Bayesian methods applied to the generalized matching law.

Abstract

We demonstrate the usefulness of Bayesian methods in developing, evaluating, and using psychological models in the experimental analysis of behavior. We do this through a case study, involving new experimental data that measure the response count and time allocation behavior in pigeons under concurrent random-ratio random-interval schedules of reinforcement. To analyze these data, we implement a series of behavioral models, based on the generalized matching law, as graphical models, and use computational methods to perform fully Bayesian inference. We demonstrate how Bayesian methods, implemented in this way, make inferences about parameters representing psychological variables, how they test the descriptive adequacy of models as accounts of behavior, and how they compare multiple competing models. We also demonstrate how the Bayesian graphical modeling approach allows for more complicated modeling structures, including hierarchical, common cause, and latent mixture structures, to formalize more complicated behavioral models. As part of the case study, we demonstrate how the statistical properties of Bayesian methods allow them to provide more direct and intuitive tests of theories and hypotheses, and how they support the creative and exploratory development of new theories and models.