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When should the Monte-Carlo method be used?
For example, why did Joel decide to use the Monte-Carlo method for Evidence Based Scheduling instead of methodically processing all user data for the past year?
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A Monte Carlo simulation considers a wide range of possibilities and helps us reduce uncertainty. A Monte Carlo simulation is very flexible; it allows us to vary risk assumptions under all parameters and thus model a range of possible outcomes.
In the 1950s Monte Carlo methods were used at Los Alamos for the development of the hydrogen bomb, and became popularized in the fields of physics, physical chemistry, and operations research.
Compared to deterministic analysis, the Monte Carlo method provides a superior simulation of risk. It gives an idea of not only what outcome to expect but also the probability of occurrence of that outcome. It is also possible to model correlated input variables.
Monte Carlo methods are commonly used when the dimensionality of the problem is too high for traditional schemes. A great introductory paper on the subject is Persi Diaconis' The Markov Chain Monte Carlo Revolution.
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