{- |
You take part in a screening test for a disease
that you have with a probability 'pDisease'.
The test can fail in two ways:
If you are ill,
the test says with probability 'pFalseNegative' that you are healthy.
If you are healthy,
it says with probability 'pFalsePositive' that you are ill.
Now consider the test is positive -
what is the probability that you are indeed ill?
-}moduleNumeric.Probability.Example.DiagnosiswhereimportqualifiedNumeric.Probability.Distribution asDistimportNumeric.Probability.Distribution ((?? ),(?=<< ),)typeProbability =RationaltypeDist a =Dist.T Probability a dataState =Healthy |Ill deriving(Eq,Ord,Show,Enum)dataFinding =Negative |Positive deriving(Eq,Ord,Show,Enum)pDisease,pFalseNegative,pFalsePositive::Probability pDisease =0.001pFalseNegative =0.01pFalsePositive =0.01dist::Dist (State ,Finding )dist =dos <-Dist.choose pDisease Ill Healthy f <-cases ofIll ->Dist.choose pFalseNegative Negative Positive Healthy ->Dist.choose pFalsePositive Positive Negative return(s ,f ){- |
Alternative way for computing the distribution.
It is usually more efficient because we do not need to switch on the healthy state.
-}distAlt::Dist (State ,Finding )distAlt =do(s ,fr )<-Dist.choose pDisease (Ill ,Dist.choose pFalseNegative Negative Positive )(Healthy ,Dist.choose pFalsePositive Positive Negative )f <-fr return(s ,f )p::Probability p =(Dist.just Ill .fst)?? (Dist.just Positive .snd)?=<< dist