commit0535107aa058300512440de6c6a6873731fc3ac4parenteb72ec258bc003a528a62f780c10612a0580f71bAuthor:Jared Tobin <jared@jtobin.ca>Date:Fri, 25 Oct 2013 08:41:06 +1300 Replace measure/measureT with integrate/integrateT.Diffstat:

M | src/Examples.hs | | | 6 | ++++++ |

M | src/Measurable/Core.hs | | | 37 | ++++++++++++++----------------------- |

2 files changed, 20 insertions(+), 23 deletions(-)diff --git a/src/Examples.hs b/src/Examples.hs@@ -34,6 +34,12 @@ normalMeasure m v = fromDensityLebesgue $ genNormal m v betaMeasure a b = fromDensityLebesgue $ genBeta a b chiSqMeasure d = fromDensityLebesgue $ genChiSq d +-- | And a measure represented directly over a sampler. +altBetaMeasure epochs a b g = do + bs <- lift $ replicateM epochs (genContVar (betaDistr a b) g) + fromObservationsT bs + + -- | A standard beta-binomial conjugate model. Notice how naturally it's -- expressed using do-notation! betaBinomialConjugate :: Double -> Double -> Int -> Measure Double Intdiff --git a/src/Measurable/Core.hs b/src/Measurable/Core.hs@@ -12,16 +12,16 @@ import qualified Data.Set as Set import Data.Traversable hiding (mapM) import Numeric.Integration.TanhSinh --- | A measure is represented as a continuation. +-- | A integrate is represented as a continuation. type Measure r a = Cont r a type MeasureT r m a = ContT r m a --- | A more measure-y alias for runCont. -measure :: Measure r a -> (a -> r) -> r -measure = runCont +-- | A more appropriate version of runCont. +integrate :: (a -> r) -> Measure r a -> r +integrate = flip runCont -measureT :: MeasureT r m a -> (a -> m r) -> m r -measureT = runContT +integrateT :: Monad m => (a -> r) -> MeasureT r m a -> m r +integrateT f = (`runContT` (return . f)) -- | Things like convolution are trivially expressed by lifted arithmetic -- operators. @@ -31,9 +31,9 @@ instance (Monad m, Num a) => Num (ContT r m a) where (*) = liftA2 (*) abs = id signum = error "signum: not supported for Measures" - fromInteger = error "fromInteger: not supported for measures" + fromInteger = error "fromInteger: not supported for integrates" --- | Create a measure from a density w/respect to counting measure. +-- | Create a integrate from a density w/respect to counting integrate. fromDensityCounting :: (Num r, Functor f, Foldable f) => (a -> r) @@ -50,7 +50,7 @@ fromDensityCountingT fromDensityCountingT p support = ContT $ \f -> fmap Foldable.sum . traverse (liftA2 (liftA2 (*)) f (return . p)) $ support --- | Create a measure from a density w/respect to Lebesgue measure. +-- | Create a integrate from a density w/respect to Lebesgue integrate. -- -- NOTE The quality of this implementation depends entirely on the underlying -- quadrature routine. As we're presently using the @@ -63,7 +63,7 @@ fromDensityLebesgue :: (Double -> Double) -> Measure Double Double fromDensityLebesgue d = cont $ \f -> quadratureTanhSinh $ liftA2 (*) f d where quadratureTanhSinh = result . last . everywhere trap --- | Create a measure from observations sampled from some distribution. +-- | Create a integrate from observations sampled from some distribution. fromObservations :: (Functor f, Foldable f, Fractional r) => f a @@ -76,14 +76,6 @@ fromObservationsT -> MeasureT r m a fromObservationsT = ContT . flip weightedAverageM --- | Integration of a function against a measure is just running a --- continuation. -integrate :: (a -> r) -> Measure r a -> r -integrate = flip measure - -integrateT :: Monad m => (a -> r) -> MeasureT r m a -> m r -integrateT f = (`measureT` (return . f)) - -- | Expectation is integration against the identity function. expectation :: Measure r r -> r expectation = integrate id @@ -93,14 +85,13 @@ expectationT = integrateT id -- | The variance is obtained by integrating against the usual function. variance :: Num r => Measure r r -> r -variance mu = measure mu (^ 2) - expectation mu ^ 2 +variance mu = integrate (^ 2) mu - expectation mu ^ 2 varianceT :: (Monad m, Num r) => MeasureT r m r -> m r -varianceT mu = liftM2 (-) (measureT mu (return . (^ 2))) - (liftM (^ 2) (expectationT mu)) +varianceT mu = liftM2 (-) (integrateT (^ 2) mu) (liftM (^ 2) (expectationT mu)) --- | The measure of the underlying space. This is trivially 1 for any --- probability measure. +-- | The integrate of the underlying space. This is trivially 1 for any +-- probability integrate. volume :: Num r => Measure r r -> r volume = integrate (const 1)