This article demonstrates the potential of using hierarchical Bayesian methods to relate models and data in the cognitive sciences. This is done using a worked example that considers an existing model of category representation, the Varying Abstraction Model (VAM), which attempts to infer the representations people use from their behavior in category learning tasks. The VAM allows for a wide variety of category representations to be inferred, but this article shows how a hierarchical Bayesian analysis can provide a unifying explanation (...) of the representational possibilities using 2 parameters. One parameter controls the emphasis on abstraction in category representations, and the other controls the emphasis on similarity. Using 30 previously published data sets, this work shows how inferences about these parameters, and about the category representations they generate, can be used to evaluate data in terms of the ongoing exemplar versus prototype and similarity versus rules debates in the literature. Using this concrete example, this article emphasizes the advantages of hierarchical Bayesian models in converting model selection problems to parameter estimation problems, and providing one way of specifying theoretically based priors for competing models. (shrink)