Monte carlo process

The goal is to estimate the possible outcomes of an uncertain event, i.e. sampling from random variable’s distribution in order to compute some quantity.

When we sample from a uniform distribution for the integers {1,2,3,4,5,6} to simulate the roll of a dice, we are performing a Monte Carlo simulation. We are also using the Monte Carlo method when we gather a random sample of data from the domain and estimate the probability distribution of the data using a histogram or density estimation method.

The more samples we take, the more accurate the approximation of the target distribution will be (law of large numbers) => can be computationally expensive to get an accurate result.