A Bayesian Framework for the Perceived Timing of Rhythmic Stimuli

Sequences of regularly spaced stimuli carry information about the timing and properties of future stimuli. Here we investigated how these expectations can affect the perceived time of stimuli and we propose a model based on the Bayesian framework. Expectation of when a future stimulus is to occur is modelled as the prior probability of a stimulus over future time. The prior is integrated with the current sensory evidence (likelihood function) to give rise to our perception, which is based on the posterior distribution. Stimuli appearing earlier than expected should then be perceptually delayed towards the peak of the prior distribution whereas stimuli presented later than expected should be anticipated. As expectations increase, for example when longer sequences are presented, the prior should become steeper and should have more influence on the perceived timing of stimuli. A second assumption of the model is that the prior should be built within every trial and is not only formed over the course experiment. In order to test the predictions of the model, we presented participants with isochronous tone sequences with an inter-stimulus interval (ISI) of 700ms. Participants reported whether the last stimulus was presented before or after a visual temporal probe. In such a way we could find the audiovisual asynchrony at which the two stimuli are perceived to be synchronous and measure any temporal distortion due to the prior. Importantly, the final stimulus was presented slightly earlier, on time, or later than expected to measure the effect of the prior. In accordance with the predictions, we find that stimuli presented earlier than expected are indeed delayed, and stimuli presented late are perceptually anticipated. However, we also find that stimuli that are presented on time are anticipated, a prediction not directly evident in the model. This could be due to a general anticipation of expected stimuli by an effect similar to prior entry, which is absent for stimuli presented too early. This effect could be modelled as the reliance on a hazard function, rather than on probability distributions. As the number of repeated stimuli increases, we observe that both the delay and the anticipation effects increase in magnitude following the predictions of the model. In another experiment we tested whether prior expectations can be built within a single trial by presenting sequences of 4 stimuli spaced at 3 different ISIs (400, 700, and 1000ms). The ISIs were randomly selected at every trial. Although participants could not know which ISI will be presented based on the previous trial, they could still generate an expectation for when a stimulus should occur based on the timing of the sequence presented on the trial. Results showed the same type of effect, namely a shift of stimuli towards expectation thus suggesting that the brain ‘resets’ after each sequence and calculates temporal expectations within each trial at least to some extent.