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 nonluminance-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 indicate 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 to regulate the influence of incoming data on existing beliefs in a dynamic environment.