Tuesday, January 27, 2015

Thoughts on Modeling

The best material model of a cat is another, or preferably the same, cat.
Norbert Wiener
Generally speaking, accurate models are a good thing. Unless, they are useless! Allow me to explain.

Consider my fair state of Florida. As Wiener claims, the most accurate model of Florida is Florida itself. But is it the most useful?

If I am a tourist visiting the state, the best model may be a Rand McNally road map.

If I am a hydrologist, the best model may be a 3D map where the waterways, the aquifers, and sinkholes are accurately represented.

If I am a political strategist, the best model may be a county/congressional district map colored in red, blue and purple.

If I am a epidemiologist, the best model may be a population density map.

A useful model for something successfully captures the key elements of that something, and de-emphasizes the rest. Judgment of the quality of a model cannot be unhooked from its intended purpose. In other words, the pursuit of accuracy for accuracy's sake is a classic beginner's mistake.

Good models separate the essential from the nonessential. Approximating or neglecting the nonessential is a skill. Approximation is a fancy way of saying, I am trading accuracy for clarity, insight or tractability.

As an aside, good cartoonists do this routinely: they exaggerate one or two key features, and and push the rest into the background. 
Essentially, all models are wrong, but some are useful.
Box and Draper

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