Most computational models of the responses of sensory neurons are based on the information in external stimuli and their feed-forward processing. Extrasensory information and top-down connections are usually incorporated on a post-hoc basis only, e.g. by postulating attentional modulations to account for features of the data that feed-forward models cannot explain. To provide a more parsimonious account of perceptual decision-making, we combine the proposal that bottom-up and top-down connections subserve Bayesian inference as the central task of the visual system (Lee & Mumford 2003) with the recent hypothesis that the brain solves this inference problem by implementing a sampling-based representation and computation (Fiser et al 2010). Since the sampling hypothesis interprets variable neuronal responses as stochastic samples from the probability distribution that the neurons represent, it leads to the strong prediction that dependencies in the internal probabilistic model that the brain has learnt will translate into observable correlated neuronal variability. We have tested this prediction by implementing a sampling-based model of a 2AFC perceptual decision-making task and directly comparing the correlation structure among its units to two sets of recently published data. In agreement with the neurophysiological data, we found that: a) noise correlations between sensory neurons dependent on the task in a specific way (Cohen & Newsome 2008); and b) that choice probabilities in sensory neurons are sustained over time, even as the psychophysical kernel decreases (Nienborg & Cumming 2009). Since our model is normative, its predictions depend primarily on the task structure, not on assumptions about the brain or any additional postulated processes. Hence we could derive additional experimentally testable predictions for neuronal correlations, variability and performance as the task changes (e. g. to fine discrimination or dynamic task switching) or due to perceptual learning during decision-making.