commit 9e2088b80c86ce3358227d53c897e45c1316c6ac
parent eb9408953e098ffb4f3592f851c89e65f40d770f
Author: Jared Tobin <jared@jtobin.ca>
Date: Tue, 19 Nov 2013 20:35:21 +1300
Remove old tests.
Diffstat:
| D | tests/Test.hs | | | 130 | ------------------------------------------------------------------------------- |
1 file changed, 0 insertions(+), 130 deletions(-)
diff --git a/tests/Test.hs b/tests/Test.hs
@@ -1,130 +0,0 @@
--- Simple examples that demonstrate some measure-fu.
-
-import Control.Applicative
-import Control.Monad
-import Data.Vector (singleton)
-import Measurable.Core
-import Numeric.SpecFunctions
-import Statistics.Distribution hiding (mean, variance)
-import Statistics.Distribution.Normal
-import Statistics.Distribution.Beta
-import Statistics.Distribution.ChiSquared
-import System.Random.MWC
-import System.Random.MWC.Distributions
-
--- | Some workhorse densities (with respect to Lebesgue measure).
-genNormal m v = density $ normalDistr m v
-genBeta a b = density $ betaDistr a b
-genChiSq d = density $ chiSquared d
-
--- | A binomial density (with respect to counting measure).
-binom p n k
- | n <= 0 = 0
- | k < 0 = 0
- | n < k = 0
- | otherwise = n `choose` k * p ^ k * (1 - p) ^ (n - k)
-
--- | Measures created from densities. Notice that the binomial measure has to
--- be treated differently than the measures absolutely continuous WRT Lebesgue
--- measure.
-normalMeasure m v = fromDensityLebesgue $ genNormal m v
-betaMeasure a b = fromDensityLebesgue $ genBeta a b
-chiSqMeasure d = fromDensityLebesgue $ genChiSq d
-binomMeasure n p = fromDensityCounting (binom p n) [0..n]
-
--- | Sampling functions.
-generateExpSamples n l g = replicateM n (exponential l g)
-generateNormalSamples n m v g = replicateM n (normal m v g)
-
--- | A standard beta-binomial conjugate model. Notice how naturally it's
--- expressed using do-notation!
-betaBinomialConjugate :: Double -> Double -> Int -> Measure Double Int
-betaBinomialConjugate a b n = do
- p <- betaMeasure a b
- binomMeasure n p
-
-main :: IO ()
-main = do
- -- Initialize our PRNG.
- g <- initialize (singleton 42)
-
- -- Generate some samples (in practice we'd usually create measures directly
- -- from samples).
- expSamples <- generateExpSamples 1000 1 g
- normSamples <- generateNormalSamples 1000 0 1 g
-
- -- Create a couple of measures from those.
- let observedExpMeasure = fromObservations expSamples
- observedNormalMeasure = fromObservations normSamples
-
- putStrLn "X ~ N(0, 1)"
- putStrLn "Y ~ empirical (observed from exponential(1))"
- putStrLn "Z ~ empirical (observed from N(0, 1))"
- putStrLn "W ~ ChiSquared(5)"
- putStrLn ""
-
- -- We can mingle our empirical measures with those created directly from
- -- densities. We can literally just add measures together (there's a
- -- convolution happening under the hood).
-
- let mu = normalMeasure 0 1 + observedExpMeasure
- putStrLn $ "E(X + Y): " ++ show (expectation mu)
-
- -- We can create pushforward/image measures by.. pushing functions onto
- -- measures.
- --
- -- The pushforward operator happens to be trusty old 'fmap', (as infix, <$>).
-
- let nu = (cos <$> normalMeasure 0 1) * (sin <$> observedNormalMeasure)
- putStrLn $ "E(cos X * sin Z): " ++ show (expectation nu)
-
- let eta = exp <$> nu
- putStrLn $ "E[e^(cos X * sin Z)]: " ++ show (expectation eta)
-
- -- At present the complexity of each Measure operation seems to *explode*, so
- -- you can't do more than a few of them without your machine locking up. I
- -- have to look into what could be done to make this reasonably efficient.
- -- But hey, experiments and such..
-
- let zeta = (exp . tanh) <$> (chiSqMeasure 5 * normalMeasure 0 1)
- putStrLn $ "E[e^(tanh (X * W))]: " ++ show (expectation zeta)
-
- putStrLn ""
-
- -- We can do probability by just taking the expectation of an indicator
- -- function, and there's a built-in cumulative distribution function.
- --
- -- P(X < 0) for example. It should be 0.5, but there is some error due to
- -- quadrature.
-
- putStrLn $ "P(X < 0): " ++ show (cdf (normalMeasure 0 1) 0)
-
- -- Everyone knows that for X ~ N(0, 1), P(0 < X < 1) is about 0.341..
-
- putStrLn $ "P(0 < X < 1): "
- ++ show (expectation $ 0 `to` 1 <$> normalMeasure 0 1)
-
- putStrLn ""
-
- -- The coolest trick of all is that monadic bind is Bayesian inference.
- -- Getting posterior predictive expectations & probabilities is thus really
- -- declarative.
-
- putStrLn "X | p ~ binomial(10, p)"
- putStrLn "p ~ beta(1, 4)"
-
- let phi = fromIntegral <$> betaBinomialConjugate 1 4 10
-
- putStrLn $ "E(X) (unconditional): "
- ++ show (expectation phi)
-
- putStrLn $ "P(X == 5): "
- ++ show (expectation $ 5 `to` 5 <$> phi)
-
- putStrLn $ "P(1 <= X <= 5): "
- ++ show (expectation $ 1 `to` 5 <$> phi)
-
- putStrLn $ "var(X): " ++ show (variance phi)
-
- -- Lots of kinks to be worked out, but this is a cool concept.
-
