Bayesian methods in cognitive modeling

Bayesian statistical methods provide a flexible and principled framework for relating cognitive models to behavioral data. They allow for cognitive models to be formalized, evaluated, and applied, supporting inferences about parameters, the testing of models, and making predictions about data. This chapter argues that Bayesian methods are most useful for cognitive modeling in allowing more ambitious accounts of cognition to be considered, including models that include hierarchical, latent-mixture, or common-cause structures. These theoretical possibilities, and the practical mechanics of using Bayesian methods implemented as graphical models, are demonstrated by means of an extended case study, involving psychophysical models of the perception of duration for auditory and visual stimuli. The case study demonstrates a number of general features of the Bayesian approach—representing uncertainty, being sensitive to model complexity, dealing with contaminants, allowing for individual differences, making predictions and generalizations, and so on—while emphasizing the role of informative prior distributions to capture theoretical assumptions about cognitive variables, and the complementary roles of parameter inference and model testing in answering research questions.