Curve-fitting typically works by trading off goodness-of-fit with simplicity, where simplicity is measured by the number of adjustable parameters. However, such methods cannot be applied in an unrestricted way. I discuss one such correction, and explain why the exception arises. The same kind of probabilistic explanation offers a surprising resolution to a common-sense dilemma.

an observation to formulate a theory, it is no surprise that the resulting theory accurately captures that observation. However, when the theory makes a novel prediction—when it predicts an observation that was not used in its formulation—this seems to provide more substantial confirmation of the theory. This paper presents a new approach to the vexed problem of understanding the epistemic difference between prediction and accommodation. In fact, there are several problems that need to be disentangled; in all of them, the (...) key is the concept of overfitting. We float the hypothesis that accommodation is a defective methodology only when the methods used to accommodate the data fail to guard against the risk of overfitting. We connect our analysis with the proposals that other philosophers have made. We also discuss its bearing on the conflict between instrumentalism and scientific realism. Introduction Predictivisms—a taxonomy Observations Formulating the problem What might Annie be doing wrong? Solutions Observations explained Mayo on severe tests The miracle argument and scientific realism Concluding comments. (shrink)

Traditional analyses of the curve fitting problem maintain that the data do not indicate what form the fitted curve should take. Rather, this issue is said to be settled by prior probabilities, by simplicity, or by a background theory. In this paper, we describe a result due to Akaike [1973], which shows how the data can underwrite an inference concerning the curve's form based on an estimate of how predictively accurate it will be. We argue that this approach throws light (...) on the theoretical virtues of parsimoniousness, unification, and non ad hocness, on the dispute about Bayesianism, and on empiricism and scientific realism. * Both of us gratefully acknowledge support from the Graduate School at the University of Wisconsin-Madison, and NSF grant DIR-8822278 (M.F.) and NSF grant SBE-9212294 (E.S.). Special thanks go to A. W. F. Edwards.William Harper. Martin Leckey. Brian Skyrms, and especially Peter Turney for helpful comments on an earlier draft. (shrink)

Forster and Sober present a solution to the curve-fitting problem based on Akaike's Theorem. Their analysis shows that the curve with the best epistemic credentials need not always be the curve that most closely fits the data. However, their solution does not, without further argument, avoid the two difficulties that are traditionally associated with the curve-fitting problem: that there are infinitely many equally good candidate-curves relative to any given set of data, and that these best candidates include curves with indefinitely (...) many bumps. (shrink)