Safe Haskell	Safe-Inferred
Language	Haskell2010

FRP.Rhine.Bayes

Contents

Inference methods
Short standard library of stochastic processes

Synopsis

runPopulationCl :: forall m cl a b. Monad m => Int -> (forall x. Population m x -> Population m x) -> ClSF (Population m) cl a b -> ClSF m cl a [(b, Log Double)]
type StochasticProcess time a = forall m. MonadDistribution m => Behaviour m time a
type StochasticProcessF time a b = forall m. MonadDistribution m => BehaviourF m time a b
whiteNoise :: Double -> StochasticProcess td Double
whiteNoiseVarying :: StochasticProcessF td Double Double
levy :: (MonadDistribution m, VectorSpace v (Diff td)) => (Diff td -> m v) -> Behaviour m td v
wiener :: (MonadDistribution m, Diff td ~ Double) => Diff td -> Behaviour m td Double
brownianMotion :: (MonadDistribution m, Diff td ~ Double) => Diff td -> Behaviour m td Double
wienerVarying :: Diff td ~ Double => StochasticProcessF td (Diff td) Double
brownianMotionVarying :: Diff td ~ Double => StochasticProcessF td (Diff td) Double
wienerLogDomain :: Diff td ~ Double => Diff td -> StochasticProcess td (Log Double)
wienerVaryingLogDomain :: Diff td ~ Double => StochasticProcessF td (Diff td) (Log Double)
poissonInhomogeneous :: (MonadDistribution m, Real (Diff td), Fractional (Diff td)) => BehaviourF m td (Diff td) Int
poissonHomogeneous :: (MonadDistribution m, Real (Diff td), Fractional (Diff td)) => Diff td -> BehaviourF m td () Int
gammaInhomogeneous :: (MonadDistribution m, Real (Diff td), Fractional (Diff td), Floating (Diff td)) => Diff td -> BehaviourF m td (Diff td) Int
bernoulliInhomogeneous :: MonadDistribution m => BehaviourF m td Double Bool

Inference methods

runPopulationCl Source #

Arguments

:: forall m cl a b. Monad m
=> Int	Number of particles
-> (forall x. Population m x -> Population m x)	Resampler (see `Population` for some standard choices)
-> ClSF (Population m) cl a b	A signal function modelling the stochastic process on which to perform inference. `a` represents observations upon which the model should condition, using e.g. `score`. It can also additionally contain hyperparameters. `b` is the type of estimated current state.
-> ClSF m cl a [(b, Log Double)]

Run the Sequential Monte Carlo algorithm continuously on a ClSF.

Short standard library of stochastic processes

type StochasticProcess time a = forall m. MonadDistribution m => Behaviour m time a Source #

A stochastic process is a behaviour that uses, as only effect, random sampling.

type StochasticProcessF time a b = forall m. MonadDistribution m => BehaviourF m time a b Source #

Like StochasticProcess, but with a live input.

whiteNoise :: Double -> StochasticProcess td Double Source #

White noise, that is, an independent normal distribution at every time step.

whiteNoiseVarying :: StochasticProcessF td Double Double Source #

Like whiteNoise, that is, an independent normal distribution at every time step.

levy Source #

Arguments

:: (MonadDistribution m, VectorSpace v (Diff td))
=> (Diff td -> m v)	The increment function at every time step. The argument is the difference between times.
-> Behaviour m td v

Construct a Lévy process from the increment between time steps.

wiener Source #

Arguments

:: (MonadDistribution m, Diff td ~ Double)
=> Diff td	Time scale of variance.
-> Behaviour m td Double

The Wiener process, also known as Brownian motion.

brownianMotion Source #

Arguments

:: (MonadDistribution m, Diff td ~ Double)
=> Diff td	Time scale of variance.
-> Behaviour m td Double

The Wiener process, also known as Brownian motion.

wienerVarying :: Diff td ~ Double => StochasticProcessF td (Diff td) Double Source #

The Wiener process, also known as Brownian motion, with varying variance parameter.

brownianMotionVarying :: Diff td ~ Double => StochasticProcessF td (Diff td) Double Source #

The Wiener process, also known as Brownian motion, with varying variance parameter.

wienerLogDomain Source #

Arguments

:: Diff td ~ Double
=> Diff td	Time scale of variance
-> StochasticProcess td (Log Double)

The wiener process transformed to the Log domain, also called the geometric Wiener process.

wienerVaryingLogDomain :: Diff td ~ Double => StochasticProcessF td (Diff td) (Log Double) Source #

See wienerLogDomain and wienerVarying.

poissonInhomogeneous :: (MonadDistribution m, Real (Diff td), Fractional (Diff td)) => BehaviourF m td (Diff td) Int Source #

Inhomogeneous Poisson point process, as described in: https://en.wikipedia.org/wiki/Poisson_point_process#Inhomogeneous_Poisson_point_process

The input is the inverse of the current rate or intensity. It corresponds to the average duration between two events.
The output is the number of events since the last tick.

poissonHomogeneous Source #

Arguments

:: (MonadDistribution m, Real (Diff td), Fractional (Diff td))
=> Diff td	The (constant) rate of the process
-> BehaviourF m td () Int

Like poissonInhomogeneous, but the rate is constant.

gammaInhomogeneous Source #

Arguments

:: (MonadDistribution m, Real (Diff td), Fractional (Diff td), Floating (Diff td))
=> Diff td	The scale parameter
-> BehaviourF m td (Diff td) Int

The Gamma process, https://en.wikipedia.org/wiki/Gamma_process.

The live input corresponds to inverse shape parameter, which is variance over mean.

bernoulliInhomogeneous :: MonadDistribution m => BehaviourF m td Double Bool Source #

The inhomogeneous Bernoulli process, https://en.wikipedia.org/wiki/Bernoulli_process

Throws a coin to a given probability at each tick. The live input is the probability.