Numeric.MCMC.Slice

This implementation performs slice sampling by first finding a bracket about a mode (using a simple doubling heuristic), and then doing rejection sampling along it. The result is a reliable and computationally inexpensive sampling routine.

The mcmc function streams a trace to stdout to be processed elsewhere, while the slice transition can be used for more flexible purposes, such as working with samples in memory.

See Neal, 2003 for the definitive reference of the algorithm.

Documentation

mcmc :: (MonadIO m, PrimMonad m, Show (t a), FoldableWithIndex (Index (t a)) t, Ixed (t a), Num (IxValue (t a)), Variate (IxValue (t a))) => Int -> IxValue (t a) -> t a -> (t a -> Double) -> Gen (PrimState m) -> m ()

Trace n iterations of a Markov chain and stream them to stdout.

>>> let rosenbrock [x0, x1] = negate (5  *(x1 - x0 ^ 2) ^ 2 + 0.05 * (1 - x0) ^ 2)
>>> withSystemRandom . asGenIO $ mcmc 3 1 [0, 0] rosenbrock
-3.854097694213343e-2,0.16688601288358407
-9.310661272172682e-2,0.2562387977415508
-0.48500122500661846,0.46245400501919076

chain :: (PrimMonad m, FoldableWithIndex (Index (f a)) f, Ixed (f a), Variate (IxValue (f a)), Num (IxValue (f a))) => Int -> IxValue (f a) -> f a -> (f a -> Double) -> Gen (PrimState m) -> m [Chain (f a) b]

Trace n iterations of a Markov chain and collect them in a list.

>>> results <- withSystemRandom . asGenIO $ mcmc 3 1 [0, 0] rosenbrock

slice :: (PrimMonad m, FoldableWithIndex (Index (t a)) t, Ixed (t a), Num (IxValue (t a)), Variate (IxValue (t a))) => IxValue (t a) -> Transition m (Chain (t a) b)

A slice sampling transition operator.

Re-exported

create :: PrimMonad m => m (Gen (PrimState m))

Create a generator for variates using a fixed seed.

createSystemRandom :: IO GenIO

Seed a PRNG with data from the system's fast source of pseudo-random numbers.

withSystemRandom :: PrimBase m => (Gen (PrimState m) -> m a) -> IO a

Seed a PRNG with data from the system's fast source of pseudo-random numbers, then run the given action.

This function is unsafe and for example allows STRefs or any other mutable data structure to escape scope:

>>> ref <- withSystemRandom $ \_ -> newSTRef 1
>>> withSystemRandom $ \_ -> modifySTRef ref succ >> readSTRef ref
2
>>> withSystemRandom $ \_ -> modifySTRef ref succ >> readSTRef ref
3

asGenIO :: (GenIO -> IO a) -> GenIO -> IO a

Constrain the type of an action to run in the IO monad.