Question

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?

Answer 1

Suppose that you want to estimate some quantity of interest. In the Joel’s example ‘ship date’ is what you want to estimate. In most such situations, there are random factors that impact our estimates.

When you have a random quantity, you typically wants to know its mean and the standard deviation so that you can take appropriate actions. In simple situations, you can model the quantity as a standard distribution (e.g., normal distribution) for which analytical formulas exist for the mean and the standard deviation. However, there exist many situations where analytical formulas do not exist. In such situations, instead of an analytic solution for the mean and the standard deviation, we resort to simulation. The idea is:

Step 1: Generate factors that impact the quantity of interest using appropriate distributions

Step 2: Compute quantity of interest

Repeat steps 1 and 2 many times and compute the empirical average and standard deviation for what you want to know.

The above is by far the typical application of monte carlo application. See the wikipedia link provided by Jarrod for several such applications and some examples of interesting applications where there is no inherent randomness (e.g., estimation of pi).