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##

AIDS test

The AIDS test problem (Example 7 of Section )
is a very standard one. Let us solve it using the Bayes factor:

Writing Bayes' theorem in this way helps a lot in understanding
what is going on. Stated in terms of signal to noise and selectivity
(see problem 1 in Section ),
we are in a situation in which the selectivity of the test
is not enough for the noisy conditions. So in order to be
practically sure that the patient declared `positive' is infected,
with this performance of the analysis,
one needs independent tests, unless the patient belongs to high-risk
classes. For example, a double independent analysis on an average
person would yield
similar^{8.22}
to that obtained in the case where a physician
had a `severe doubt'
(i.e.
HIV)
that the patient could be infected:
We see then that, as discussed several times
(see Section ), the conclusion obtained by
arbitrary probability inversion is equivalent to assuming
uniform priors.

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Giulio D'Agostini
2003-05-15