flat-mcmc-1.5.2: Painless general-purpose sampling.

Copyright(c) 2016 Jared Tobin
MaintainerJared Tobin <jared@jtobin.ca>
Safe HaskellNone



This is the 'affine invariant ensemble' or AIEMCMC algorithm described in Goodman and Weare, 2010. It is a reasonably efficient and hassle-free sampler, requiring no mucking with tuning parameters or local proposal distributions.

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

See http://msp.org/camcos/2010/5-1/camcos-v5-n1-p04-p.pdf for the definitive reference of the algorithm.



mcmc :: (MonadIO m, PrimMonad m) => Int -> Ensemble -> (Particle -> Double) -> Gen (PrimState m) -> m () Source #

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

Note that the Markov chain is defined over the space of ensembles, so you'll need to provide an ensemble of particles for the start location.

>>> import Numeric.MCMC.Flat
>>> import Data.Vector.Unboxed (toList)
>>> :{
>>> let rosenbrock xs = negate (5  *(x1 - x0 ^ 2) ^ 2 + 0.05 * (1 - x0) ^ 2)
            where [x0, x1] = toList xs
>>> :}
>>> :{
>>> let origin = ensemble [
>>> particle [negate 1.0, negate 1.0]
>>> , particle [negate 1.0, 1.0]
>>> , particle [1.0, negate 1.0]
>>> , particle [1.0, 1.0]
>>> ]
>>> :}
>>> withSystemRandom . asGenIO $ mcmc 2 origin rosenbrock

flat :: PrimMonad m => Transition m Chain Source #

The flat transition operator for driving a Markov chain over a space of ensembles.

type Particle = Vector Double Source #

A particle is an n-dimensional point in Euclidean space.

You can create a particle by using the particle helper function, or just use Data.Vector.Unboxed.fromList.

type Ensemble = Vector Particle Source #

An ensemble is a collection of particles.

The Markov chain we're interested in will run over the space of ensembles, so you'll want to build an ensemble out of a reasonable number of particles to kick off the chain.

You can create an ensemble by using the ensemble helper function, or just use Data.Vector.fromList.

type Transition (m :: Type -> Type) a = StateT a (Prob m) () #

A generic transition operator.

Has access to randomness via the underlying Prob monad.

data Target a #

A Target consists of a function from parameter space to the reals, as well as possibly a gradient.

Most implementations assume a log-target, so records are named accordingly.




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
>>> withSystemRandom $ \_ -> modifySTRef ref succ >> readSTRef ref

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

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

ensemble :: [Vector Double] -> Vector (Vector Double) Source #

A type-specialized alias for Data.Vector.fromList.

Use this to create ensembles from lists of particles.

particle :: [Double] -> Vector Double Source #

A type-specialized alias for Data.Vector.Unboxed.fromList

Use this to create particles from lists of doubles.