Hybrid and Generalized Bayesian Cram\'{e}r-Rao Inequalities via Information Geometry

• URL: http://arxiv.org/abs/2104.01061v1
• Date: Fri, 2 Apr 2021 14:21:49 GMT
• Title: Hybrid and Generalized Bayesian Cram\'{e}r-Rao Inequalities via Information Geometry
• Authors: Kumar Vijay Mishra and M. Ashok Kumar
• Abstract summary: This chapter summarizes the recent results which extend this framework to more general Cram'er-Rao inequalities. We apply Eguchi's theory to a generalized form of Czsisz'ar $f$-divergence.
• Score: 15.33401602207049
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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