The question of cognitive architecture—how cognitive processes are temporally organized—has arisen in many areas of psychology. This question has proved difficult to answer, with many proposed solutions turning out to be spurious. Systems factorial technology (Townsend & Nozawa, 1995) provided the first rigorous empirical and analytical method of identifying cognitive architecture, using the survivor interaction contrast (SIC) to determine when people are using multiple sources of information in parallel or in series. Although the SIC is based on rigorous nonparametric mathematical modeling of response time distributions, for many years inference about cognitive architecture has relied solely on visual assessment. Houpt and Townsend (2012) recently introduced null hypothesis significance tests, and here we develop both parametric and nonparametric (encompassing prior) Bayesian inference. We show that the Bayesian approaches can have considerable advantages.