Much of scientific psychology and cognitive science can be viewed as a search to understand the mechanisms and dynamics of perception, thought and action. Two processing attributes of particular interest to psychologists are the architecture, or temporal relationships between sub-processes of the system, and the stopping rule, which dictates how many of the sub-processes must be completed for the system to finish. The Survivor Interaction Contrast (SIC) is a powerful tool for assessing the architecture and stopping rule of a mental process model. Thus far, statistical analysis of the SIC has been limited to null-hypothesis- significance tests. In this talk we will demonstrate two Bayesian approaches to assessing the architecture and stopping rule of a process. The first is a nonparametric Bayesian model that examines posterior distributions over SIC forms. This model is based on Dirichlet process priors for the response time distributions. The second is a parametric approach in which we compare hierarchical Bayesian models of the sub-process completion time distributions using varying architecture and stopping rule possibilities.