Alarm.hs

module Alarm where

import Probability (Dist, Probability, choose, (??), (|||))

type PBool = Dist Bool


flp :: Float -> PBool
flp p = choose p True False


-- * Alarm network

-- | prior burglary 1%
b :: PBool
b = flp 0.01

-- | prior earthquake 0.1%
e :: PBool
e = flp 0.001

-- | conditional probability of alarm given burglary and earthquake
a :: Bool -> Bool -> PBool
a b0 e0 =
 case (b0,e0) of
 (False,False) -> flp 0.01
 (False,True) -> flp 0.1
 (True,False) -> flp 0.7
 (True,True) -> flp 0.8


-- | conditional probability of john calling given alarm
j :: Bool -> PBool
j a0 = if a0 then flp 0.8 else flp 0.05

-- | conditional probability of mary calling given alarm
m :: Bool -> PBool
m a0 = if a0 then flp 0.9 else flp 0.1

-- | calculate the full joint distribution
data Burglary = B { 	burglary :: Bool,
			earthquake :: Bool,
			alarm :: Bool,
			john :: Bool,
			mary :: Bool }
	deriving (Eq, Ord, Show)

bJoint :: Dist Burglary
bJoint = do b' <- b 		-- burglary
 e' <- e 		-- earthquake
 a' <- a b' e' 	-- alarm
	 j' <- j a' 		-- john
	 m' <- m a' 		-- mary
	 return (B b' e' a' j' m')

-- | what is the probability that mary calls given that john calls?
pmj :: Probability
pmj = mary ?? bJoint ||| john