The mental representations of perceptual and cognitive stimuli vary on many dimensions. In addition, because of quantal fluctuations in the stimulus, spontaneous neural activity, and fluctuations in arousal and attentiveness, mental events are characterized by an inherent variability. During the last several years, a number of models and theories have been developed that explicitly assume the appropriate mental representation is both multidimensional and probabilistic. This new approach has the potential to revolutionize the study of perception and cognition in the same way that signal detection theory revolutionized the study of psychophysics. This unique volume is the first to critically survey this important new area of research.