# Monte Carlo Methods

Simulation Techniques, Statistical Analysis Techniques

Monte Carlo methods are a class of computational algorithm that are used to test the performance of estimators and accuracy of test statistics, given some artificially generated data drawn from a model with an assumed ‘true’ structure.  It involves the following steps:
1. Specify the model, including its formula, true parameter values, and distribution of errors.  The explanatory variables would also need to be specified i.e. whether their values are fixed or randomly selected, and if the latter, their distribution and sample size.
2. Generate an artificial set of observations from this model.
3. Calculate the values for the test statistics or estimators using these observations and store the results.
4. Repeat steps 2 and 3 many times (often thousands of times).
5. Evaluate the performance of the estimator or the accuracy of the test statistic based on the set of stored results e.g. find the mean and standard error of the stored results.

Monte Carlo
methods have been applied in many fields, including mathematics, physics, engineering, telecommunications, finance, insurance, and the development of artificial intelligence.