Information geometry is the study of statistical models from a Riemannian geometric point of view. The Fisher information matrix plays the role of a Riemannian metric in this framework. This tool helps us obtain Cram\'{e}r-Rao lower bound (CRLB). This chapter summarizes the recent results which extend this framework to more general Cram\'{e}r-Rao inequalities. We apply Eguchi's theory to a generalized form of Czsisz\'ar $f$-divergence to obtain a Riemannian metric that, at once, is used to obtain deterministic CRLB, Bayesian CRLB, and their generalizations.

翻译：信息几何学是从里曼语几何角度对统计模型进行研究的。 渔业信息矩阵在这个框架中扮演了里曼语测量仪的作用。 这个工具帮助我们获得Cram\\ {e}r- Rao 较低的约束( CRLB) 。 本章总结了将这一框架扩大到更普遍的Cram\ {e}r- Rao不平等的最新结果。 我们将Eguchi的理论应用到一种普遍形式的Czsisz\ ar $f$- divegence 上, 以获得一种里曼语测量仪, 立即用于获得确定性的 CRLB、 Bayesian CRLB 及其概括性。