The predictive processing theory of cognition and neural encoding dictates that hierarchical regions in the neocortex learn and encode predictive hypotheses of current and future stimuli. To better handle uncertainty these regions must also learn, infer, and encode the precision of stimuli. In this treatment we investigate the potential of handling uncertainty within a single learned predictive model. We exploit the rich predictive models formed by the learning of temporal sequences within a Hierarchical Temporal Memory (HTM) framework, a cortically inspired connectionist system of self-organizing predictive cells. We weight a cell’s feedforward response by the degree of its own temporal expectations of a response. We test this model on data that has been saturated with temporal or spatial noise, and show significant improvements over traditional HTM systems. In addition we perform an experiment based on the Posner cuing task and show that the system displays phenomena consistent with attention and biased competition. We conclude that the observed effects are similar to those of precision encoding.