According to Bayesian, "inverse optics" accounts of vision, perceiving is inferring the most likely state of the world given noisy sensory data. This inference depends not only on prior beliefs about the world but also on an internal model specifying how world states translate to visual sensations. Alternative accounts explain perceptual decisions as a rule-based process, with no role for such beliefs about perception. Here, we contrast the two alternatives, focusing on decisions about perceptual absence as a critical test case. We present data from three preregistered experiments where participants performed a near-threshold detection task under different levels of partial stimulus occlusion, thereby visibly manipulating the measurement function going from external world states to internal perceptual states. We find that decisions about presence and absence are differentially sensitive to sensory evidence and occlusion. Furthermore, we observe reliably opposite individual-level effects of occlusion on decisions about absence. Our model accounts for these findings by postulating robust individual differences in the incorporation of beliefs about visibility into perceptual inferences, independent of population variability in visibility itself. We discuss implications for the varied and inferential nature of visual perception more broadly. (PsycInfo Database Record (c) 2025 APA, all rights reserved).