Figure 11.

Simulation of the force-matching task. The x axes denote time in 100 ms time bins; the y axes force in Newtons. Left panels: in the first part of this simulation an internal force is generated from a prior belief about the cause v_i, followed by the presentation of an external force. Posterior beliefs about the hidden states (upper right panel) are similar, but the confidence interval around the force for the internally generated state is much broader. This is because sensory level precision must be attenuated in order to allow proprioceptive predictions to be fulfilled by reflex arcs instead of being corrected by sensory input: i.e., the confidence intervals around v_i must be narrower than those around x_i to allow movement to proceed. If perceived intensity of the sensation is associated with the lower 90% confidence bound of the estimate of hidden state (highlighted by the dotted line), it will be lower when the force is self generated than when the force is exogenous (the difference is highlighted by the arrow). Right panels: the simulation was repeated but the external force was matched to the lower bound of the 90% confidence interval of the internal force. This means that internally generated force is now greater than the externally applied force (double-headed arrow, upper left panel). This reproduces the normal psychophysics of the force-matching illusion that can be regarded as entirely Bayes-optimal, under appropriate levels of precision.