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:
- 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.
- Generate an artificial set of
observations from this model.
- Calculate the values for the
test statistics or estimators
using these observations and store the results.
- Repeat steps 2 and 3 many
times (often thousands of times).
- 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.
See
also:
Bootstrapping
Cross-validation
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