Abstract

The van Trees inequality relates the ensemble mean squared error of an estimator to a Bayesian version of the Fisher information. The Ziv-Zakai inequality relates the ensemble mean squared error of an estimator to the minimum probability of error for the task of detecting a change in the parameter. In this work we complete this circle by deriving an inequality that relates this minimum probability of error to the Bayesian version of the Fisher information. We discuss this result for both scalar and vector parameters. In the process we discover that an important intermediary in the calculation is the total variation of the posterior probability distribution function for the parameter given the data. This total variation is of interest in its own right since it may be easier to compute than the other figures of merit discussed here.

© 2020 Optical Society of America

Relation between Bayesian Fisher information and Shannon information for detecting a change in a parameter

Eric Clarkson
J. Opt. Soc. Am. A 36(7) 1209-1214 (2019)

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

Eric Clarkson and Fangfang Shen
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Quantifying the loss of information from binning list-mode data

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Using Fisher information to approximate ideal-observer performance on detection tasks for lumpy-background images

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Asymptotic ideal observers and surrogate figures of merit for signal detection with list-mode data

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