measurable

commit 66cb8fd8695ca17cc9a9775bb4aebf4173502ce4
parent 2d5933893beac67d65e93928e34000d99ec997d5
Author: Jared Tobin <jared@jtobin.ca>
Date:   Sat, 19 Oct 2013 17:26:29 +1300

Add Num instance, wacky tanh example.

Diffstat:
M
src/Measurable.hs
 | 
14
+++++++++++---
M
tests/Test.hs
 | 
11
++++++++---

2 files changed, 19 insertions(+), 6 deletions(-)
diff --git a/src/Measurable.hs b/src/Measurable.hs
@@ -48,6 +48,14 @@ import Numeric.Integration.TanhSinh
 
 newtype Measure a = Measure { measure :: (a -> Double) -> Double }
 
+instance Num a => Num (Measure a) where
+  (+)         = convolute
+  (-)         = msubtract
+  (*)         = mproduct
+  abs         = id
+  signum mu   = error "fromInteger: not supported for Measures"
+  fromInteger = error "fromInteger: not supported for Measures"
+
 instance Fractional a => Monoid (Measure a) where
   mempty  = identityMeasure
   mappend = convolute
@@ -94,19 +102,19 @@ fromDensity :: (Double -> Double) -> Measure Double
 fromDensity d = Measure $ \f -> quadratureTanhSinh $ liftM2 (*) f d
   where quadratureTanhSinh = result . last . everywhere trap
 
--- | Measure addition is convolution.  
+-- | Measure addition is convolution.  Assumes independence.
 convolute :: Num a => Measure a -> Measure a -> Measure a
 convolute mu nu = Measure $ \f -> measure nu
                             $ \y -> measure mu
                               $ \x -> f (x + y)
 
--- | Measure subtraction. (does this make sense?)
+-- | Measure subtraction.  Assumes independence.
 msubtract :: Num a => Measure a -> Measure a -> Measure a
 msubtract mu nu = Measure $ \f -> measure nu
                             $ \y -> measure mu
                               $ \x -> f (x - y)
 
--- | Measure multiplication. (does this make sense?)
+-- | Measure multiplication.  Assumes independence.
 mproduct :: Num a => Measure a -> Measure a -> Measure a
 mproduct mu nu = Measure $ \f -> measure nu
                            $ \y -> measure mu
diff --git a/tests/Test.hs b/tests/Test.hs
@@ -29,7 +29,7 @@ main = do
 
   let mu  = fromDensity standardNormal
       nu  = fromObservations expSamples
-      rho = convolute (push cos mu) (push sin nu)
+      rho = (push cos mu) * (push sin nu)
       eta = push exp rho
 
   putStrLn $ "mean of normal samples (should be around 0):                " ++ 
@@ -45,7 +45,7 @@ main = do
 
   -- Subtraction of measures?
 
-  let iota = mu `msubtract` mu
+  let iota = mu - mu
   
   putStrLn $ "let X, Y be independent N(0, 1).  mean of X - Y:            " ++
                show (mean iota)
@@ -56,10 +56,15 @@ main = do
 
   let phi  = fromDensity $ genLocationNormal 2
       xi   = fromDensity $ genLocationNormal 3
-      zeta = mproduct phi xi
+      zeta = phi * xi
 
   putStrLn $ "let X ~ N(2, 1), Y ~ N(3, 1). mean of XY (should be 6)      " ++
                show (mean zeta)
   putStrLn $ "let X ~ N(2, 1), Y ~ N(3, 1). variance of XY (should be 14) " ++
                show (variance zeta)
 
+  let alpha = fromDensity $ density $ chiSquared 5
+
+  putStrLn $ "let X ~ N(2, 1), Y ~ chisq(5).  variance of exp (tanh XY)   " ++
+               show (variance . push (exp . tanh) $ mu * nu)
+