Bayesian cognitive modeling has become a prominent tool for the cognitive sciences aiming at a deeper understanding of the human mind and applications in cognitive systems, e.g., humanoid or wearable robotics. Such approaches can capture human behavior adequately with a focus on the crossmodal processing of sensory information. The rubber foot illusion is a paradigm in which such integration is relevant. After experimental stimulation, many participants perceive their real limb closer to an artificial replicate than it actually is. A measurable effect of this recalibration on localization is called the proprioceptive drift. We investigate whether the Bayesian causal inference model can estimate the proprioceptive drift observed in empirical studies. Moreover, we juxtapose two models employing informed prior distributions on limb location against an existing model assuming uniform prior distribution. The model involving empirically informed prior information yields better predictions of the proprioceptive drift regarding the rubber foot illusion when evaluated with separate experimental data. Contrary, the uniform model produces implausibly narrow position estimates that seem due to the precision ratio between the contributing sensory channels. We conclude that an informed prior on limb localization is a plausible and necessary modification to the Bayesian causal inference model when applied to limb illusions. Future research could overcome the remaining discrepancy between model predictions and empirical observation by investigating the changes in sensory precision as a function of distance between the eyes and respective limbs.