(A) In a classical psychophysics task, the subject receives stimuli xt on independent trials, generates sensory observations yt, forms beliefs about the stimulus , and (B) makes a single decision ut (e.g., whether the target stimulus was present or absent). (C) The researcher has a model of how the agent makes decisions and measures the subject’s sensitivity and decision criterion by inverting this model. For example, one can estimate the agent’s visual uncertainty by computing the width of a psychometric function. (D) In a continuous psychophysics task, a continuous stream of stimuli is presented. The subject has an internal model of the dynamics of the task, which they use to form a belief about the state of the world and then perform continuously actions (E) based on their belief and subjective costs. (F) The researcher observes the subject’s behavior and inverts this internal model, fo example, using Bayesian inference applied to optimal control under uncertainty.