# The Relation Between Bayesian Fisher Information and Shannon Information for Detecting a Change in a Parameter

@article{Clarkson2019TheRB, title={The Relation Between Bayesian Fisher Information and Shannon Information for Detecting a Change in a Parameter}, author={Eric Clarkson}, journal={Journal of the Optical Society of America. A, Optics, image science, and vision}, year={2019}, volume={36 7}, pages={ 1209-1214 } }

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…

## 6 Citations

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

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This work derives an inequality that relates this minimum probability of error to the Bayesian version of the Fisher information, and discovers that an important intermediary in the calculation is the total variation of the posterior probability distribution function for the parameter given the data.

### Bayesian Fisher Information and Detection of a Small Change in a Parameter

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