We previously proposed a Bayesian model of multisensory integration in spatial orientation (1). Using a Gaussian prior, centered on an upright head orientation, this model could explain various perceptual observations in roll-tilted participants, such as the subjective visual vertical, the subjective body tilt (1), the rod-and-frame effect (2), as well as their clinical (3) and age-related deficits (4). Because it is generally assumed that the prior reflects an accumulated history of previous head orientations, and recent work on natural head motion suggests non-Gaussian statistics, we examined how the model would perform with a non-Gaussian prior. In the present study, we first experimentally generalized the previous observations in showing that also the natural statistics of head orientation are characterized by long tails, best quantified as a t-location-scale distribution. Next, we compared the performance of the Bayesian model and various model variants using such a t-distributed prior to the original model with the Gaussian prior on their accounts of previously published data of the subjective visual vertical and subjective body tilt tasks. All of these variants performed substantially worse than the original model, suggesting a special value of the Gaussian prior. We provide computational and neurophysiological reasons for the implementation of such a prior, in terms of its associated precision-accuracy trade-off in vertical perception across the tilt range.