We present a fully Bayesian approach to using Wiener diffusion as an account of the time-course of two-alternative decision-making. Using graphical modeling, and MCMC methods to draw posterior samples, we reconsider the seminal data of Ratcliff and Rouder (1998), who tested three observers in a brightness discrimination task under both speed and accuracy conditions. Our model employs hierarchical Bayesian methods to model the psychophysical relationship between stimulus properties and drift rates, and relies on latent assignment methods to infer contaminants in the data. We find evidence, consistent with the original analysis, that task instructions affect boundary separation, and that the model accounts for decisions and response time distributions well. But we also observe a number of results that are inconsistent with the original analysis, relating to the psychophysical function, and the nature of the theoretically important cross-over effect. We also show that our Bayesian approach has the potential to estimate model parameters accurately using a small fraction of the original data set. |