Simulation Studies

Simulation provides a way to examine the outcomes of a set of process rules (a model) given a set of starting conditions. People use simulations in a number of ways. The least acceptable way is to use it as a replacement for empirical studies that use real data. However if a model has been validated against real data, then, with some caveats, a simulation can be used this way to predict outcomes using different starting conditions that haven't previously been examined empirically (in short, what-if scenarios).

But where simulation really shines is in proving that, given a set of starting conditions, a proposed process can indeed lead to a claimed output. In other words, it provides a logic check, which is particularly useful when the proposed model is simply to complicated too understand directly, or is not amenable to mathematical proof.

For example, suppose you are trying to explain why there are more girls in India than boys (which we are going to pretend is an absolute fact). You propose a provocative theory: that Indians have a preference for boy babies, so when a couple has their first child, if it's a boy they may choose to have no more children. But if it's a girl, they are likely try again in hopes of getting a boy. Since gender of children tends to run in families, what happens is that "girl families" have a ton of children, while "boy families" have few kids. Ultimate result: more girls than boys.

This sounds plausible, but could be wrong. Not wrong in the sense that it is not the real reason why there are so many girls in India, but wrong in that the proposed process would not actually lead to an end result of more girls than boys. A simulation can test your logic. You can program a world of simulated couples that follow the proposed rules perfectly. Letting the simulation run, you can see whether, at the end, there are more girls than boys, and this "experiment" can be repeated thousands of times to see how often that set of rules leads to the result of more girls than boys. If those are the results, you know that the logic of your theory works: it is a viable mechanism for yielding more girls than boys.

The important thing to realize is that this says nothing about the actual reasons why there are more girls than boys in India. We have a theory, and through simulation we have tested the theory with respect to its internal logic. We have shown that in fact, the proposed process will lead to an excess of girls. But it doesn't mean that this is in fact the process that is actually operating in India: other processes could lead to the same result.

It is also useful to note that if you can run a simulation to test your theory, it means you have really gotten it clear in your mind. It has progressed way past the hand-waving phase. In fact, I would call the theory a model at that point.