Pareto分布的Fisher-Rao几何与Jeffreys先验
Fisher-Rao Geometry and Jeffreys Prior for Pareto Distribution
摘要：
本文研究了双参数Pareto分布族的Fisher-Rao几何。证明了它的几何结构与Poincaré上半平面模型等距，并给出了相应的连通度、曲率和测地线的显式表达式.然后将其应用于贝叶斯推理，考虑Jeffreys先验确定的体积形式。此外，还计算了先验分布的后验分布，为Pareto分布的贝叶斯推断提供了一种系统的方法。
英文摘要：
In this paper, we investigate the Fisher-Rao geometry of the two-parameter family of Pareto distribution. We prove that its geometrical structure is isometric to the Poincaré upper half-plane model, and then study the corresponding geometrical features by presenting explicit expressions for connection, curvature and geodesics. It is then applied to Bayesian inference by considering the Jeffreys prior determined by the volume form. In addition, the posterior distribution from the prior is computed, providing a systematic method to the Bayesian inference for Pareto distribution.
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