Despite the increasing significance of sense of agency (SoA) research, the literature lacks a formal model: what computational principles underlie SoA, the registration that oneself initiated an action that caused something to happen? We theorize SoA in the framework of optimal Bayesian cue integration with mutually involved principles, namely, reliability of action and outcome sensory signals, their consistency with the causation of the outcome by the action, and the prior belief in causation. We used our Bayesian model to explain the intentional binding effect, hailed as reliable indicator of SoA. Our model explains temporal binding in both self-intended and unintentional actions suggesting that intentionality is not strictly necessary given high confidence in the action causing the outcome. Our Bayesian model also explains that if the sensory cues are reliable, SoA can emerge even for unintended actions. Our formal model therefore posits a precision-dependent causal agency.The number of scientific contributions being added to the theoretical literature of sense of agency (SoA) has significantly increased at least in the past two decades 1,2 . The concept has garnered considerable attention in psychology, philosophy, neuroscience and psychopathology 3 . SoA is the registration 4 that the self initiates an action in order to interact with and influence its external environment 5 . It has been posited that SoA is fundamental to the experience of volition 6-9 and to self-consciousness because of its self-other distinction 10-12 , and the degradation of this experience characterizes certain psychiatric and neurological disorders [13][14][15] . Furthermore, SoA has recently been suggested to underpin neuroethics and law due to the role it plays in the social concept of responsibility for one's own actions 5,9,16,17 .Despite its increasing significance, the literature still lacks the computational principles that underlie SoA. We theorize SoA as the confidence in one's perception of the actionoutcome effect and that it is consistent (e.g., spatially or temporally) with the hypothesis that the action caused the outcome. We adapted the model of Sato, Toyoizumi and Aihara 18 that was originally used to explain the ventriloquism effect as a Bayesian estimate of a common cause behind the consistency of the audiovisual stimuli. Formalizing SoA by this Bayesian psychophysics principle distinguishes our theory from existing works.We compared the predictions of our model to the results of two pertinent intentional binding studies. Intentional binding, which is the perceived compression of the time interval between voluntary action and its outcome, has been reported as reliable implicit measure of SoA and has been used in a large number of studies providing valuable analyses on the temporal perception of action-outcome effects and the nature of SoA 19 . The seminal experiment of Haggard, Clark & Kalogeras 6 investigated the perceived action-outcome timing effects in three conditions: voluntary wherein the subject intentionally...