What are Monte Carlo methods?

The Monte Carlo method is a type of algorithm that reveals a distribution by randomly sampling its elements again and again. For example, say there are 40 red marbles, 20 green marbles, 25 orange marbles, and 15 blue marbles in a bag. The bag is opaque and has a narrow opening; you dip your hand inside and pick up five marbles at random, note down their colours, and put them back. The Monte Carlo method is based on the idea that by repeating this process over and over again, you will develop a better idea of the marbles’ colour distribution. The more times you randomly sample the marbles, the better your estimate.

Monte Carlo methods are frequently used to estimate the odds of an event occurring when doing so by other means is too difficult. If a sample is very complicated -- e.g. the billions of particles produced during an experiment at the Large Hadron Collider -- a Monte Carlo algorithm itself will require a lot of computing power. But its great advantage is that computers can sample and record multiple samples in parallel, keeping the power demand lower than other methods.

Such algorithms have applications in aerodynamics, power plant design, quantum mechanics, several areas of engineering, computer graphics, artificial intelligence models, and risk-estimating in finance. The method is named for a casino in Monaco, where Polish physicist Stanislaw Ulam was inspired by the way his uncle gambled to come up with the idea.