What is the Monte Carlo Method?

The Monte Carlo simulation is named after Monaco's famous casino. It can help people mathematically represent some very complex interactions in physics, chemistry, engineering, economics, and environmental dynamics.

When scientists use computers to try to predict complex trends and events, they often apply a

When the problem to be solved arises from some kind of event

Construct or describe probability processes

For problems that are inherently random, such as particle transport problems, this is mainly to correctly describe and simulate this.

Monte Carlo simulation usually solves various mathematical problems by constructing random numbers that conform to certain rules. Monte Carlo simulation is an effective method to obtain numerical solutions for those problems where it is difficult to obtain an analytical solution or the analytical solution is not complicated at all due to the calculation is too complicated. The most common application of general Monte Carlo simulation in mathematics is Monte Carlo integration.

The Monte Carlo algorithm indicates that the more samples, the closer the optimal solution is. For example, if there are 100 apples in the basket, let me close my eyes and take one apple at a time to pick the largest one. So I randomly picked one, then randomly compared one with it, leaving a big one, and then randomly picked one ... Every time I took it, the apples left were at least not smaller than the last time. The more times I pick it, the bigger the apples I pick, but I ca nt be sure to pick the biggest one unless I pick it 100 times. This apple picking algorithm belongs to the Monte Carlo algorithm. Tell us the sample size is large enough to be closest to the probability of the required solution.

Monte Carlo simulations are also widely used in financial engineering, macroeconomics, biomedicine, and computational physics (such as particle transport calculations, quantum thermodynamic calculations, and aerodynamic calculations).

With the development of computer technology, Monte Carlo simulation has gained rapid popularity in the last 10 years. Modern Monte Carlo simulations no longer need to do experiments by themselves, but rely on the computer's high-speed operation capabilities, making the time-consuming and laborious experimental process a quick and easy task. It is not only used to solve many complex scientific problems, but also often used by project managers.

With computer technology, Monte Carlo simulations achieve two major advantages:

First, it is simple and saves the complicated process of mathematical journal guidance and calculus, so that ordinary people can understand and master it;

The second is fast. Simplicity and speed are the technical basis for the application of Monte Carlo methods in modern project management. ^[2]