The three main steps of the Monte Carlo method:
Describe or construct a probabilistic process:
This probability process can be described and simulated for existing problems with random properties. For deterministic problems without random properties, a probability process needs to be constructed artificially.
Sampling using probability distributions
: Random variables with known probability distributions are generated by computer. Commonly used probability distributions include uniform distribution, normal distribution, exponential distribution, Poisson distribution, etc.
Establish various estimates
: After constructing a random probability model and sampling from it, a random variable must be determined as the solution to the required problem. Generally, the arithmetic mean of sub-random sampling results is used as the approximate value of the solution.
Among them, generating random variables with known probability distributions is the key step of the Monte Carlo method. When the probability model of random variables is not known to obey that distribution, uniform distribution can be used to construct; various measurement errors, shooting hit rates, and human Height and weight obey normal distribution; exponential distribution can be used in queuing theory and reliability analysis; Poisson distribution can be used in product inspection, queuing system, physics and other fields.