To stabilize our position in space we use visual information as well as non-visual physical motion cues. However, visual cues can be ambiguous: visually perceived motion may be caused by self-movement, movement of the environment, or both. The nervous system must combine the ambiguous visual cues with noisy physical motion cues to resolve this ambiguity and control our body posture. Here we have developed a Bayesian model that formalizes how the nervous system could solve this problem. In this model, the nervous system combines the sensory cues to estimate the movement of the body. We analytically demonstrate that, as long as visual stimulation is fast in comparison to the uncertainty in our perception of body movement, the optimal strategy is to weight visually perceived movement velocities proportional to a power law. We find that this model accounts for the nonlinear influence of experimentally induced visual motion on human postural behavior both in our data and in previously published results.