Response inhibition refers to the ability to stop an ongoing response, such as rapidly halting when the traffic light turns red. Response inhibition is the hallmark of executive functions and has received-and continues to receive-considerable attention in the field of experimental, clinical, and neuropsychology. The proposed project focuses on two recently developed cognitive process models of inhibition: the stop-signal race diffusion model (SS-RDM) and the stop-signal linear ballistic accumulator (SS-LBA). Both models conceptualize inhibition as a race between a set of evidence accumulators: one set that is associated with the ongoing response, and another that is associated with the stop response. The difference between the models lies in the mathematical formulation of evidence accumulation. Contrary to traditional models of response inhibition, process models provide parameter estimates that can be directly interpreted in terms of well-defined cognitive processes, such as the rate of evidence accumulation and response caution. Despite this conceptual advantage, the applicability of the SS-RDM and SS-LBA is limited by the large number of observations that are necessary for accurate parameter estimation and by the lack of adequate hypothesis testing techniques. The current project proposes to overcome these limitations with Bayesian inference. My first goal is to provide a Bayesian hierarchical implementation of the SS-RDM and SS-LBA that can substantially decrease the necessary number of observations. My second goal is to develop a Bayesian model selection method that allows researchers to formally evaluate nested and non-nested hypotheses in the SS-RDM and SS-LBA using reversible jump Markov chain Monte Carlo sampling. My overall objective is to create an integrated framework and corresponding software that will enable investigators to address fundamental and applied research questions about the nature and development of response inhibition using relatively small data sets and state-of-the-art Bayesian hypothesis testing techniques.