Information Geometry
本文回顾了概率分布流形的几何结构及其应用，展示了C. R. Rao教授1945年开创的信息几何思想如何在统计科学、人工智能、信号处理等领域发展和普及。
Summary Statistical inference is constructed upon a statistical model consisting of a parameterised family of probability distributions, which forms a manifold. It is important to study the geometry of the manifold. It was Professor C. R. Rao who initiated information geometry in his monumental paper published in 1945. It not only included fundamentals of statistical inference such as the Cramér–Rao theorem and Rao–Blackwell theorem but also proposed differential geometry of a manifold of probability distributions. It is a Riemannian manifold where Fisher–Rao information plays the role of the metric tensor. It took decades for the importance of the geometrical structure to be recognised. The present article reviews the structure of the manifold of probability distributions and its applications and shows how the original idea of Professor Rao has been developed and popularised in the wide sense of statistical sciences including AI, signal processing, physical sciences and others.