English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The relative $\alpha$-entropy is the R\'enyi analog of relative entropy andarises prominently in information-theoretic problems. Recent informationgeometric investigations on this quantity have enabled the generalization ofthe Cram\'{e}r-Rao inequality, which provides a lower bound for the variance ofan estimator of an escort of the underlying parametric probabilitydistribution. However, this framework remains unexamined in the Bayesianframework. In this paper, we propose a general Riemannian metric based onrelative $\alpha$-entropy to obtain a generalized Bayesian Cram\'{e}r-Raoinequality. This establishes a lower bound for the variance of an unbiasedestimator for the $\alpha$-escort distribution starting from an unbiasedestimator for the underlying distribution. We show that in the limiting casewhen the entropy order approaches unity, this framework reduces to theconventional Bayesian Cram\'{e}r-Rao inequality. Further, in the absence ofpriors, the same framework yields the deterministic Cram\'{e}r-Rao inequality.

Generalized Bayesian Cram\'{e}r-Rao Inequality via Information Geometry of Relative $\alpha$-Entropy