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A Bayesian approach to diffusion process models of decision-making

The Wiener diffusion model, and its extension to the Ratcliff diffusion model, are powerful and well developed process accounts of the time course of human decisionmaking in two-choice tasks. Typically these models have been applied using standard frequentist statistical methods for relating model parameters to behavioral data. Although this approach has achieved notable successes, we argue that the adoption of Bayesian methods promises to broaden the scope of the psychological problems the models can address. In a Bayesian setting, it is straightforward to include linear, non-linear, and categorical covariates of the basic model parameters, and so provide a much richer characterization of individual differences, the properties of stimuli, the effects of task instructions, and a range of other important issues. In this paper, we provide an example of the Bayesian possibilities by applying the Ratcliff diffusion model to a benchmark data set involving a brightness discrimination task. We simultaneously use a categorical covariate and nonlinear regression to model the psychophysical function in a theoretically satisfying way. We also use Bayesian inference on latent class assignment variables to identify and accommodate contaminant data at the level of individual trials, categorizing them as ‘diffusion’ trials, ‘guesses’, and ‘delayed startup’ trials. Using our application as a concrete example, we discuss the potential benefits of applying the Bayesian framework to process models in the cognitive sciences.