2010/10/07 by Sudhakar Prasad, Prasad, Sudhakar · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Applications (stat.AP) #FOS: Computer and information sciences #Information Theory (cs.IT) #Neural Networks and Applications #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1010.1508
openalex publication_date 2010/10/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
I present several new relations between mutual information (MI) and statistical estimation error for a system that can be regarded simultaneously as a communication channel and as an estimator of an input parameter. I first derive a second-order result between MI and Fisher information (FI) that is valid for sufficiently narrow priors, but arbitrary channels. A second relation furnishes a lower bound on the MI in terms of the minimum mean-squared error (MMSE) on the Bayesian estimation of the input parameter from the channel output, one that is valid for arbitrary channels and priors. The existence of such a lower bound, while extending previous work relating the MI to the FI that is valid only in the asymptotic and high-SNR limits, elucidates further the fundamental connection between information and estimation theoretic measures of fidelity. The remaining relations I present are inequalities and correspondences among MI, FI, and MMSE in the presence of nuisance parameters.