The ability to make inferences about the current state of a dynamic process requires ongoing assessments of the stability and reliability of data generated by that process. We found that these assessments, as defined by a normative model, were reflected in non–luminance–mediated changes in pupil diameter of human subjects performing a predictive–inference task. Brief changes in pupil diameter reflected assessed instabilities in a process that generated noisy data. Baseline pupil diameter reflected the reliability with which recent data indicated the current state of the data–generating process and individual differences in expectations about the rate of instabilities. Together these pupil metrics predicted the influence of new data on subsequent inferences. Moreover, a task– and luminance–independent manipulation of pupil diameter predictably altered the influence of new data. Thus, pupil–linked arousal systems can help regulate the influence of incoming data on existing beliefs in a dynamic environment.