Section 11.2 Models and Probabilistic Thinking
Despite the difficulty inherent in building models that accommodate uncertainty, we have little alternative unless we wish to only build models of things we think we can predict with 100% accuracy. And fortunately, our models do not always have to be perfectly correct in order to generate useful predictions or explanations. As the statistician George Box famously said, “all models are wrong, but some are useful.”
An important part of learning to do good statistical analysis is learning to think clearly about models so that you can pick out a model that is useful for whatever it is you want to accomplish. And the first step toward understanding many statistical models is learning to think about the world in probabilistic terms, as we’ve done here in this chapter. Probabilistic thinking asks questions like:
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Based on what I do know and what I don’t know, what can I predict?
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How does adding or removing different pieces of information change my prediction?
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How much uncertainty is there in my prediction?
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How often will my prediction differ greatly from what actually happens (even if my model is correct)?
