Question

Suppose the true prevalence of strokes among tmb patients is 20%. What is the predictive value positive of the non-invasive test based on this information?

Answer 1

Put very briefly Bayes theorem interrelates:

the likelihood (a posteriori, after the event) that X is true given Y was observed, P(X|Y),

the likelihood X will be true, (a priori, prior to the event) P(X), and

the likelihood that Y occurs given X is true, P(Y|X).

Where:

P(X|Y) =   P(X)P(Y|X)

                  P( Y)

None of which is very intelligible, nor explains how Bayes theorem is useful, what it assumes, or why its application might be controversial.