A Bayesian approach to diffusion process models of decision-making

The Wiener diffusion model, and its extension to the Rat-cliff diffusion model, are powerful and well developed process accounts of the time course of human decision-making in two-choice tasks. Typically these models have been applied using standard frequentist statistical meth-ods for relating model parameters to behavioral data. Al-though 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 straight-forward to include linear, non-linear, and categorical co-variates 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 pro-vide an example of the Bayesian possibilities by applying the Ratcliff diffusion model to a benchmark data set in-volving a brightness discrimination task. We simultane-ously 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, catego-rizing them as ‘diffusion ’ trials, ‘guesses’, and ‘delayed startup ’ trials. Using our application as a concrete ex-ample, we discuss the potential benefits of applying the Bayesian framework to process models in the cognitive sciences