Rationing, errors and mammogram math
nytimes.com
nytimes.com
Using conditional probability, or bayes theorem to calculate a conditional probabilitiy, does not make something bayesian analysis.
I haven't read the original report (it's on my list) but what is presented in this article isn't really anything except probability. It would be bayesian if they put a distribution on the proportion of people that have a "certain cancer."
He uses the mammogram statistics as an example to explain Bayes' Theorem.
This is the kind of example that we can give to grade school kids and have them work it out. It would be a great "ah ha!" moment for some of them.