MH.hs

{-# LANGUAGE ImportQualifiedPost #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# OPTIONS_GHC -Wno-name-shadowing #-}

module Control.Monad.Bayes.Inference.Lazy.MH where

import Control.Monad.Bayes.Class (Log (ln))
import Control.Monad.Bayes.Sampler.Lazy
  ( Sampler (runSampler),
    Tree (..),
    Trees (..),
    randomTree,
  )
import Control.Monad.Bayes.Weighted (Weighted, weighted)
import Control.Monad.Extra (iterateM)
import Control.Monad.State.Lazy (MonadState (get, put), runState)
import System.Random (RandomGen (split), getStdGen, newStdGen)
import System.Random qualified as R

mh :: forall a. Double -> Weighted Sampler a -> IO [(a, Log Double)]
mh p m = do
  -- Top level: produce a stream of samples.
  -- Split the random number generator in two
  -- One part is used as the first seed for the simulation,
  -- and one part is used for the randomness in the MH algorithm.
  g <- newStdGen >> getStdGen
  let (g1, g2) = split g
  let t = randomTree g1
  let (x, w) = runSampler (weighted m) t
  -- Now run step over and over to get a stream of (tree,result,weight)s.
  let (samples, _) = runState (iterateM step (t, x, w)) g2
  -- The stream of seeds is used to produce a stream of result/weight pairs.
  return $ map (\(_, x, w) -> (x, w)) samples
  where
    --   where
    {- NB There are three kinds of randomness in the step function.
    1. The start tree 't', which is the source of randomness for simulating the
    program m to start with. This is sort-of the point in the "state space".
    2. The randomness needed to propose a new tree ('g1')
    3. The randomness needed to decide whether to accept or reject that ('g2')
    The tree t is an argument and result,
    but we use a state monad ('get'/'put') to deal with the other randomness '(g,g1,g2)' -}

    -- step :: RandomGen g => (Tree, a, Log Double) -> State g (Tree, a, Log Double)
    step (t, x, w) = do
      -- Randomly change some sites
      g <- get
      let (g1, g2) = split g
      let t' = mutateTree p g1 t
      -- Rerun the model with the new tree, to get a new
      -- weight w'.
      let (x', w') = runSampler (weighted m) t'
      -- MH acceptance ratio. This is the probability of either
      -- returning the new seed or the old one.
      let ratio = w' / w
      let (r, g2') = R.random g2
      put g2'
      if r < min 1 (exp $ ln ratio)
        then return (t', x', w')
        else return (t, x, w)

-- Replace the labels of a tree randomly, with probability p
mutateTree :: forall g. RandomGen g => Double -> g -> Tree -> Tree
mutateTree p g (Tree a ts) =
  let (a', g') = (R.random g :: (Double, g))
      (a'', g'') = R.random g'
   in Tree
        { currentUniform = if a' < p then a'' else a,
          lazyUniforms = mutateTrees p g'' ts
        }

mutateTrees :: RandomGen g => Double -> g -> Trees -> Trees
mutateTrees p g (Trees t ts) =
  let (g1, g2) = split g
   in Trees
        { headTree = mutateTree p g1 t,
          tailTrees = mutateTrees p g2 ts
        }