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Forster, Malcolm R. (2001): "The New Science of Simplicity," in Arnold
Zellner, Hugo Keuzenkamp, and Michael McAleer (eds.), Simplicity,
Inference and Modelling, pp. 83-117. Cambridge: Cambridge University Press.
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The
problem
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Preliminaries
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A
milieu of methods and an easy example
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Predictive
accuracy as a goal of model selection
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A
‘normality’ assumption and the geometry of parameter space
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Comparing
selection criteria
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The
charge that AIC is inconsistent
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Summary
of results
|
There was time when statistics was a mere footnote to the
methodology of science; concerned only with the mundane task of estimating the size of
observational errors and designing experiments. That was because statistical methods
assumed a fixed background "model", and only methodology was concerned with the
selection of the model. Simplicity was an issue in methodology, but not in statistics. All
that has changed. Statistics has expanded to cover model selection, and simplicity has
appeared in statistics with a form and precision that it never attained in the methodology
of science. This is the new science of simplicity.
This paper lays a foundation for all forms of model selection from hypothesis
testing and cross validation to the newer AIC and BIC methods that trade off simplicity
and fit. These methods are evaluated with respect to a common goal of maximizing
predictive accuracy. Within this framework, there is no relevant sense in which AIC is
inconsistent, despite an almost universally cited claim to the contrary. Asymptotic
properties are not pivotal in the comparison of selection methods. The real differences
show up in intermediate sized data sets. Computer computations suggest that there
are no global optimums—the dilemma is between performing poorly in one set of
circumstance or performing poorly in another. |