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module Probability.Distribution.Cauchy where
import Probability.Random
import MCMC
---- cauchy
foreign import bpcall "Distribution:" cauchy_density :: Double -> Double -> Double -> LogDouble
foreign import bpcall "Distribution:" cauchy_quantile :: Double -> Double -> Double -> Double
foreign import bpcall "Distribution:" sample_cauchy :: Double -> Double -> IO Double
cauchy_bounds = realLine
cauchy_effect x = add_move $ sliceSample x cauchy_bounds
data Cauchy = Cauchy Double Double
instance Dist Cauchy where
type Result Cauchy = Double
dist_name _ = "Cauchy"
instance IOSampleable Cauchy where
sampleIO (Cauchy m s) = sample_cauchy m s
instance HasPdf Cauchy where
pdf (Cauchy m s) x = cauchy_density m s x
instance Dist1D Cauchy where
cdf (Cauchy m s) x = undefined
instance ContDist1D Cauchy where
quantile (Cauchy m s) p = cauchy_quantile m s p
instance HasAnnotatedPdf Cauchy where
annotated_densities dist@(Cauchy m s) x = do
in_edge "m" m
in_edge "s" s
return ([pdf dist x],())
instance Sampleable Cauchy where
sample dist@(Cauchy mu sigma) = RanDistribution2 dist cauchy_effect
cauchy m s = Cauchy m s
---- half_cauchy
-- Let's assume that the distribution is (i) continuous and (ii) symmetric around 0.
data Half d = (Result d ~ Double) => Half d
instance Dist d => Dist (Half d) where
type Result (Half d) = Double
dist_name dist = "Half" ++ dist_name dist
instance IOSampleable d => IOSampleable (Half d) where
sampleIO (Half dist) = abs <$> sampleIO dist
-- Ignoring 0 assumes the distribution is continuous.
instance HasPdf d => HasPdf (Half d) where
pdf (Half dist) x | x < 0 = 0
| x == 0 = pdf dist x
| otherwise = pdf dist x + pdf dist (-x)
instance Dist1D d => Dist1D (Half d) where
cdf (Half dist) x | x > 0 = cdf dist x - cdf dist (-x)
| otherwise = 0
-- This assumes that dist is symmetric around 0.
instance ContDist1D d => ContDist1D (Half d) where
quantile (Half dist) p = quantile dist ((p+1)/2)
instance HasPdf d => HasAnnotatedPdf (Half d) where
annotated_densities dist = make_densities $ pdf dist
instance Sampleable d => Sampleable (Half d) where
sample (Half dist) = abs <$> sample dist
half_cauchy s = Half $ cauchy 0 s
|
