Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules, which cannot account for the approximation errors. Our aim is to design a method for moment transformation of Gaussian random variables, which accounts for the error in the numerically computed mean. We employ an instance of Bayesian quadrature, called Gaussian process quadrature (GPQ), which allows us to treat the integral itself as a random variable, where the integral variance informs us about the incurred integration error. Experiments on the coordinate transformation and nonlinear filtering examples show that the proposed GPQ moment transform performs better than the classical transforms.

中文翻译：

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高斯过程正交矩变换

计算变换后的随机变量的矩是许多工程应用中出现的问题。目前的矩变换方法大多基于经典的求积法则，无法解释近似误差。我们的目标是设计一种高斯随机变量的矩变换方法，该方法解释了数值计算平均值的误差。我们采用贝叶斯求积的一个实例，称为高斯过程求积 (GPQ)，它允许我们将积分本身视为一个随机变量，其中积分方差告诉我们发生的积分误差。坐标变换和非线性滤波示例的实验表明，所提出的 GPQ 矩变换比经典变换性能更好。