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Abstract:
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A valuable, though too often unappreciated distinction in statistics is between two kinds of statistical models: empirical models and iconic models. Both are important in science, though different scientific disciplines tend to place more emphasis on one than the other. Their relative importance in statistics is shifting, as massive data sets become increasingly common. I examine the differences between the two models, and their implications for statistics. Empirical models are perhaps particularly susceptible to issues of problem misspecification. This is different from the more familiar model misspecification, but is arguably more serious. These ideas are explored, and illustrated with some real problems.
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