Goal.Probability.Distributions

Various instances of statistical manifolds, with a focus on exponential families. In the documentation we use \(X\) to indicate a random variable with the distribution being documented.

Univariate

data Bernoulli

The Bernoulli family with Boolean SamplePoints. (because why not). The source coordinate is \(P(X = True)\).

Instances

DuallyFlat Bernoulli

Defined in Goal.Probability.Distributions

Methods

dualPotential :: (PotentialCoordinates Bernoulli #* Bernoulli) -> Double

Legendre Bernoulli

Defined in Goal.Probability.Distributions

Methods

potential :: (PotentialCoordinates Bernoulli # Bernoulli) -> Double

Manifold Bernoulli

Defined in Goal.Probability.Distributions

Associated Types

type Dimension Bernoulli :: Nat

Discrete Bernoulli

Defined in Goal.Probability.Distributions

Associated Types

type Cardinality Bernoulli :: Nat

Methods

sampleSpace :: Proxy Bernoulli -> Sample Bernoulli

Statistical Bernoulli

Defined in Goal.Probability.Distributions

Associated Types

type SamplePoint Bernoulli

ExponentialFamily Bernoulli

Defined in Goal.Probability.Distributions

Methods

sufficientStatistic :: SamplePoint Bernoulli -> Mean # Bernoulli

averageSufficientStatistic :: Sample Bernoulli -> Mean # Bernoulli

logBaseMeasure :: Proxy Bernoulli -> SamplePoint Bernoulli -> Double

Riemannian Natural Bernoulli

Defined in Goal.Probability.Distributions

Methods

metric :: (Natural # Bernoulli) -> Natural #* Tensor Bernoulli Bernoulli

flat :: (Natural # Bernoulli) -> (Natural # Bernoulli) -> Natural #* Bernoulli

sharp :: (Natural # Bernoulli) -> (Natural #* Bernoulli) -> Natural # Bernoulli

Transition Mean c Bernoulli => MaximumLikelihood c Bernoulli

Defined in Goal.Probability.Distributions

Methods

mle :: Sample Bernoulli -> c # Bernoulli

AbsolutelyContinuous Mean Bernoulli

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Mean Bernoulli -> Sample Bernoulli -> [Double]

densities :: Point Mean Bernoulli -> Sample Bernoulli -> [Double]

AbsolutelyContinuous Natural Bernoulli

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Natural Bernoulli -> Sample Bernoulli -> [Double]

densities :: Point Natural Bernoulli -> Sample Bernoulli -> [Double]

AbsolutelyContinuous Source Bernoulli

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Source Bernoulli -> Sample Bernoulli -> [Double]

densities :: Point Source Bernoulli -> Sample Bernoulli -> [Double]

Transition c Source Bernoulli => Generative c Bernoulli

Defined in Goal.Probability.Distributions

Methods

samplePoint :: Point c Bernoulli -> Random (SamplePoint Bernoulli)

sample :: Int -> Point c Bernoulli -> Random (Sample Bernoulli)

Transition Mean Natural Bernoulli

Defined in Goal.Probability.Distributions

Methods

transition :: (Mean # Bernoulli) -> Natural # Bernoulli

Transition Mean Source Bernoulli

Defined in Goal.Probability.Distributions

Methods

transition :: (Mean # Bernoulli) -> Source # Bernoulli

Transition Natural Mean Bernoulli

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Bernoulli) -> Mean # Bernoulli

Transition Natural Source Bernoulli

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Bernoulli) -> Source # Bernoulli

Transition Source Mean Bernoulli

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # Bernoulli) -> Mean # Bernoulli

Transition Source Natural Bernoulli

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # Bernoulli) -> Natural # Bernoulli

LogLikelihood Natural Bernoulli Bool

Defined in Goal.Probability.Distributions

Methods

logLikelihood :: [Bool] -> (Natural # Bernoulli) -> Double

logLikelihoodDifferential :: [Bool] -> (Natural # Bernoulli) -> Natural #* Bernoulli

KnownNat k => Riemannian Mean (Replicated k Bernoulli)

Defined in Goal.Probability.Distributions

Methods

metric :: (Mean # Replicated k Bernoulli) -> Mean #* Tensor (Replicated k Bernoulli) (Replicated k Bernoulli)

flat :: (Mean # Replicated k Bernoulli) -> (Mean # Replicated k Bernoulli) -> Mean #* Replicated k Bernoulli

sharp :: (Mean # Replicated k Bernoulli) -> (Mean #* Replicated k Bernoulli) -> Mean # Replicated k Bernoulli

KnownNat k => Riemannian Natural (Replicated k Bernoulli)

Defined in Goal.Probability.Distributions

Methods

metric :: (Natural # Replicated k Bernoulli) -> Natural #* Tensor (Replicated k Bernoulli) (Replicated k Bernoulli)

flat :: (Natural # Replicated k Bernoulli) -> (Natural # Replicated k Bernoulli) -> Natural #* Replicated k Bernoulli

sharp :: (Natural # Replicated k Bernoulli) -> (Natural #* Replicated k Bernoulli) -> Natural # Replicated k Bernoulli

type PotentialCoordinates Bernoulli

Defined in Goal.Probability.Distributions

type PotentialCoordinates Bernoulli = Natural

type Dimension Bernoulli

Defined in Goal.Probability.Distributions

type Dimension Bernoulli = 1

type Cardinality Bernoulli

Defined in Goal.Probability.Distributions

type Cardinality Bernoulli = 2

type SamplePoint Bernoulli

Defined in Goal.Probability.Distributions

type SamplePoint Bernoulli = Bool

data Binomial (n :: Nat)

A distribution over the sum of True realizations of n Bernoulli random variables. The Source coordinate is the probability of \(P(X = True)\) for each Bernoulli random variable.

Instances

KnownNat n => Transition Mean Natural (Binomial n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Mean # Binomial n) -> Natural # Binomial n

KnownNat n => Transition Mean Source (Binomial n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Mean # Binomial n) -> Source # Binomial n

KnownNat n => Transition Natural Mean (Binomial n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Binomial n) -> Mean # Binomial n

KnownNat n => Transition Natural Source (Binomial n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Binomial n) -> Source # Binomial n

KnownNat n => Transition Source Mean (Binomial n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # Binomial n) -> Mean # Binomial n

KnownNat n => Transition Source Natural (Binomial n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # Binomial n) -> Natural # Binomial n

(KnownNat n, Transition Mean c (Binomial n)) => MaximumLikelihood c (Binomial n)

Defined in Goal.Probability.Distributions

Methods

mle :: Sample (Binomial n) -> c # Binomial n

KnownNat n => AbsolutelyContinuous Mean (Binomial n)

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Mean (Binomial n) -> Sample (Binomial n) -> [Double]

densities :: Point Mean (Binomial n) -> Sample (Binomial n) -> [Double]

KnownNat n => AbsolutelyContinuous Natural (Binomial n)

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Natural (Binomial n) -> Sample (Binomial n) -> [Double]

densities :: Point Natural (Binomial n) -> Sample (Binomial n) -> [Double]

KnownNat n => AbsolutelyContinuous Source (Binomial n)

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Source (Binomial n) -> Sample (Binomial n) -> [Double]

densities :: Point Source (Binomial n) -> Sample (Binomial n) -> [Double]

(KnownNat n, Transition c Source (Binomial n)) => Generative c (Binomial n)

Defined in Goal.Probability.Distributions

Methods

samplePoint :: Point c (Binomial n) -> Random (SamplePoint (Binomial n))

sample :: Int -> Point c (Binomial n) -> Random (Sample (Binomial n))

KnownNat n => LogLikelihood Natural (Binomial n) Int

Defined in Goal.Probability.Distributions

Methods

logLikelihood :: [Int] -> (Natural # Binomial n) -> Double

logLikelihoodDifferential :: [Int] -> (Natural # Binomial n) -> Natural #* Binomial n

KnownNat n => DuallyFlat (Binomial n)

Defined in Goal.Probability.Distributions

Methods

dualPotential :: (PotentialCoordinates (Binomial n) #* Binomial n) -> Double

KnownNat n => Legendre (Binomial n)

Defined in Goal.Probability.Distributions

Methods

potential :: (PotentialCoordinates (Binomial n) # Binomial n) -> Double

KnownNat n => Manifold (Binomial n)

Defined in Goal.Probability.Distributions

Associated Types

type Dimension (Binomial n) :: Nat

KnownNat n => Discrete (Binomial n)

Defined in Goal.Probability.Distributions

Associated Types

type Cardinality (Binomial n) :: Nat

Methods

sampleSpace :: Proxy (Binomial n) -> Sample (Binomial n)

KnownNat n => Statistical (Binomial n)

Defined in Goal.Probability.Distributions

Associated Types

type SamplePoint (Binomial n)

KnownNat n => ExponentialFamily (Binomial n)

Defined in Goal.Probability.Distributions

Methods

sufficientStatistic :: SamplePoint (Binomial n) -> Mean # Binomial n

averageSufficientStatistic :: Sample (Binomial n) -> Mean # Binomial n

logBaseMeasure :: Proxy (Binomial n) -> SamplePoint (Binomial n) -> Double

type PotentialCoordinates (Binomial n)

Defined in Goal.Probability.Distributions

type PotentialCoordinates (Binomial n) = Natural

type Dimension (Binomial n)

Defined in Goal.Probability.Distributions

type Dimension (Binomial n) = 1

type Cardinality (Binomial n)

Defined in Goal.Probability.Distributions

type Cardinality (Binomial n) = n + 1

type SamplePoint (Binomial n)

Defined in Goal.Probability.Distributions

type SamplePoint (Binomial n) = Int

data Categorical (n :: Nat)

A Categorical distribution where the probability of the first category \(P(X = 0)\) is given by the normalization constraint.

Instances

KnownNat n => Transition Mean Natural (Categorical n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Mean # Categorical n) -> Natural # Categorical n

Transition Mean Source (Categorical n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Mean # Categorical n) -> Source # Categorical n

KnownNat n => Transition Natural Mean (Categorical n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Categorical n) -> Mean # Categorical n

KnownNat n => Transition Natural Source (Categorical n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Categorical n) -> Source # Categorical n

Transition Source Mean (Categorical n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # Categorical n) -> Mean # Categorical n

KnownNat n => Transition Source Natural (Categorical n)

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # Categorical n) -> Natural # Categorical n

(KnownNat n, Transition Mean c (Categorical n)) => MaximumLikelihood c (Categorical n)

Defined in Goal.Probability.Distributions

Methods

mle :: Sample (Categorical n) -> c # Categorical n

KnownNat n => AbsolutelyContinuous Mean (Categorical n)

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Mean (Categorical n) -> Sample (Categorical n) -> [Double]

densities :: Point Mean (Categorical n) -> Sample (Categorical n) -> [Double]

KnownNat n => AbsolutelyContinuous Natural (Categorical n)

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Natural (Categorical n) -> Sample (Categorical n) -> [Double]

densities :: Point Natural (Categorical n) -> Sample (Categorical n) -> [Double]

KnownNat n => AbsolutelyContinuous Source (Categorical n)

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Source (Categorical n) -> Sample (Categorical n) -> [Double]

densities :: Point Source (Categorical n) -> Sample (Categorical n) -> [Double]

(KnownNat n, Transition c Source (Categorical n)) => Generative c (Categorical n)

Defined in Goal.Probability.Distributions

Methods

samplePoint :: Point c (Categorical n) -> Random (SamplePoint (Categorical n))

sample :: Int -> Point c (Categorical n) -> Random (Sample (Categorical n))

KnownNat n => LogLikelihood Natural (Categorical n) Int

Defined in Goal.Probability.Distributions

Methods

logLikelihood :: [Int] -> (Natural # Categorical n) -> Double

logLikelihoodDifferential :: [Int] -> (Natural # Categorical n) -> Natural #* Categorical n

KnownNat n => DuallyFlat (Categorical n)

Defined in Goal.Probability.Distributions

Methods

dualPotential :: (PotentialCoordinates (Categorical n) #* Categorical n) -> Double

KnownNat n => Legendre (Categorical n)

Defined in Goal.Probability.Distributions

Methods

potential :: (PotentialCoordinates (Categorical n) # Categorical n) -> Double

KnownNat n => Manifold (Categorical n)

Defined in Goal.Probability.Distributions

Associated Types

type Dimension (Categorical n) :: Nat

KnownNat n => Discrete (Categorical n)

Defined in Goal.Probability.Distributions

Associated Types

type Cardinality (Categorical n) :: Nat

Methods

sampleSpace :: Proxy (Categorical n) -> Sample (Categorical n)

KnownNat n => Statistical (Categorical n)

Defined in Goal.Probability.Distributions

Associated Types

type SamplePoint (Categorical n)

KnownNat n => ExponentialFamily (Categorical n)

Defined in Goal.Probability.Distributions

Methods

sufficientStatistic :: SamplePoint (Categorical n) -> Mean # Categorical n

averageSufficientStatistic :: Sample (Categorical n) -> Mean # Categorical n

logBaseMeasure :: Proxy (Categorical n) -> SamplePoint (Categorical n) -> Double

type PotentialCoordinates (Categorical n)

Defined in Goal.Probability.Distributions

type PotentialCoordinates (Categorical n) = Natural

type Dimension (Categorical n)

Defined in Goal.Probability.Distributions

type Dimension (Categorical n) = n

type Cardinality (Categorical n)

Defined in Goal.Probability.Distributions

type Cardinality (Categorical n) = n

type SamplePoint (Categorical n)

Defined in Goal.Probability.Distributions

type SamplePoint (Categorical n) = Int

categoricalWeights :: Transition c Source (Categorical n) => (c # Categorical n) -> Vector (n + 1) Double

Returns the probabilities over the whole sample space \((0 \ldots n)\) of the given categorical distribution.

data Poisson

The Manifold of Poisson distributions. The Source coordinate is the rate of the Poisson distribution.

Instances

DuallyFlat Poisson

Defined in Goal.Probability.Distributions

Methods

dualPotential :: (PotentialCoordinates Poisson #* Poisson) -> Double

Legendre Poisson

Defined in Goal.Probability.Distributions

Methods

potential :: (PotentialCoordinates Poisson # Poisson) -> Double

Legendre CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

potential :: (PotentialCoordinates CoMPoisson # CoMPoisson) -> Double

Manifold Poisson

Defined in Goal.Probability.Distributions

Associated Types

type Dimension Poisson :: Nat

Statistical Poisson

Defined in Goal.Probability.Distributions

Associated Types

type SamplePoint Poisson

ExponentialFamily Poisson

Defined in Goal.Probability.Distributions

Methods

sufficientStatistic :: SamplePoint Poisson -> Mean # Poisson

averageSufficientStatistic :: Sample Poisson -> Mean # Poisson

logBaseMeasure :: Proxy Poisson -> SamplePoint Poisson -> Double

ExponentialFamily CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

sufficientStatistic :: SamplePoint CoMPoisson -> Mean # CoMPoisson

averageSufficientStatistic :: Sample CoMPoisson -> Mean # CoMPoisson

logBaseMeasure :: Proxy CoMPoisson -> SamplePoint CoMPoisson -> Double

Transition Mean c Poisson => MaximumLikelihood c Poisson

Defined in Goal.Probability.Distributions

Methods

mle :: Sample Poisson -> c # Poisson

AbsolutelyContinuous Mean Poisson

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Mean Poisson -> Sample Poisson -> [Double]

densities :: Point Mean Poisson -> Sample Poisson -> [Double]

AbsolutelyContinuous Natural Poisson

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Natural Poisson -> Sample Poisson -> [Double]

densities :: Point Natural Poisson -> Sample Poisson -> [Double]

AbsolutelyContinuous Natural CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

logDensities :: Point Natural CoMPoisson -> Sample CoMPoisson -> [Double]

densities :: Point Natural CoMPoisson -> Sample CoMPoisson -> [Double]

AbsolutelyContinuous Source Poisson

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Source Poisson -> Sample Poisson -> [Double]

densities :: Point Source Poisson -> Sample Poisson -> [Double]

Transition c Source Poisson => Generative c Poisson

Defined in Goal.Probability.Distributions

Methods

samplePoint :: Point c Poisson -> Random (SamplePoint Poisson)

sample :: Int -> Point c Poisson -> Random (Sample Poisson)

Transition c Source CoMPoisson => Generative c CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

samplePoint :: Point c CoMPoisson -> Random (SamplePoint CoMPoisson)

sample :: Int -> Point c CoMPoisson -> Random (Sample CoMPoisson)

Transition Mean Natural Poisson

Defined in Goal.Probability.Distributions

Methods

transition :: (Mean # Poisson) -> Natural # Poisson

Transition Mean Source Poisson

Defined in Goal.Probability.Distributions

Methods

transition :: (Mean # Poisson) -> Source # Poisson

Transition Natural Mean Poisson

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Poisson) -> Mean # Poisson

Transition Natural Mean CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

transition :: (Natural # CoMPoisson) -> Mean # CoMPoisson

Transition Natural Source Poisson

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Poisson) -> Source # Poisson

Transition Natural Source CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

transition :: (Natural # CoMPoisson) -> Source # CoMPoisson

Transition Source Mean Poisson

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # Poisson) -> Mean # Poisson

Transition Source Mean CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

transition :: (Source # CoMPoisson) -> Mean # CoMPoisson

Transition Source Natural Poisson

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # Poisson) -> Natural # Poisson

Transition Source Natural CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

transition :: (Source # CoMPoisson) -> Natural # CoMPoisson

LogLikelihood Natural Poisson Int

Defined in Goal.Probability.Distributions

Methods

logLikelihood :: [Int] -> (Natural # Poisson) -> Double

logLikelihoodDifferential :: [Int] -> (Natural # Poisson) -> Natural #* Poisson

LogLikelihood Natural CoMPoisson Int

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

logLikelihood :: [Int] -> (Natural # CoMPoisson) -> Double

logLikelihoodDifferential :: [Int] -> (Natural # CoMPoisson) -> Natural #* CoMPoisson

type PotentialCoordinates Poisson

Defined in Goal.Probability.Distributions

type PotentialCoordinates Poisson = Natural

type PotentialCoordinates CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

type PotentialCoordinates CoMPoisson = Natural

type Dimension Poisson

Defined in Goal.Probability.Distributions

type Dimension Poisson = 1

type SamplePoint Poisson

Defined in Goal.Probability.Distributions

type SamplePoint Poisson = Int

data VonMises

The Manifold of VonMises distributions. The Source coordinates are the mean and concentration.

Instances

Legendre VonMises

Defined in Goal.Probability.Distributions

Methods

potential :: (PotentialCoordinates VonMises # VonMises) -> Double

Manifold VonMises

Defined in Goal.Probability.Distributions

Associated Types

type Dimension VonMises :: Nat

Statistical VonMises

Defined in Goal.Probability.Distributions

Associated Types

type SamplePoint VonMises

ExponentialFamily VonMises

Defined in Goal.Probability.Distributions

Methods

sufficientStatistic :: SamplePoint VonMises -> Mean # VonMises

averageSufficientStatistic :: Sample VonMises -> Mean # VonMises

logBaseMeasure :: Proxy VonMises -> SamplePoint VonMises -> Double

AbsolutelyContinuous Natural VonMises

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Natural VonMises -> Sample VonMises -> [Double]

densities :: Point Natural VonMises -> Sample VonMises -> [Double]

AbsolutelyContinuous Source VonMises

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Source VonMises -> Sample VonMises -> [Double]

densities :: Point Source VonMises -> Sample VonMises -> [Double]

Generative Natural VonMises

Defined in Goal.Probability.Distributions

Methods

samplePoint :: Point Natural VonMises -> Random (SamplePoint VonMises)

sample :: Int -> Point Natural VonMises -> Random (Sample VonMises)

Generative Source VonMises

Defined in Goal.Probability.Distributions

Methods

samplePoint :: Point Source VonMises -> Random (SamplePoint VonMises)

sample :: Int -> Point Source VonMises -> Random (Sample VonMises)

Transition Natural Mean VonMises

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # VonMises) -> Mean # VonMises

Transition Natural Source VonMises

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # VonMises) -> Source # VonMises

Transition Source Mean VonMises

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # VonMises) -> Mean # VonMises

Transition Source Natural VonMises

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # VonMises) -> Natural # VonMises

LogLikelihood Natural VonMises Double

Defined in Goal.Probability.Distributions

Methods

logLikelihood :: [Double] -> (Natural # VonMises) -> Double

logLikelihoodDifferential :: [Double] -> (Natural # VonMises) -> Natural #* VonMises

type PotentialCoordinates VonMises

Defined in Goal.Probability.Distributions

type PotentialCoordinates VonMises = Natural

type Dimension VonMises

Defined in Goal.Probability.Distributions

type Dimension VonMises = 2

type SamplePoint VonMises

Defined in Goal.Probability.Distributions

type SamplePoint VonMises = Double

Multivariate

data Dirichlet (k :: Nat)

A Dirichlet manifold contains distributions over weights of a Categorical distribution.

Instances

KnownNat k => Transition Natural Mean (Dirichlet k)

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Dirichlet k) -> Mean # Dirichlet k

KnownNat k => Transition Natural Source (Dirichlet k)

Defined in Goal.Probability.Distributions

Methods

transition :: (Natural # Dirichlet k) -> Source # Dirichlet k

KnownNat k => Transition Source Natural (Dirichlet k)

Defined in Goal.Probability.Distributions

Methods

transition :: (Source # Dirichlet k) -> Natural # Dirichlet k

KnownNat k => AbsolutelyContinuous Natural (Dirichlet k)

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Natural (Dirichlet k) -> Sample (Dirichlet k) -> [Double]

densities :: Point Natural (Dirichlet k) -> Sample (Dirichlet k) -> [Double]

KnownNat k => AbsolutelyContinuous Source (Dirichlet k)

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point Source (Dirichlet k) -> Sample (Dirichlet k) -> [Double]

densities :: Point Source (Dirichlet k) -> Sample (Dirichlet k) -> [Double]

(KnownNat k, Transition c Source (Dirichlet k)) => Generative c (Dirichlet k)

Defined in Goal.Probability.Distributions

Methods

samplePoint :: Point c (Dirichlet k) -> Random (SamplePoint (Dirichlet k))

sample :: Int -> Point c (Dirichlet k) -> Random (Sample (Dirichlet k))

KnownNat k => LogLikelihood Natural (Dirichlet k) (Vector k Double)

Defined in Goal.Probability.Distributions

Methods

logLikelihood :: [Vector k Double] -> (Natural # Dirichlet k) -> Double

logLikelihoodDifferential :: [Vector k Double] -> (Natural # Dirichlet k) -> Natural #* Dirichlet k

KnownNat k => Legendre (Dirichlet k)

Defined in Goal.Probability.Distributions

Methods

potential :: (PotentialCoordinates (Dirichlet k) # Dirichlet k) -> Double

KnownNat k => Manifold (Dirichlet k)

Defined in Goal.Probability.Distributions

Associated Types

type Dimension (Dirichlet k) :: Nat

KnownNat k => Statistical (Dirichlet k)

Defined in Goal.Probability.Distributions

Associated Types

type SamplePoint (Dirichlet k)

KnownNat k => ExponentialFamily (Dirichlet k)

Defined in Goal.Probability.Distributions

Methods

sufficientStatistic :: SamplePoint (Dirichlet k) -> Mean # Dirichlet k

averageSufficientStatistic :: Sample (Dirichlet k) -> Mean # Dirichlet k

logBaseMeasure :: Proxy (Dirichlet k) -> SamplePoint (Dirichlet k) -> Double

type PotentialCoordinates (Dirichlet k)

Defined in Goal.Probability.Distributions

type PotentialCoordinates (Dirichlet k) = Natural

type Dimension (Dirichlet k)

Defined in Goal.Probability.Distributions

type Dimension (Dirichlet k) = k

type SamplePoint (Dirichlet k)

Defined in Goal.Probability.Distributions

type SamplePoint (Dirichlet k) = Vector k Double

LocationShape

newtype LocationShape l s

A LocationShape Manifold is a Product of some location Manifold and some shape Manifold.

Constructors

LocationShape (l, s)

Instances

DuallyFlat Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

dualPotential :: (PotentialCoordinates Normal #* Normal) -> Double

Legendre Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

potential :: (PotentialCoordinates Normal # Normal) -> Double

Legendre CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

potential :: (PotentialCoordinates CoMPoisson # CoMPoisson) -> Double

ExponentialFamily Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

sufficientStatistic :: SamplePoint Normal -> Mean # Normal

averageSufficientStatistic :: Sample Normal -> Mean # Normal

logBaseMeasure :: Proxy Normal -> SamplePoint Normal -> Double

ExponentialFamily CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

sufficientStatistic :: SamplePoint CoMPoisson -> Mean # CoMPoisson

averageSufficientStatistic :: Sample CoMPoisson -> Mean # CoMPoisson

logBaseMeasure :: Proxy CoMPoisson -> SamplePoint CoMPoisson -> Double

Riemannian Mean Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

metric :: (Mean # Normal) -> Mean #* Tensor Normal Normal

flat :: (Mean # Normal) -> (Mean # Normal) -> Mean #* Normal

sharp :: (Mean # Normal) -> (Mean #* Normal) -> Mean # Normal

Riemannian Natural Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

metric :: (Natural # Normal) -> Natural #* Tensor Normal Normal

flat :: (Natural # Normal) -> (Natural # Normal) -> Natural #* Normal

sharp :: (Natural # Normal) -> (Natural #* Normal) -> Natural # Normal

Transition Mean c Normal => MaximumLikelihood c Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

mle :: Sample Normal -> c # Normal

AbsolutelyContinuous Mean Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

logDensities :: Point Mean Normal -> Sample Normal -> [Double]

densities :: Point Mean Normal -> Sample Normal -> [Double]

AbsolutelyContinuous Natural Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

logDensities :: Point Natural Normal -> Sample Normal -> [Double]

densities :: Point Natural Normal -> Sample Normal -> [Double]

AbsolutelyContinuous Natural CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

logDensities :: Point Natural CoMPoisson -> Sample CoMPoisson -> [Double]

densities :: Point Natural CoMPoisson -> Sample CoMPoisson -> [Double]

AbsolutelyContinuous Source Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

logDensities :: Point Source Normal -> Sample Normal -> [Double]

densities :: Point Source Normal -> Sample Normal -> [Double]

Transition c Source Normal => Generative c Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

samplePoint :: Point c Normal -> Random (SamplePoint Normal)

sample :: Int -> Point c Normal -> Random (Sample Normal)

Transition c Source CoMPoisson => Generative c CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

samplePoint :: Point c CoMPoisson -> Random (SamplePoint CoMPoisson)

sample :: Int -> Point c CoMPoisson -> Random (Sample CoMPoisson)

Transition Mean Natural Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Mean # Normal) -> Natural # Normal

Transition Mean Source Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Mean # Normal) -> Source # Normal

Transition Natural Mean Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Natural # Normal) -> Mean # Normal

Transition Natural Mean CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

transition :: (Natural # CoMPoisson) -> Mean # CoMPoisson

Transition Natural Source Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Natural # Normal) -> Source # Normal

Transition Natural Source CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

transition :: (Natural # CoMPoisson) -> Source # CoMPoisson

Transition Source Mean Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Source # Normal) -> Mean # Normal

Transition Source Mean CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

transition :: (Source # CoMPoisson) -> Mean # CoMPoisson

Transition Source Natural Normal

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Source # Normal) -> Natural # Normal

Transition Source Natural CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

transition :: (Source # CoMPoisson) -> Natural # CoMPoisson

LogLikelihood Natural Normal Double

Defined in Goal.Probability.Distributions.Gaussian

Methods

logLikelihood :: [Double] -> (Natural # Normal) -> Double

logLikelihoodDifferential :: [Double] -> (Natural # Normal) -> Natural #* Normal

LogLikelihood Natural CoMPoisson Int

Defined in Goal.Probability.Distributions.CoMPoisson

Methods

logLikelihood :: [Int] -> (Natural # CoMPoisson) -> Double

logLikelihoodDifferential :: [Int] -> (Natural # CoMPoisson) -> Natural #* CoMPoisson

(KnownNat n, KnownNat (Triangular n)) => Transition Mean Natural (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Mean # MultivariateNormal n) -> Natural # MultivariateNormal n

KnownNat n => Transition Mean Source (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Mean # MultivariateNormal n) -> Source # MultivariateNormal n

(KnownNat n, KnownNat (Triangular n)) => Transition Natural Mean (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Natural # MultivariateNormal n) -> Mean # MultivariateNormal n

KnownNat n => Transition Natural Source (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Natural # MultivariateNormal n) -> Source # MultivariateNormal n

KnownNat n => Transition Source Mean (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Source # MultivariateNormal n) -> Mean # MultivariateNormal n

KnownNat n => Transition Source Natural (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Source # MultivariateNormal n) -> Natural # MultivariateNormal n

(KnownNat n, KnownNat k) => Transition Natural Source (Affine Tensor (MVNMean n) (Replicated n Normal) (MVNMean k))

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Natural # Affine Tensor (MVNMean n) (Replicated n Normal) (MVNMean k)) -> Source # Affine Tensor (MVNMean n) (Replicated n Normal) (MVNMean k)

(KnownNat n, KnownNat k) => Transition Natural Source (Affine Tensor (MVNMean n) (MultivariateNormal n) (MVNMean k))

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Natural # Affine Tensor (MVNMean n) (MultivariateNormal n) (MVNMean k)) -> Source # Affine Tensor (MVNMean n) (MultivariateNormal n) (MVNMean k)

Transition Natural Source (Affine Tensor NormalMean Normal NormalMean)

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Natural # Affine Tensor NormalMean Normal NormalMean) -> Source # Affine Tensor NormalMean Normal NormalMean

(KnownNat n, KnownNat k) => Transition Source Natural (Affine Tensor (MVNMean n) (Replicated n Normal) (MVNMean k))

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Source # Affine Tensor (MVNMean n) (Replicated n Normal) (MVNMean k)) -> Natural # Affine Tensor (MVNMean n) (Replicated n Normal) (MVNMean k)

(KnownNat n, KnownNat k) => Transition Source Natural (Affine Tensor (MVNMean n) (MultivariateNormal n) (MVNMean k))

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Source # Affine Tensor (MVNMean n) (MultivariateNormal n) (MVNMean k)) -> Natural # Affine Tensor (MVNMean n) (MultivariateNormal n) (MVNMean k)

Transition Source Natural (Affine Tensor NormalMean Normal NormalMean)

Defined in Goal.Probability.Distributions.Gaussian

Methods

transition :: (Source # Affine Tensor NormalMean Normal NormalMean) -> Natural # Affine Tensor NormalMean Normal NormalMean

(KnownNat n, Transition Mean c (MultivariateNormal n)) => MaximumLikelihood c (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

mle :: Sample (MultivariateNormal n) -> c # MultivariateNormal n

(KnownNat n, KnownNat (Triangular n)) => AbsolutelyContinuous Natural (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

logDensities :: Point Natural (MultivariateNormal n) -> Sample (MultivariateNormal n) -> [Double]

densities :: Point Natural (MultivariateNormal n) -> Sample (MultivariateNormal n) -> [Double]

(KnownNat n, KnownNat (Triangular n)) => AbsolutelyContinuous Source (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

logDensities :: Point Source (MultivariateNormal n) -> Sample (MultivariateNormal n) -> [Double]

densities :: Point Source (MultivariateNormal n) -> Sample (MultivariateNormal n) -> [Double]

(KnownNat n, KnownNat (Triangular n), Transition c Source (MultivariateNormal n)) => Generative c (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

samplePoint :: Point c (MultivariateNormal n) -> Random (SamplePoint (MultivariateNormal n))

sample :: Int -> Point c (MultivariateNormal n) -> Random (Sample (MultivariateNormal n))

KnownNat n => LogLikelihood Natural (MultivariateNormal n) (Vector n Double)

Defined in Goal.Probability.Distributions.Gaussian

Methods

logLikelihood :: [Vector n Double] -> (Natural # MultivariateNormal n) -> Double

logLikelihoodDifferential :: [Vector n Double] -> (Natural # MultivariateNormal n) -> Natural #* MultivariateNormal n

(Statistical l, Statistical s, Product (LocationShape l s), Storable (SamplePoint s), SamplePoint l ~ SamplePoint s, AbsolutelyContinuous c (LocationShape l s), KnownNat n) => AbsolutelyContinuous c (LocationShape (Replicated n l) (Replicated n s))

Defined in Goal.Probability.Distributions

Methods

logDensities :: Point c (LocationShape (Replicated n l) (Replicated n s)) -> Sample (LocationShape (Replicated n l) (Replicated n s)) -> [Double]

densities :: Point c (LocationShape (Replicated n l) (Replicated n s)) -> Sample (LocationShape (Replicated n l) (Replicated n s)) -> [Double]

(KnownNat n, KnownNat (Triangular n)) => DuallyFlat (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

dualPotential :: (PotentialCoordinates (MultivariateNormal n) #* MultivariateNormal n) -> Double

(KnownNat n, KnownNat (Triangular n)) => Legendre (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

potential :: (PotentialCoordinates (MultivariateNormal n) # MultivariateNormal n) -> Double

(KnownNat n, KnownNat (Triangular n)) => ExponentialFamily (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

Methods

sufficientStatistic :: SamplePoint (MultivariateNormal n) -> Mean # MultivariateNormal n

averageSufficientStatistic :: Sample (MultivariateNormal n) -> Mean # MultivariateNormal n

logBaseMeasure :: Proxy (MultivariateNormal n) -> SamplePoint (MultivariateNormal n) -> Double

(Manifold l, Manifold s) => Manifold (LocationShape l s)

Defined in Goal.Probability.Distributions

Associated Types

type Dimension (LocationShape l s) :: Nat

(Manifold l, Manifold s) => Product (LocationShape l s)

Defined in Goal.Probability.Distributions

Associated Types

type First (LocationShape l s)

type Second (LocationShape l s)

Methods

join :: (c # First (LocationShape l s)) -> (c # Second (LocationShape l s)) -> c # LocationShape l s

split :: (c # LocationShape l s) -> (c # First (LocationShape l s), c # Second (LocationShape l s))

(Statistical l, Manifold s) => Statistical (LocationShape l s)

Defined in Goal.Probability.Distributions

Associated Types

type SamplePoint (LocationShape l s)

(Manifold l, Manifold s) => Translation (LocationShape l s) l

Defined in Goal.Probability.Distributions

Methods

(>+>) :: (c # LocationShape l s) -> (c # l) -> c # LocationShape l s

anchor :: (c # LocationShape l s) -> c # l

(KnownNat n, Manifold l, Manifold s) => Translation (Replicated n (LocationShape l s)) (Replicated n l)

Defined in Goal.Probability.Distributions

Methods

(>+>) :: (c # Replicated n (LocationShape l s)) -> (c # Replicated n l) -> c # Replicated n (LocationShape l s)

anchor :: (c # Replicated n (LocationShape l s)) -> c # Replicated n l

type PotentialCoordinates Normal

Defined in Goal.Probability.Distributions.Gaussian

type PotentialCoordinates Normal = Natural

type PotentialCoordinates CoMPoisson

Defined in Goal.Probability.Distributions.CoMPoisson

type PotentialCoordinates CoMPoisson = Natural

type PotentialCoordinates (MultivariateNormal n)

Defined in Goal.Probability.Distributions.Gaussian

type PotentialCoordinates (MultivariateNormal n) = Natural

type PotentialCoordinates (LocationShape l s)

Defined in Goal.Probability.Distributions

type PotentialCoordinates (LocationShape l s) = Natural

type Dimension (LocationShape l s)

Defined in Goal.Probability.Distributions

type Dimension (LocationShape l s) = Dimension (l, s)

type First (LocationShape l s)

Defined in Goal.Probability.Distributions

type First (LocationShape l s) = First (l, s)

type Second (LocationShape l s)

Defined in Goal.Probability.Distributions

type Second (LocationShape l s) = Second (l, s)

type SamplePoint (LocationShape l s)

Defined in Goal.Probability.Distributions

type SamplePoint (LocationShape l s) = SamplePoint l