The Stochastics of Diagnostic and Threat Detection Tests Open Access
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This dissertation addresses some probabilistic and statistical issues that arise in the context of diagnostic tests in medicine, and tests for threat detection in national security. Such tests by their very nature are imperfect, and when perfect are expensive to implement. Diagnostic tests spawn a host of issues, and a coherent way to address these is via a decision-theoretic paradigm. To invoke this paradigm one needs to gain an appreciation of the mathematical architecture of diagnostic tests; the first half of this dissertation is devoted to such an exercise. A byproduct of this exercise, which turns out to be one of the key contributions of this dissertation, is the solution of a long standing problem in diagnostics. The solution is based on the notion of dinegentropy, which is a rarely, if ever, discussed information-theoretic measure. The second half of this dissertation pertains to inferential issues posed by two adversarial parameters in diagnostics. Such issues call for the development of families of bivariate distributions on the unit square with negative dependence and some mathematically desirable closure properties. The development of such a family broadens the scope of this dissertation, and this together with some newly introduced notions of econometric inequalities, constitute two other contributions of this dissertation. The dissertation closes with some ideas for future research. One pertains to the formal elicitation of utilities in diagnostics, while the other pertains to a decision-theoretic approach for designing cost-effective sampling plans for assessing the efficacy of diagnostic tests.