The incidence of the disease may be different for different populations while the test manufacturer may not know where and on which patients the test is going to be used.
Also, serious diseases are often tested multiple times by different tests. What would a Bayes-ignorant doctor do with positives from tests A and B which are accompanied with information: “when test A is positive, the patient has 90% chance of having the syndrome” and “when test B is positive, the patient has 75% chance of having the syndrome”? I’d guess most statistically illiterate doctors would go with the estimate of the test done last.
The incidence of the disease may be different for different populations while the test manufacturer may not know where and on which patients the test is going to be used.
Also, serious diseases are often tested multiple times by different tests. What would a Bayes-ignorant doctor do with positives from tests A and B which are accompanied with information: “when test A is positive, the patient has 90% chance of having the syndrome” and “when test B is positive, the patient has 75% chance of having the syndrome”? I’d guess most statistically illiterate doctors would go with the estimate of the test done last.