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:The American statistician 2007-05, Vol.61 (2), p.132-138
Main Authors: Capotorti, Andrea, Lad, Frank, Sanfilippo, Giuseppe
Format: Article
Language:English
Subjects:
Asbestosis
Coherence
Conditional probabilities
Distribution theory
Exact sciences and technology
Exchangeability
FTP
Fundamental theorem of prevision
Fundamental theorems
General topics
Line segments
Linear programming
Lungs
Mathematics
Matrices
Medical diagnosis
Predictive values
Probabilities
Probability
Probability and statistics
Probability bounds
Probability theory and stochastic processes
Quadratic programming
Radiology
Sciences and techniques of general use
Second opinions
Sensitivity
Specificity
Statistical analysis
Statistical median
Statistics
Theorems
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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:0003-1305
1537-2731
DOI:10.1198/000313007X190943