Optimal gain model.

A) Error estimation model. The random errors are Gaussian distributed. For any given error as indicated by the green dot the estimate for that error is contaminated by perceptual noise of the form . Depending on the current perceptual noise instance the participant will either answer correctly for the left/right judgement task (white area under the curve) or incorrectly (grey area). The higher the variance in perceptual noise compared to the motor noise the higher the chance of perceiving the error incorrectly in which case correction movements would lead to bigger errors on average. Thus, to be able to correct for the perceived error in an optimal way to minimize end-point variance the level of perceptual noise has to be weighed against prior knowledge of the distribution of the pointing errors . B) Theoretical ratio between the standard deviations in final endpoint after correcting and initial error versus the correction gain for several different levels of perceptual noise. Values below one mean better performance after making the corrections. Values above one mean worse performance. Optimal gains can be estimated by determining the gains for which the end point variance after correcting is lowest (red curve).