It is often useful to know what percentage of units with positive tests is actually infected. This is a property of the site, more than it is a property of the particular screening test used. This quantity g is called the predictive value of a positive test. However, in practice, no such procedure is absolutely perfect. In most circumstances the presence of antibodies corresponds to presence of the virus itself.
Blood banks use pre-donation questionnaires to try to avoid accepting such units of blood.
In Session 2, we shall see that if reliable estimates of the conditional probabilities g and d were available, they would provide the basis for an improved estimate of p . In fact, this possibility provides a simple illustration of the important estimation technique known as the Gibbs sampler. Suppose that a screening test for a particular disease is to be given to all available members of a population. The goal is to detect the disease early enough that a cure is still possible. This test is relatively cheap, convenient, and safe.