Cramer-Rao bound analog of Bayes rule

TL;DR

This paper explores a generalized property of the Cramer-Rao bound that captures parameter interdependencies in vector models, extending previous results beyond additive noise and illustrating with examples.

Contribution

It introduces a CRB analog to Bayes' rule applicable to more general models and vector parameters, broadening the scope of existing bounds.

Findings

General property of CRB for vector parameters

Extension beyond additive noise models

Illustrative examples demonstrating the CRB analog

Abstract

In this lecture note, we show a general property of the Cramer-Rao bound (CRB) that quantifies the interdependencies between the parameters in a vector. The presented result is valid for more general models than the additive noise model and also generalizes previous results to vector parameters. The CRB analog to Bayes' rule will be illustrated via two examples.