Numeric.Probability.Example.Diagnosis

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?

Documentation

type Probability = Rational

type Dist a = T Probability a

data State

Constructors

Healthy

Ill

Instances

Enum State

Defined in Numeric.Probability.Example.Diagnosis

Methods

succ :: State -> State

pred :: State -> State

toEnum :: Int -> State

fromEnum :: State -> Int

enumFrom :: State -> [State]

enumFromThen :: State -> State -> [State]

enumFromTo :: State -> State -> [State]

enumFromThenTo :: State -> State -> State -> [State]

Show State

Defined in Numeric.Probability.Example.Diagnosis

Methods

showsPrec :: Int -> State -> ShowS

show :: State -> String

showList :: [State] -> ShowS

Eq State

Defined in Numeric.Probability.Example.Diagnosis

Methods

(==) :: State -> State -> Bool

(/=) :: State -> State -> Bool

Ord State

Defined in Numeric.Probability.Example.Diagnosis

Methods

compare :: State -> State -> Ordering

(<) :: State -> State -> Bool

(<=) :: State -> State -> Bool

(>) :: State -> State -> Bool

(>=) :: State -> State -> Bool

max :: State -> State -> State

min :: State -> State -> State

data Finding

Constructors

Negative

Positive

Instances

Enum Finding

Defined in Numeric.Probability.Example.Diagnosis

Methods

succ :: Finding -> Finding

pred :: Finding -> Finding

toEnum :: Int -> Finding

fromEnum :: Finding -> Int

enumFrom :: Finding -> [Finding]

enumFromThen :: Finding -> Finding -> [Finding]

enumFromTo :: Finding -> Finding -> [Finding]

enumFromThenTo :: Finding -> Finding -> Finding -> [Finding]

Show Finding

Defined in Numeric.Probability.Example.Diagnosis

Methods

showsPrec :: Int -> Finding -> ShowS

show :: Finding -> String

showList :: [Finding] -> ShowS

Eq Finding

Defined in Numeric.Probability.Example.Diagnosis

Methods

(==) :: Finding -> Finding -> Bool

(/=) :: Finding -> Finding -> Bool

Ord Finding

Defined in Numeric.Probability.Example.Diagnosis

Methods

compare :: Finding -> Finding -> Ordering

(<) :: Finding -> Finding -> Bool

(<=) :: Finding -> Finding -> Bool

(>) :: Finding -> Finding -> Bool

(>=) :: Finding -> Finding -> Bool

max :: Finding -> Finding -> Finding

min :: Finding -> Finding -> Finding

pDisease :: Probability

pFalseNegative :: Probability

pFalsePositive :: Probability

dist :: Dist (State, Finding)

distAlt :: Dist (State, Finding)

Alternative way for computing the distribution. It is usually more efficient because we do not need to switch on the healthy state.

p :: Probability