Using priors to formalize theory: optimal attention and the generalized context model.

Formal models in psychology are used to make theoretical ideas precise and allow them to be evaluated quantitatively against data. We focus on one important--but under-used and incorrectly maligned--method for building theoretical assumptions into formal models, offered by the Bayesian statistical approach. This method involves capturing theoretical assumptions about the psychological variables in models by placing informative prior distributions on the parameters representing those variables. We demonstrate this approach of casting basic theoretical assumptions in an informative prior by considering a case study that involves the generalized context model (GCM) of category learning. We capture existing theorizing about the optimal allocation of attention in an informative prior distribution to yield a model that is higher in psychological content and lower in complexity than the standard implementation. We also highlight that formalizing psychological theory within an informative prior distribution allows standard Bayesian model selection methods to be applied without concerns about the sensitivity of results to the prior. We then use Bayesian model selection to test the theoretical assumptions about optimal allocation formalized in the prior. We argue that the general approach of using psychological theory to guide the specification of informative prior distributions is widely applicable and should be routinely used in psychological modeling.