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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:
 HIVPositive

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

HIVPositive   Positive

similar8.22 to that obtained in the case where a physician had a severe doubt' (i.e. HIV) that the patient could be infected:

HIVPositiveHIV

We see then that, as discussed several times (see Section ), the conclusion obtained by arbitrary probability inversion is equivalent to assuming uniform priors.

Next: Gold/silver ring problem Up: Solution to some problems Previous: Solution to some problems   Contents
Giulio D'Agostini 2003-05-15