behavior of repeatedly tossing a coin.
Monte Carlo and random numbers
The main idea behind this method is that the results are computed based on repeated random sampling and statistical analysis. The Monte Carlo simulation is, in fact,
random experimentations, in the case that, the results of these experiments are not well known.
Monte Carlo simulations are typically characterized by many unknown parameters, many of which are difficult to obtain experimentally.
Monte Carlo simulation methods do not always require truly random numbers to be useful (although, for some applications such as primality testing, unpredictability is vital).
Many of the most useful techniques use deterministic, pseudorandom sequences, making it easy to test and re-run simulations.
The only quality usually necessary to make good simulations is for the pseudo-random sequence to appear "random enough" in a certain sense.
...
