  Diagnostic testing is germane to a variety of scenarios in medicine, pandemic
tracking, threat detection, and signal processing. This is an expository paper
with some original results. Here we first set up a mathematical architecture
for diagnostics, and explore its probabilistic underpinnings. Doing so enables
us to develop new metrics for assessing the efficacy of different kinds of
diagnostic tests, and for solving a long standing open problem in diagnostics,
namely, comparing tests when their receiver operating characteristic curves
cross. The first is done by introducing the notion of what we call, a Gini
Coefficient; the second by invoking the information theoretic notion of
dinegentropy. Taken together, these may be seen a contribution to the state of
the art of diagnostics. The spirit of our work could also be relevant to the
much discussed topic of batch testing, where each batch is defined by the
partitioning strategy used to create it. However this possibility has not been
explored here in any detail. Rather, we invite the attention of other
researchers to investigate this idea, as future work.
