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Paper Detail

Paper Title A Family of Bayesian Cramer-Rao Bounds, and Consequences for Log-Concave Priors
Paper IdentifierFR2.R5.1
Authors Efe Aras, Kuan-Yun Lee, Ashwin Pananjady, Thomas Courtade, University of California, Berkeley, United States
Session Information Theory for Estimation
Location Saint Victor, Level 3
Session Time Friday, 12 July, 11:40 - 13:00
Presentation Time Friday, 12 July, 11:40 - 12:00
Manuscript  Click here to download the manuscript
Abstract Under minimal regularity assumptions, we establish a family of information-theoretic Bayesian Cramer-Rao bounds, indexed by probability measures that satisfy a logarithmic Sobolev inequality. This family includes as a special case the known Bayesian Cramer-Rao bound (or van Trees inequality), and its less widely known entropic improvement due to Efroimovich. For the setting of a log-concave prior, we obtain a Bayesian Cramer-Rao bound which holds for any (possibly biased) estimator and, unlike the van Trees inequality, does not depend on the Fisher information of the prior.