We present a simple method to approximate Rao's distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating Rao's distances between successive nearby normal distributions on the curves by the square root of Jeffreys divergence, the symmetrized Kullback-Leibler 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 both lower and upper bounds. Finally, we present several information-geometric properties of the Calvo and Oller's isometric embedding.

翻译：本文提出了一种近似多元正态分布间Rao距离的简单方法，其核心思想是通过离散化连接正态分布的曲线，并利用Jeffreys散度（对称化Kullback-Leibler散度）的平方根来近似曲线上相邻相近正态分布间的Rao距离。我们实验性地考察了正态分布在普通参数化、自然参数化与期望参数化下的线性插值曲线，并将这些曲线与基于Calvo与Oller等距嵌入（将Fisher-Rao $d$ 元正态流形映射至 $(d+1)\times(d+1)$ 对称正定矩阵锥）导出的曲线进行比较 [Journal of multivariate analysis 35.2 (1990): 223-242]。通过将数值近似结果与上下界进行对比，我们报告了实验结果并评估了近似技术的质量。最后，我们揭示了Calvo与Oller等距嵌入的若干信息几何性质。