The environment is shaped by two sources of temporal uncertainty: the discrete probability of whether an event will occur and-if it does-the continuous probability of when it will happen. These two types of uncertainty are fundamental to every form of anticipatory behavior including learning, decision-making, and motor planning. It remains unknown how the brain models the two uncertainty parameters and how they interact in anticipation. It is commonly assumed that the discrete probability of whether an event will occur has a fixed effect on event expectancy over time. In contrast, we first demonstrate that this pattern is highly dynamic and monotonically increases across time. Intriguingly, this behavior is independent of the continuous probability of when an event will occur. The effect of this continuous probability on anticipation is commonly proposed to be driven by the hazard rate (HR) of events. We next show that the HR fails to account for behavior and propose a model of event expectancy based on the probability density function of events. Our results hold for both vision and audition, suggesting independence of the representation of the two uncertainties from sensory input modality. These findings enrich the understanding of fundamental anticipatory processes and have provocative implications for many aspects of behavior and its neural underpinnings.
Keywords: anticipation; catch trial; probability learning; reaction time; temporal–probabilistic inference.