We present a simple method to approximate Rao's distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating Rao distances between successive nearby normal distributions on the curves by the square root of Jeffreys divergence. We consider experimentally the linear interpolation curves in the ordinary, natural and expectation parameterizations of the normal distributions, and compare these curves with a curve derived from the Calvo and Oller's isometric embedding of the Fisher-Rao $d$-variate normal manifold into the cone of $(d+1)\times (d+1)$ symmetric positive-definite matrices [Journal of multivariate analysis 35.2 (1990): 223-242]. We report on our experiments and assess the quality of our approximation technique by comparing the numerical approximations with lower and upper bounds. Finally, we present some information-geometric properties of the Calvo and Oller's isometric embedding.

翻译：我们提出了一种简单的方法来逼近多元正态分布之间的Rao距离，该方法基于离散化连接正态分布的曲线，并通过Jeffreys散度的平方根来逼近曲线上相邻正态分布之间的Rao距离。我们实验性地考虑了正态分布在普通参数化、自然参数化和期望参数化下的线性插值曲线，并将这些曲线与基于Calvo和Oller的Fisher-Rao $d$元正态流形到$(d+1)\times(d+1)$对称正定矩阵锥的等距嵌入（《多元分析杂志》35.2 (1990): 223-242）导出的曲线进行了比较。我们报告了实验结果，并通过将数值逼近值与上下界进行比较来评估逼近技术的质量。最后，我们展示了Calvo和Oller等距嵌入的一些信息几何性质。