types.md

Type Hierarchy

All samplers and distributions provided in this package are organized into a type hierarchy described as follows.

Sampleable

The root of this type hierarchy is Sampleable. The abstract type Sampleable subsumes any types of objects from which one can draw samples, which particularly includes samplers and distributions. Formally, Sampleable is defined as

abstract type Sampleable{F<:VariateForm,S<:ValueSupport} end

It has two type parameters that define the kind of samples that can be drawn therefrom.

Distributions.Sampleable
Base.rand(::Distributions.Sampleable)

VariateForm

Distributions.VariateForm

The VariateForm subtypes defined in Distributions.jl are:

Type	A single sample	Multiple samples
Univariate == ArrayLikeVariate{0}	a scalar number	A numeric array of arbitrary shape, each element being a sample
Multivariate == ArrayLikeVariate{1}	a numeric vector	A matrix, each column being a sample
Matrixvariate == ArrayLikeVariate{2}	a numeric matrix	An array of matrices, each element being a sample matrix

ValueSupport

Distributions.ValueSupport

The ValueSupport sub-types defined in Distributions.jl are:

Distributions.Discrete
Distributions.Continuous

Type	Default element type	Description	Examples
Discrete	Int	Samples take countably many values	${0,1,2,3}$, $\mathbb{N}$
Continuous	Float64	Samples take uncountably many values	$[0, 1]$, $\mathbb{R}$

Multiple samples are often organized into an array, depending on the variate form.

The basic functionalities that a sampleable object provides are to retrieve information about the samples it generates and to draw samples. Particularly, the following functions are provided for sampleable objects:

length(::Sampleable)
size(::Sampleable)
nsamples(::Type{Sampleable}, ::Any)
eltype(::Type{Sampleable})
rand(::AbstractRNG, ::Sampleable)
rand!(::AbstractRNG, ::Sampleable, ::AbstractArray)

Distributions

We use Distribution, a subtype of Sampleable as defined below, to capture probabilistic distributions. In addition to being sampleable, a distribution typically comes with an explicit way to combine its domain, probability density function, and many other quantities.

abstract type Distribution{F<:VariateForm,S<:ValueSupport} <: Sampleable{F,S} end

Distributions.Distribution

To simplify the use in practice, we introduce a series of type alias as follows:

const UnivariateDistribution{S<:ValueSupport}   = Distribution{Univariate,S}
const MultivariateDistribution{S<:ValueSupport} = Distribution{Multivariate,S}
const MatrixDistribution{S<:ValueSupport}       = Distribution{Matrixvariate,S}
const NonMatrixDistribution = Union{UnivariateDistribution, MultivariateDistribution}

const DiscreteDistribution{F<:VariateForm}   = Distribution{F,Discrete}
const ContinuousDistribution{F<:VariateForm} = Distribution{F,Continuous}

const DiscreteUnivariateDistribution     = Distribution{Univariate,    Discrete}
const ContinuousUnivariateDistribution   = Distribution{Univariate,    Continuous}
const DiscreteMultivariateDistribution   = Distribution{Multivariate,  Discrete}
const ContinuousMultivariateDistribution = Distribution{Multivariate,  Continuous}
const DiscreteMatrixDistribution         = Distribution{Matrixvariate, Discrete}
const ContinuousMatrixDistribution       = Distribution{Matrixvariate, Continuous}

All methods applicable to Sampleable also apply to Distribution. The API for distributions of different variate forms are different (refer to [univariates](@ref univariates), [multivariates](@ref multivariates), and [matrix](@ref matrix-variates) for details).