Abstract

We derive a connection between the performance of statistical estimators and the performance of the ideal observer on related detection tasks. Specifically, we show how the task-specific Shannon information for the task of detecting a change in a parameter is related to the Fisher information and to the Bayesian Fisher information. We have previously shown that this Shannon information is related via an integral transform to the minimum probability of error on the same task. We then outline a circle of relations starting with this minimum probability of error and ensemble mean squared error for an estimator via the Ziv–Zakai inequality, then the ensemble mean squared error and the Bayesian Fisher information via the van Trees inequality, and finally the Bayesian Fisher information and the Shannon information for a detection task via the work presented here.

© 2019 Optical Society of America

Probability of error for detecting a change in a parameter and Bayesian Fisher information

Eric Clarkson
J. Opt. Soc. Am. A 37(2) 174-181 (2020)

Shannon information for joint estimation/detection tasks and complex imaging systems

Eric Clarkson and Johnathan B. Cushing
J. Opt. Soc. Am. A 33(3) 286-292 (2016)

Shannon information and receiver operating characteristic analysis for multiclass classification in imaging

Eric Clarkson and Johnathan B. Cushing
J. Opt. Soc. Am. A 33(5) 930-937 (2016)

Shannon information and ROC analysis in imaging

Eric Clarkson and Johnathan B. Cushing
J. Opt. Soc. Am. A 32(7) 1288-1301 (2015)

Fisher information and surrogate figures of merit for the task-based assessment of image quality

Eric Clarkson and Fangfang Shen
J. Opt. Soc. Am. A 27(10) 2313-2326 (2010)