Interval timing, temporal averaging, and cue integration

Abstract

In a series of recent experiments, we found that if rats are presented with two temporal cues, each signifying that reward will be delivered after a different duration elapses (e.g., tone-10 seconds / light-20 seconds), they will behave as if they have computed a weighted average of these respective durations. In the current article, we argue that this effect, referred to as "temporal averaging", can be understood within the context of Bayesian Decision Theory. Specifically, we propose and provide preliminary data showing that, when averaging, rats weight different durations based on the relative variability of the information their respective cues provide.

Keywords: Bayesian; Interval timing; cue combination; cue integration; maximum likelihood estimation; multisensory integration; temporal averaging; time perception.

Figure 1

Probe trial data from a temporal averaging experiment adapted with permission from Kurti et al. [7]. Short and long refer to trials where the short and long cues were presented in isolation. Compound refers to responding during trials in which both the short and long cues were presented simultaneously.

Figure 2

Schematic of Bayesian weighting during compound trials. Top left: Hypothetical short and long probe trial responding. Top right: Data from the same short and long distributions. However, for each cue, the proportion of maximal response rate across time is expressed as a proportion of the peak time (100% corresponds to the maximums of either function). Plotting the data in this way shows that relative variability in short cue responding is higher than the long cue, despite the fact that the opposite is true in terms of absolute variability. Bottom right: The equation used to compute predicted compound peak times based on the relative variation (CV) in responding to the short and long cue. Bottom left: Same as top left; however, predicted compound responding is now plotted. Note that increased relative variation for the short cue causes the compound function to fall closer to the long duration.

Figure 3

Scatterplot of actual compound peak times from rats in all prior temporal averaging experiments and predicted compound peak times under BDT based on relative variation in component cue responding. A line of best fit with a constrained intercept of zero is also plotted (slope=1.08, R=.891).

Figure 4

Average accuracy of Bayesian predictions for rats in each study and across all rats. Accuracy was computed for each rat by dividing the predicted compound peak time by the actual compound peak time. Values of 1 represent perfect accuracy, whereas values above and below 1 correspond to over and under-prediction, respectively. The criterion durations and reinforcement probabilities of the short and long cues are included next to each study citation.