Human response time (RT) data are widely used in experimental psychology to evaluate theories of mental processing. Typically, the data constitute the times taken by a subject to react to a succession of stimuli under varying experimental conditions. Because of the sequential nature of the experiments there are trends (due to learning, fatigue, fluctuations in attentional state, etc.) and serial dependencies in the data. The data also exhibit extreme observations that can be attributed to lapses, intrusions from outside the experiment, and errors occurring during the experiment. Any adequate analysis should account for these features and quantify them accurately. Recognizing that Bayesian hierarchical models are an excellent modeling tool, we focus on the elaboration of a realistic likelihood for the data and on a careful assessment of the quality of fit that it provides. We judge quality of fit in terms of the predictive performance of the model. We demonstrate how simple Bayesian hierarchical models can be built for several RT sequences, differentiating between subject-specific and condition-specific effects. (Contains 1 table, 7 figures and 2 footnotes.)