A Gentle Introduction to Monte Carlo Sampling for Probability

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Monte Carlo methods are a class of techniques for randomly sampling a probability distribution. There are many problem domains where describing or estimating the probability distribution is relatively straightforward, but calculating a desired quantity is intractable. This may be due to many reasons, such as the stochastic nature of the domain or an exponential number of random variables. Instead, a desired quantity can be approximated by using random sampling, referred to as Monte Carlo methods. These methods were initially used around the time that the first computers were created and remain pervasive through all fields of science and engineering, including artificial intelligence and machine learning.