A Taste of Monte Carlo Simulation

There are many areas in which we want to predict the future.

For example what will happen to my retirement account in five years? What will the weather be like next week? What is the inflation rate going to be over the next few years? How likely is it that my iPhone will fail or break within a year?

In traditional forecasts, we create a model that projects outcomes based on certain inputs or variables. These are entered into a model which relates the inputs mathematically to produce outputs. These inputs are single-point estimates or our "best guess." Since the inputs are point estimates, the outputs will be single point estimates as well. In other words, we have to have complete confidence in the accuracy of our inputs (e.g. inflation rate, failure rates, investment rate of return, GDP, etc.) if we want to believe the output is exactly correct.

Since forecast inputs are effectively predicting the future, for any real world phenomena the actual values are not known with absolute certainty.

To incorporate this uncertainty, each single-point input estimate can be replaced by a probability distribution that more accurately reflects the range of possibilities for that input.

The output will then be a range of possibilities or a probability distribution. To obtain this probability distribution on the output, we sample the input. The input is sampled based on the probability distribution associated with this input. For each sample we obtain one output value.

Using Monte Carlo simulation we repeat this process over and over multiple times to get a range of outputs based on a range of inputs.
This range of outputs represents the output probability distribution which gives us a more realistic set of possibilities for the future.

With this information we can begin to answer questions such as:
How likely is it that I will achieve millionaire status when I retire?
How likely is it that 100 of these units will fail within the next 10 years? what is the most important contributing factor to sales growth?