Reassessing Accuracy Rates of Median Decisions

We show how Bruno de Finetti's fundamental theorem of prevision has computable applications in statistical problems that involve only partial information. Specifically, we assess accuracy rates for median decision procedures used in the radiological diagnosis of asbestosis. Conditional exchange...

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Bibliographic Details
Published in:arXiv.org 2017-09
Main Authors: Capotorti, Andrea, Lad, Frank, Sanfilippo, Giuseppe
Format: Article
Language:English
Subjects:
Asbestos
Asbestosis
Decision theory
Median (statistics)
Quadratic programming
Online Access:Get full text
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Summary:We show how Bruno de Finetti's fundamental theorem of prevision has computable applications in statistical problems that involve only partial information. Specifically, we assess accuracy rates for median decision procedures used in the radiological diagnosis of asbestosis. Conditional exchangeability of individual radiologists' diagnoses is recognized as more appropriate than independence which is commonly presumed. The FTP yields coherent bounds on probabilities of interest when available information is insufficient to determine a complete distribution. Further assertions that are natural to the problem motivate a partial ordering of conditional probabilities, extending the computation from a linear to a quadratic programming problem.
ISSN:2331-8422
DOI:10.48550/arxiv.1709.05637