What is the Monte Carlo method?

Under the Monte Carlo method, one of the ways of statistical modeling is commonly understood, which, in turn, was based on the concept of a "black box".

The Monte Carlo method is used in those cases when the use of the analytical model of the phenomenon is difficult or quite impossible (for example, in solving problems in queuing theory, investigating operations reduced to the study of random processes, etc.).

Let us consider in more detail the Monte Carlo method in economics.

The application of this method of statistical modeling can be illustrated by an example from the theory of queues. So, let's assume that it is required to find out how long and how often it is necessary to wait for customers in the queue at a certain (initially set) bandwidth of some store. These calculations, in the first place, are necessary to decide whether to expand the store. As is known, the buyers' approach, as a rule, is random or uncertain, therefore, the distribution of the so-called approach time, that is, the gap between each two successive arrivals of buyers, can be independently established based on available information. On the other hand, the service time of each customer also has a random character, therefore, its distribution can also be detected. So, before us are two stochastic processes, the direct interaction of which creates a queue.

As practice shows, using the Monte-Carlo method in real life, you can randomly go through all the possibilities many times while keeping the same distribution characteristics. As a result, it will be possible to artificially recreate the whole picture of this process. Then, repeating this picture again, each time changing the conditions, you can get statistics, as if they were collected in real time.

In the same way, you can recreate several times the artificial picture of the work of almost any store, using the Monte Carlo method in practice. Simulation modeling in this case will repeat real data. The two stochastic processes described above are again obtained. Their alternate interaction in the end result will again issue a "queue" with practically the same indicators as in real life.

Consequently, the Monte Carlo method in science consists in artificial modeling through multiple repetitions in random implementations. It is important to note that so-called single implementations are otherwise referred to as statistical tests.

To understand what the random selection mechanism implies, simply use the most common dice. However, in practice, as a rule, tables of random numbers are used. In addition, at the moment, special programs are used for computers, which are called generators of random numbers among specialists. In fact, the Monte Carlo method is simple enough, effective and convenient, which causes its widespread use, both in economics and in other exact sciences.