Bayesian Fisher Information, Shannon Information, and ROC Analysis for Classification Tasks

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 deriv...

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Bibliographic Details
Main Author: Clarkson, Eric
Format: Conference Proceeding
Language:English
Subjects:
Bayes methods
Computers
Cost function
Estimation
Fisher information
Imaging
information theory
ROC analysis
Shannon information
Task analysis
Online Access:Request full text
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Summary: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.
ISSN:2576-2303
DOI:10.1109/IEEECONF51394.2020.9443339