-- |
-- Module      :  Mcmc.Proposal.Generic
-- Description :  Generic interface to create proposals
-- Copyright   :  (c) Dominik Schrempf 2020
-- License     :  GPL-3.0-or-later
--
-- Maintainer  :  dominik.schrempf@gmail.com
-- Stability   :  unstable
-- Portability :  portable
--
-- Creation date: Thu May 14 20:26:27 2020.
module Mcmc.Proposal.Generic
  ( genericContinuous,
    genericDiscrete,
  )
where

import Mcmc.Proposal
import Numeric.Log
import Statistics.Distribution

-- | Generic function to create proposals for continuous parameters ('Double').
genericContinuous ::
  (ContDistr d, ContGen d) =>
  -- | Probability distribution
  d ->
  -- | Forward operator.
  --
  -- For example, for a multiplicative proposal on one variable the forward
  -- operator is @(*)@, so that @x * u = y@.
  (a -> Double -> a) ->
  -- | Inverse operator.
  --
  -- For example, 'recip' for a multiplicative proposal on one variable, since
  -- @y * (recip u) = x * u * (recip u) = x@.
  --
  -- Required for biased proposals.
  Maybe (Double -> Double) ->
  -- | Function to compute the absolute value of the determinant of the Jacobian
  -- matrix. For example, for a multiplicative proposal on one variable, we have
  --
  -- @
  -- detJacobian _ u = Exp $ log $ recip u
  -- @
  --
  -- That is, the determinant of the Jacobian matrix of multiplication is just
  -- the reciprocal value of @u@ (with conversion to log domain).
  --
  -- Required for proposals for which absolute value of the determinant of the
  -- Jacobian differs from 1.0.
  --
  -- Conversion to log domain is necessary, because some determinants of
  -- Jacobians are very small (or large).
  Maybe (a -> Double -> Log Double) ->
  ProposalSimple a
genericContinuous :: d
-> (a -> Double -> a)
-> Maybe (Double -> Double)
-> Maybe (a -> Double -> Log Double)
-> ProposalSimple a
genericContinuous d
d a -> Double -> a
f Maybe (Double -> Double)
mInv Maybe (a -> Double -> Log Double)
mJac a
x GenIO
g = do
  Double
u <- d -> GenIO -> IO Double
forall d (m :: * -> *).
(ContGen d, PrimMonad m) =>
d -> Gen (PrimState m) -> m Double
genContVar d
d GenIO
g
  let r :: Log Double
r = case Maybe (Double -> Double)
mInv of
        Maybe (Double -> Double)
Nothing -> Log Double
1.0
        Just Double -> Double
fInv ->
          let qXY :: Log Double
qXY = Double -> Log Double
forall a. a -> Log a
Exp (Double -> Log Double) -> Double -> Log Double
forall a b. (a -> b) -> a -> b
$ d -> Double -> Double
forall d. ContDistr d => d -> Double -> Double
logDensity d
d Double
u
              qYX :: Log Double
qYX = Double -> Log Double
forall a. a -> Log a
Exp (Double -> Log Double) -> Double -> Log Double
forall a b. (a -> b) -> a -> b
$ d -> Double -> Double
forall d. ContDistr d => d -> Double -> Double
logDensity d
d (Double -> Double
fInv Double
u)
           in Log Double
qYX Log Double -> Log Double -> Log Double
forall a. Fractional a => a -> a -> a
/ Log Double
qXY
      j :: Log Double
j = case Maybe (a -> Double -> Log Double)
mJac of
        Maybe (a -> Double -> Log Double)
Nothing -> Log Double
1.0
        Just a -> Double -> Log Double
fJac -> a -> Double -> Log Double
fJac a
x Double
u
  (a, Log Double, Log Double) -> IO (a, Log Double, Log Double)
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x a -> Double -> a
`f` Double
u, Log Double
r, Log Double
j)
{-# INLINEABLE genericContinuous #-}

-- | Generic function to create proposals for discrete parameters ('Int').
genericDiscrete ::
  (DiscreteDistr d, DiscreteGen d) =>
  -- | Probability distribution.
  d ->
  -- | Forward operator, e.g. (+), so that x + dx = x'.
  (a -> Int -> a) ->
  -- | Inverse operator, e.g., 'negate', so that x' + (negate dx) = x. Only
  -- required for biased proposals.
  Maybe (Int -> Int) ->
  ProposalSimple a
genericDiscrete :: d -> (a -> Int -> a) -> Maybe (Int -> Int) -> ProposalSimple a
genericDiscrete d
d a -> Int -> a
f Maybe (Int -> Int)
mfInv a
x GenIO
g = do
  Int
u <- d -> GenIO -> IO Int
forall d (m :: * -> *).
(DiscreteGen d, PrimMonad m) =>
d -> Gen (PrimState m) -> m Int
genDiscreteVar d
d GenIO
g
  let r :: Log Double
r = case Maybe (Int -> Int)
mfInv of
        Maybe (Int -> Int)
Nothing -> Log Double
1.0
        Just Int -> Int
fInv ->
          let qXY :: Log Double
qXY = Double -> Log Double
forall a. a -> Log a
Exp (Double -> Log Double) -> Double -> Log Double
forall a b. (a -> b) -> a -> b
$ d -> Int -> Double
forall d. DiscreteDistr d => d -> Int -> Double
logProbability d
d Int
u
              qYX :: Log Double
qYX = Double -> Log Double
forall a. a -> Log a
Exp (Double -> Log Double) -> Double -> Log Double
forall a b. (a -> b) -> a -> b
$ d -> Int -> Double
forall d. DiscreteDistr d => d -> Int -> Double
logProbability d
d (Int -> Int
fInv Int
u)
           in Log Double
qYX Log Double -> Log Double -> Log Double
forall a. Fractional a => a -> a -> a
/ Log Double
qXY
  (a, Log Double, Log Double) -> IO (a, Log Double, Log Double)
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x a -> Int -> a
`f` Int
u, Log Double
r, Log Double
1.0)
{-# INLINEABLE genericDiscrete #-}