Modeling individual differences with Dirichlet processes

Abstract

We introduce a Bayesian framework for modeling individual differences, in which subjects are assumed to belong to one of a potentially infinite number of groups. In this model, the groups observed in any particular data set are not viewed as a fixed set that fully explain the variation between individuals, but rather as representatives of a latent, arbitrarily rich structure. As more people are seen, the number of observed groups is allowed to grow, as more details about the individual differences are revealed. We use the Dirichlet process – a distribution widely used in nonparametric Bayesian statistics – to define a prior for the model, allowing us to learn flexible parameter distributions without overfitting the data, or requiring the complex computations typically required for determining the dimensionality of a model. As an initial demonstration of the approach, we present an application of the method to categorization data.