Before I started studying statistics, references to a mysterious "Monte Carlo Method" made it seem like the most cryptic thing in the data-analysis universe. People were developing programs dedicated solely to Monte Carlo, and offering special workshops and seminars. It seemed so great and terrible that someone like me—mere mortal that I am—would never be able to understand it.
Fast-forward a few years, and now that I have some experience with it, I'm wondering why Monte Carlo has the reputation it does. The fact of the matter is, at least from a data analysis perspective, Monte Carlo simulation is not that difficult.
The Wizard of Oz Goes to Monte Carlo
Remember how Dorothy and her companions in the Wizard of Oz were so intimidated by the wizard's smoke and mirrors? His fearsome reputation had spread throughout Oz to the extent that our heroes barely possessed the courage to enter his chamber. They feared that not only wouldn't Oz help them, he might even do them harm.
I think the Monte Carlo method has become like the Wizard of Oz for many people. But as with the supposedly dreadful wizard, look behind the Monte Carlo curtain and you'll find a method that's not only less ferocious than it's made out to be, but is actually quite approachable and easy to work with.
Business blogger Alan Nicol reached a similar conclusion in his very useful article, Demystifying Monte Carlo.
Nicol even offers as concise, yet complete, a rationale for doing Monte Carlo as I've ever seen:
Why would we want to do a Monte Carlo Simulation? There could be hundreds of reasons and thousands of examples, but they all reduce down to one thing: predicting performance without conducting hundreds of experiments or building thousands of samples.
In a world of limited resources — especially time — this is a pretty powerful argument for giving the Monte Carlo method a try.
Nicol doesn't delve into the history, but it's worth noting that Monte Carlo was pioneered by the Manhattan Project scientists who developed the first atomic weapon in the 1940s. Faced with very limited supplies of uranium, they turned to simulation to compute reliable probabilities, and thus reduced the amount of raw material needed for testing.
Monte Carlo Simulation with Statistical Software: A Hands-on Example
If you'd like to try doing a Monte Carlo simulation yourself, but you're not sure how to get started, you might check out an article I worked on with one of Minitab's technical training specialists. The article details how to do Monte Carlo simulations using both a known engineering formula and an equation derived from a designed experiment.
The article explains that while simulations with many factors can be complex, doing even the most complicated Monte Carlo simulation boils down to four simple steps:
- Identify a mathematical model of the activity or process you want to explore.
- Define the parameters (like mean and standard deviation) for each factor in your model.
- Create random data according to those parameters.
- Simulate and analyze the output of your process.
The article goes on to demonstrate exactly how to do a simulation for a real-world example in Minitab Statistical Software.
If you check out the article and follow along with the simulation we did, step-by-step, I hope it will help you see how accessible and practical the "great and terrible" Monte Carlo method really is.