@inproceedings{73e95526523b48b092fb103a445e3e8f,
title = "Bayesian Fisher Information and Detection of a Small Change in a Parameter",
abstract = "We have previously shown how the Bayesian Fisher Information (BFI) is related to the average of the Minimum Probability of Error (MPE) for the task of detecting a small change in a parameter. The prior probabilities for the two hypotheses corresponding to two nearby values of the parameter are derived from the prior distribution on the parameter, as they are for the Ziv-Zakai inequality. The average in this result and others to be discussed is performed over the parameter values using the prior. We extend this result to the case where a cost function is assigned to the detection task. In this case we determine the lowest order approximation of the average of the Bayesian Risk for the detection task. We have shown that there is a similar relation between the average Shannon Information (SI) for this detection task and the BFI, and that there is an integral relation between SI for any detection task and the MPE for that task. We will show the Bayesian perspective on this last result, and how these two results about SI are related.",
keywords = "Fisher information, ROC analysis, Shannon information, information theory",
author = "Eric Clarkson",
note = "Funding Information: ACKNOWLEDGEMENTS This material is based upon work supported by the National Institutes of Health under R01-EB000803 and P41-EB002035. Funding Information: This work was funded by the NIBIB Publisher Copyright: {\textcopyright} 2020 IEEE.; 54th Annual Conference on Information Sciences and Systems, CISS 2020 ; Conference date: 18-03-2020 Through 20-03-2020",
year = "2020",
month = mar,
doi = "10.1109/CISS48834.2020.1570625392",
language = "English (US)",
series = "2020 54th Annual Conference on Information Sciences and Systems, CISS 2020",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
booktitle = "2020 54th Annual Conference on Information Sciences and Systems, CISS 2020",
}