Natural statistics of head roll: implications for Bayesian inference in spatial orientation

We previously proposed a Bayesian model of multisensory integration in spatial orientation. 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, the rod-and-frame effect, as well as their clinical and age-related deficits. 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.

我们此前提出了一种面向空间定向任务的多感觉整合贝叶斯模型（Bayesian model）。该模型以直立头部定向为中心构建高斯先验（Gaussian prior），可解释倾斜滚动状态下受试者的多种感知现象，包括主观视觉垂直（subjective visual vertical）、主观身体倾斜、棒框效应（rod-and-frame effect），以及与之相关的临床与年龄相关性感知缺陷。由于学界普遍认为先验分布反映了个体既往头部定向的累积历史，且近期针对头部自然运动的研究表明其统计特性呈非高斯分布，我们据此检验了该模型在采用非高斯先验时的表现。在本研究中，我们首先通过实验拓展了既往研究结论，证实头部定向的自然统计特性同样具有厚尾特征，最适合用t位置尺度分布（t-location-scale distribution）进行量化。随后，我们针对已发表的主观视觉垂直与主观身体倾斜任务数据集，对比了采用该t分布先验的贝叶斯模型及其多种变体，与原始高斯先验模型的表现。所有变体的表现均显著劣于原始模型，这表明高斯先验具有独特的应用价值。我们还从倾斜范围内垂直感知的精度-准确率权衡（precision-accuracy trade-off）角度，为该类先验的实现机制提供了计算与神经生理学层面的解释依据。