Hybrid and Generalized Bayesian Cramér-Rao Inequalities via Information Geometry

04/02/2021

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by   Kumar Vijay Mishra, et al.

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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 Cramér-Rao lower bound (CRLB). This chapter summarizes the recent results which extend this framework to more general Cramér-Rao inequalities. We apply Eguchi's theory to a generalized form of Czsiszár f-divergence to obtain a Riemannian metric that, at once, is used to obtain deterministic CRLB, Bayesian CRLB, and their generalizations.