In Flaw of Averages, Sam Savage uses the illustration of shaking a ladder to explain why someone would want to use Monte Carlo simulation. Before climbing a ladder, most people shake the ladder a little to make sure it’s sturdy.
When you position a ladder and climb it immediately, you’re saying that you’re satisfied that the ladder’s position is safe. You’re assuming it will stay in the position you placed it. But when you shake the ladder, you’re testing how it will behave at a variety of nearby positions. If the ladder remains sturdy, you have more confidence that accidental motions while you’re on the ladder are not likely to cause an accident. When you stick a single number into a model, you’re acting like someone climbing a ladder immediately. When you stick in a series of random inputs, it’s like you’re shaking the ladder.
The latest INFORMS podcast features an interview with Sam Savage (audio). He mentions the ladder analogy and adds an observation that I don’t recall seeing in his book. One criticism of Monte Carlo methods is that the validity of your results depends on the validity of your input distributions. It’s better to have realistic input distributions, but it’s better to perform a simulation with an incorrect distribution than to not try random input at all. The distribution of random forces likely to result from working while standing on a ladder is different from the distribution of forces from shaking the ladder with your hands. But that doesn’t mean it isn’t a good idea to shake the ladder anyway.
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