{- |
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?
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Enum)pDisease ,pFalseNegative ,pFalsePositive ::Probability pDisease :: Probability
pDisease =Probability
0.001pFalseNegative :: Probability
pFalseNegative =Probability
0.01pFalsePositive :: Probability
pFalsePositive =Probability
0.01dist ::Dist (State ,Finding )dist :: Dist (State, Finding)
dist =doState
s <-forall prob a. Num prob => prob -> a -> a -> T prob a
Dist.choose Probability
pDisease State
Ill State
Healthy Finding
f <-caseState
s ofState
Ill ->forall prob a. Num prob => prob -> a -> a -> T prob a
Dist.choose Probability
pFalseNegative Finding
Negative Finding
Positive State
Healthy ->forall prob a. Num prob => prob -> a -> a -> T prob a
Dist.choose Probability
pFalsePositive Finding
Positive Finding
Negative forall (m :: * -> *) a. Monad m => a -> m a
return(State
s ,Finding
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 :: Dist (State, Finding)
distAlt =do(State
s ,T Probability Finding
fr )<-forall prob a. Num prob => prob -> a -> a -> T prob a
Dist.choose Probability
pDisease (State
Ill ,forall prob a. Num prob => prob -> a -> a -> T prob a
Dist.choose Probability
pFalseNegative Finding
Negative Finding
Positive )(State
Healthy ,forall prob a. Num prob => prob -> a -> a -> T prob a
Dist.choose Probability
pFalsePositive Finding
Positive Finding
Negative )Finding
f <-T Probability Finding
fr forall (m :: * -> *) a. Monad m => a -> m a
return(State
s ,Finding
f )p ::Probability p :: Probability
p =(forall a. Eq a => a -> Event a
Dist.just State
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dist