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module Probability.Distribution.RecDist where
import Probability.Random
import Control.Monad.Fix
{- NOTE: Recursive distributions.
We can *sample* from recursive distributions without actually creating a distribution object:
> do
> ...
> rec let distFor node = case (parent tree node) of Just p -> normal (xs!p) (sigma^2); Nothing -> rootDist
> xs <- sample $ independent [ distFor node | node <- nodes ]
> ...
This is equivalent to:
> do
> ...
> distFunc xs = independent [distFor node | node <- nodes ] where
> distFor node = case (parent tree node) of Just p -> normal (xs!p) (sigma^2); Nothing -> rootDist
> xs <- sample $ recDist distFunc
> ...
But its we can't *observe* from the distribution unless we specify the distribution function.
> do
> ...
> distFunc xs = independent [distFor node | node <- nodes ] where
> distFor node = case (parent tree node) of Just p -> normal (xs!p) (sigma^2); Nothing -> rootDist
> observe xs (recDist distFunc)
> ...
In PGMs, perhaps we could write something like
> x ~ mkArray(nodes, node, normal( if node == root then rootMean else x[parent(node)], sigma^2))
In strict PPLs, it might be possible to generate values at nodes of the tree by doing something like:
> xRoot ~ rootDist
> xsLeft ~ generate(leftSubtree, xRoot)
> xsRight ~ generate(rightSubtree, xRoot)
> xs = {root:xRoot} + xsLeft + xsRight
This should work fine for purely sampling-based methods. But for MCMC methods we often want to compute
the prior density of the xs, and then it seems like this would not work.
-}
data RecDist d = RecDist (Result d->d)
instance Dist d => Dist (RecDist d) where
type Result (RecDist d) = Result d
instance (Dist d, IOSampleable d) => IOSampleable (RecDist d) where
sampleIO (RecDist f) = mfix (\value -> sampleIO (f value))
instance (Dist d, HasPdf d) => HasPdf (RecDist d) where
pdf (RecDist f) x = pdf (f x) x
instance (Dist d, HasAnnotatedPdf d) => HasAnnotatedPdf (RecDist d) where
type DistProperties (RecDist d) = DistProperties d
annotated_densities (RecDist f) x = annotated_densities (f x) x
instance (Dist d, Sampleable d) => Sampleable (RecDist d) where
sample (RecDist f) = mfix (\value -> sample (f value))
recDist = RecDist
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