It was (not) me: Causal Inference of Agency in goal-directed actions
Authors: Beck Tobias , Wilke Carlo , Wirxel Barbara , Endres* Dominik , Lindner Axel , Giese* Martin 
Published: March 2011

AbstractSummary:The perception of one's own actions depends on both sensory information and predictions derived from internal forward models [1]. The integration of these information sources depends critically on whether perceptual consequences are associated with one’s own action (sense of agency) or with changes in the external world that are not related to the action. The perceived effects of actions should thus critically depend on the consistency between the predicted and the actual sensory consequences of actions. To test this idea, we used a virtual-reality setup to manipulate the consistency between pointing movements and their visual consequences and investigated the influence of this manipulation on self-action perception. We then asked whether a Bayesian causal inference model, which assumes a latent agency variable controlling the attributed influence of the own action on perceptual consequences [2,3], would account for the empirical data: if the percept was attributed to the own action, visual and internal information should fuse in a Bayesian optimal manner, while this should not be the case if the visual stimulus was attributed to external influences. The model correctly fits the data, showing that small deviations between predicted and actual sensory information were still attributed to one’s own action, while this was not the case for large deviations when subjects relied more on internal information. We discuss the performance of this causal inference model in comparison to alternative biologically feasible statistical models applying methods for Bayesian model comparison.
Experiment:
Participants were seated in front of a horizontal board on which their right hand was placed with the index finger on a haptic marker, representing the starting point for each trial. Participants were instructed to execute straight, fast (quasi-ballistic) pointing movements of fixed amplitude, but without an explicit visual target. The hand was obstructed from the view of the participants, and visual feedback about the peripheral part of the movement was provided by a cursor. Feedback was either veridical or rotated against the true direction of the hand movement by predefined angles. After each trial participants were asked to report the subjectively experienced direction of the executed hand movement by placing a mouse-cursor into that direction.

Model:
We compared two probabilistic models: Both include a binary random gating variable (agency) that models the sense of ‘agency’; that is the belief that the visual feedback is influenced by the subject’s motor action. The first model assumes that both the visual feedback xv and the internal motor state estimate xe are directly caused by the (unobserved) real motor state xt (Fig. 1). The second model assumes instead that the expected visual feedback depends on the perceived direction of the own motor action xe (Fig. 2).

Results:
Both models are in good agreement with the data. Fig. A shows the model fit for Model 1 superpositioned to the data from a single subject. Fig. B shows the belief that the visual stimulus was influenced by the own action, which decreases for large deviations between predicted and real visual feedback. Bayesian model comparison shows a better fit for model 1.

Citations
[1] Wolpert D.M, Gharamani, Z, Jordan, M. (1995) Science, 269, 1880-1882.[2] Körding KP, Beierholm E, Ma WJ, Quartz S, Tenenbaum JB, et al (2007) PLoS ONE 2(9): e943.[3] Shams, L., Beierholm, U. (2010) TiCS, 14: 425-432.Acknowledgements This work was supported by the BCCN Tübingen (FKZ: 01GQ1002), the CIN Tübingen, the European Union (FP7-ICT-215866 project SEARISE), the DFG and the Hermann and Lilly Schilling Foundation.