{- 
  ESIV - Expected Site Information Value from SNPs

  Information value is the log odds for each allele, times the probablity of observing it
  not using any prior (or prior is 50/50)

  Biallelic:
  abs (avg(p1,p2)*log(p1/p2) - (1-avg(p1,p2))*log((1-p1)/(1-p2))
-}

module ESIV where

import Count
import AgrestiCoull

-- given a z-score `z` for confidence interval, and a
-- minimum error rate `epsilon`, calculate the ESIV conservatively
-- using the conf interval boundaries as frequencies.
esiv :: Double -> Double -> Counts -> Counts -> Double
esiv z epsilon c1 c2 = let
  t1 = covC c1
  t2 = covC c2
  in sum [abs $ esiv1 z epsilon (x,t1-x) (y,t2-y) | (x,y) <- zip (toList c1) (toList c2)]

esiv1 :: Double -> Double -> (Int, Int) -> (Int, Int) -> Double
esiv1 z eps (a1,b1) (a2,b2) 
    | j1+eps<i2 = esiv_score (j1+eps/2) (i2-eps/2)
    | i1>j2+eps = esiv_score (i1-eps/2) (j2+eps/2) 
    | otherwise     = 0
        where
          (i1,j1) = confidenceInterval z a1 b1
          (i2,j2) = confidenceInterval z a2 b2

esiv_score :: Double -> Double -> Double
esiv_score p1 p2 = (p1+p2)/2*logBase 2 (p1/p2)