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Description: Many decisions must be made with incomplete information. The ability to evaluate the resulting uncertainty is a key aspect of metacognition. As both confidence judgments and reaction times are expected to be closely related to sensory uncertainty, a mathematical model of human perceptual decision-making should be able to explain them both. We propose the new dynamical evidence and visibility model, an extension of the popular drift diffusion model of decision making, to account for choices, reaction times and confidence at the same time. We compare model fits of the dynamical evidence and visibility model with the two-stage dynamical signal detection theory and several versions of the race model of decision making.