| Copyright | (c) 2015 Jared Tobin |
|---|---|
| License | MIT |
| Maintainer | Jared Tobin <jared@jtobin.ca> |
| Stability | unstable |
| Portability | ghc |
| Safe Haskell | None |
| Language | Haskell2010 |
Numeric.MCMC.Slice
Contents
Description
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.
- 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 ()
- 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]
- 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)
- create :: PrimMonad m => m (Gen (PrimState m))
- createSystemRandom :: IO GenIO
- withSystemRandom :: PrimBase m => (Gen (PrimState m) -> m a) -> IO a
- asGenIO :: (GenIO -> IO a) -> GenIO -> IO a
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
createSystemRandom :: IO GenIO #
Seed a PRNG with data from the system's fast source of pseudo-random
numbers. All the caveats of withSystemRandom apply here as well.
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 ("/dev/urandom" on Unix-like systems or
RtlGenRandom on Windows), then run the given action.
This is a somewhat expensive function, and is intended to be called
only occasionally (e.g. once per thread). You should use the Gen
it creates to generate many random numbers.