The Curve-Fitting Problem, Akaike-type Model Selection, and the Error Statistical Approach

The curve-fitting problem is often viewed as an exemplar which encapsulates the multitude of dimensions and issues associated with inductive inference, including underdetermination and the reliability of inference. The prevailing view is that the ‘fittest’ curve is one which provides the optimal trade-off between goodness-of-fit and simplicity, with the Akaike Information Criterion (AIC) the preferred method. The paper argues that the AIC-type procedures do not provide an adequate solution to the curve fitting problem because (a) they have no criterion to assess when a curve captures the regularities in the data inadequately, and (b) they are prone to unreliable inferences. The thesis advocated is that for more satisfactory answers one needs to view the curvefitting problem in the context of error-statistical approach where (i) statistical adequacy provides a criterion for selecting the fittest curve and (ii) the error probabilities can be used to calibrate the reliability of inductive inference. This thesis is illustrated by comparing the Kepler and Ptolemaic models in terms of statistical adequacy, showing that the latter does not ‘save the phenomena’ as often claimed. This calls into question the view concerning the pervasiveness of the problem of underdetermination; statistically adequate ‘fittest’ curves are rare, not common. ∗Thanks are due to Deborah Mayo and Clark Glymour for valuable suggestions and comments on an earlier draft of the paper.