Model Selection and the Multiplicity of Patterns in Empirical Data

Abstract

Several quantitative techniques for choosing among data models are available. Among these are techniques based on algorithmic information theory, minimum description length theory, and the Akaike information criterion. All these techniques are designed to identify a single model of a data set as being the closest to the truth. I argue, using examples, that many data sets in science show multiple patterns, providing evidence for multiple phenomena. For any such data set, there is more than one data model that must be considered close to the truth. I conclude that, since the established techniques for choosing among data models are unequipped to handle these cases, they cannot be regarded as adequate.