Reassessing Accuracy Rates of Median Decisions

TL;DR

This paper applies de Finetti's fundamental theorem of prevision to evaluate the accuracy of median decision procedures in radiological diagnosis, emphasizing the importance of conditional exchangeability over independence.

Contribution

It introduces a novel application of the FTP to derive bounds on diagnostic accuracy, accounting for partial information and conditional exchangeability among radiologists.

Findings

Coherent bounds on accuracy rates are derived using FTP.

Conditional exchangeability is more appropriate than independence.

Extension from linear to quadratic programming improves bounds computation.

Abstract

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.