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Internal Representations of Temporal Statistics and Feedback Calibrate Motor-Sensory Interval Timing

Figure 1

Comparison of response profiles for different ideal observers in the timing task.

The responses of four different ideal observers (columns a–d) to a discrete set of possible stimuli durations are shown (top row); for visualization purpose, each stimulus duration in this plot is associated with a specific color. The behavior crucially depends on the combination of the modelled observer's temporal sensorimotor noise (likelihood), prior expectations and loss function (rows 2–4); see Figure 2 bottom for a description of the observer model. For instance, the observer's sensorimotor variability could be constant across all time intervals (column a) or grow linearly in the interval, according to the ‘scalar’ property of interval timing (column b–d). An observer could be approximating the true, discrete distribution of intervals as a Gaussian (columns a–b) or with a uniform distribution (columns c–d). Moreover, the observer could be minimizing a typical quadratic loss function (columns a–c) or a skewed cost imposed through an external source of feedback (column d). Yellow shading highlights the changes of each model (column) from model (a). All changes to the observer's model components considerably affect the statistics of the predicted responses, summarized by response bias, i.e. average difference between the response and true stimulus duration, and standard deviation (bottom two rows). For instance, all models predict a central tendency in the response (that is, a bias that shifts responses approximately towards the center of the interval range), but bias profiles show characteristic differences between models.

Figure 1