在本文中，我们提出了一种在贝叶斯神经网络中执行近似高斯推理（Tagi）的分析方法。该方法使得后尺寸矢量和对角线协方差矩阵的分析高斯推断用于重量和偏差。提出的方法具有$ \ mathcal {o}（n）$的计算复杂性，与参数$ n $的数量，并且对回归和分类基准测试的测试确认，对于相同的网络架构，它匹配依赖于梯度背交的现有方法的性能。

In order for automated mobile vehicles to navigate in the real world with minimal collision risks, it is necessary for their planning algorithms to consider uncertainties from measurements and environmental disturbances. In this paper, we consider analytical solutions for a conservative approximation of the mutual probability of collision between two robotic vehicles in the presence of such uncertainties. Therein, we present two methods, which we call unitary scaling and principal axes rotation, for decoupling the bivariate integral required for efficient approximation of the probability of collision between two vehicles including orientation effects. We compare the conservatism of these methods analytically and numerically. By closing a control loop through a model predictive guidance scheme, we observe through Monte-Carlo simulations that directly implementing collision avoidance constraints from the conservative approximations remains infeasible for real-time planning. We then propose and implement a convexification approach based on the tightened collision constraints that significantly improves the computational efficiency and robustness of the predictive guidance scheme.