Bayes - Medreonet

P(hypothesis) = probability of the hypothesis being true before
we collect and analyze the set of data = PR prevalence of
infection
We test the animal and get a positive result. This is the data
collection.
P(data | hypothesis) = Likelihood function obtained after the
experiment = probability of a positive test result (the data we
got) given that the animal is infected (that's our hypothesis) = it
is the Sensitivity of our diagnostic test!
P(data) = Probability of all possible cases giving those data. A
positive animal can be a either True positive or a False positive.
Probability of being a True positive is PR times Sensitivity of the test
Probability of being a False positive is (1-PR) times (1-Specificity of the
test)
so, the Predictive value of a positive result to a diagnostic
test, i.e. the probability of our positive animal being infected is:
P
( )
( hypothesis)
⋅ P(
data / hypothesis)
PR ⋅ Sensitivity
P hypothesis | data =
=
P( data) PR ⋅ Sensitivity + ( 1−
PR) ⋅( 1−
Specificity)