module Numeric.Learn where
import Data.Ratio
import qualified Data.Map as Map
type Prob = Ratio Integer
newtype Distro a = Distro { runDistro :: Map.Map a Prob }
deriving (Eq,Ord,Read,Show)
data Result = Positive | Negative
uniformPDF :: (Ord k) => [k] -> Distro k
uniformPDF xs = Distro $ foldl (\thisMap elt ->
Map.insert elt (1 % len) thisMap) Map.empty xs
where len = fromIntegral (length xs)
uniformPrior :: Integer -> Distro Prob
uniformPrior granularity = uniformPDF xs
where xs = map ( % granularity) [0..granularity]
singleCoin :: Distro Prob -> Result -> Distro Prob
singleCoin (Distro probs) result = Distro $ Map.mapWithKey (update result) probs
where update Positive = \pE1gHi pHi -> (pE1gHi / pE1) * pHi
update Negative = \pE1gHi pHi -> ((1 pE1gHi) / (1 pE1)) * pHi
pE1 = Map.foldWithKey (\k a acc -> acc + k * a) 0 probs
coins :: Distro Prob -> Int -> Int -> Distro Prob
coins distro heads tails = foldl (\thisDistro result ->
singleCoin thisDistro result) distro results
where results = (take heads $ repeat Positive) ++ (take tails $ repeat Negative)
listify :: Distro k -> [(k, Prob)]
listify = Map.toList . runDistro