Continuations

Last Uncertainty Wednesday, I introduced sensitivity and specificity as measures of how good a test is (or using the language of our framework, how strong a signal is). We derived the following formula P(B | H) = P(B)/P(H) * P(H | B) which relates P(B | H), i.e. the probability of the state of the world being B conditional on receiving signal H, to P(H | B), i.e. the probability of receiving signal H when the world is B, aka the sensitivity of the test. Let’s rewrite this slightly to get a be...

Today’s Uncertainty Wednesday is a further continuation of the PSA Test example, but I got tired of the boring title and wanted to give the post as more, well, specific one. Last Wednesday I wrote that sensitivity and specificity are “widely used to assess the quality of medical tests.” Here are their definitions taken from Wikipedia Sensitivity = probability of a positive test given that the patient has the disease Specificity = probability of a negative test given that the patient is well U...