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 curve by 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方法，用于近似多元正态分布之间的Rao距离。该方法基于对连接正态分布的曲线进行离散化，并通过Jeffreys散度近似曲线上相邻近正态分布之间的Rao距离。我们实验性地考察了正态分布在普通、自然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等人提出的Fisher-Rao d维正态流形等距嵌入到(d+1)×(d+1)对称正定矩阵锥中的曲线进行了比较[Journal of multivariate analysis 35.2 (1990): 223-242]。我们报告了实验结果，并通过将数值近似值与上下界进行比较来评估近似技术的质量。最后，我们介绍了Calvo和Oller等距嵌入的一些信息几何性质。