Bayesian Methods in Cognitive Modeling

Abstract

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.

Bayesian methods applied to the generalized matching law

“…Formal models that capture the richness of these sorts of theories are often difficult to analyze using classical statistical methods, but can be handled in a principled way by Bayesian methods. As Lee (, ) argues, this flexibility frees researchers to develop models creatively, unconstrained by limitations in statistical methods.…”

“…This sort of model structure is sometimes known as a common cause model, and is basic to the empirical sciences. As Lee () points out, one of the reasons to believe in models in physics is that latent variables like the mass of an object influence multiple physical phenomena, like momentum, charge, and gravitational forces. Common cause models provide the capability to test theoretical breadth in psychological phenomena, such as the invariance we found for sensitivity across behavioral measures.…”

“…Collectively, as Lee (, ) argues, hierarchical, common cause, and latent mixture model structures allow for enormous flexibility in developing models of psychological processes. They allow for models to be developed with greater theoretical depth, in which the relationships between psychological variables at different levels of abstraction are modeled hierarchically.…”

“…While the group‐and‐individual model in Figure allowed for continuous individual differences, under the assumption that the bias of each pigeon came from a uni‐modal Gaussian distribution, it did not allow for this sort of subgroup structure. Qualitative individual differences of this type can be incorporated using latent mixture models, also sometimes known as latent class models (Lee, , ). The basic idea is to introduce a discrete parameter that indicates which of several possible group distributions an individual bias parameter is drawn from.…”

“…In the last twenty or so years, however, many areas of psychology involving mathematical and statistical models have moved toward the widespread adoption of Bayesian methods (Kruschke, ; Lee, ). There are now many examples of psychological models—in areas including perception, memory, learning, development, categorization, decision making, and problem solving—being implemented and evaluated within the Bayesian framework.…”