The difference in the HIV case is that we have an actual population sample that justifies our chosen base rate. That is to say, this isn't a "prior belief", thi

The difference in the HIV case is that we have an actual population sample that justifies our chosen base rate. That is to say, this isn't a "prior belief", this is a measured statistic. It's applicability is precisely because the population of individuals getting an HIV test is random from the general population, from which we have a measured statistic. But the use of the base rate in this case does not justify the usage of informative priors in every case. >Unless applying your screening to a population somehow magically eliminates all variation that previously existed across the populations But it might. The "population" of graduated + passed screening bears no a priori relationship to the population of entering freshmen precisely because this is a non-random sample, orders of magnitude smaller than the original population. Furthermore, there is further evidence that there is no relationship precisely because of the studies that show that entrance exams bare little correlation to college success past the first year.