Type Hierarchy
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 |
---|---|---|
|
a scalar number |
A numeric array of arbitrary shape, each element being a sample |
|
a numeric vector |
A matrix, each column being a sample |
|
a numeric matrix |
An array of matrices, each element being a sample matrix |
ValueSupport
#
Distributions.ValueSupport
— Type
ValueSupport
Abstract type that specifies the support of elements of samples.
It is either Discrete
or Continuous
.
The ValueSupport
sub-types defined in Distributions.jl
are:
#
Distributions.Discrete
— Type
Discrete <: ValueSupport
This type represents the support of a discrete random variable.
It is countable. For instance, it can be a finite set or a countably infinite set such as the natural numbers.
See also: Continuous
, ValueSupport
#
Distributions.Continuous
— Type
Continuous <: ValueSupport
This types represents the support of a continuous random variable.
It is uncountably infinite. For instance, it can be an interval on the real line.
See also: Discrete
, ValueSupport
Type | Default element type | Description | Examples |
---|---|---|---|
|
|
Samples take countably many values |
, |
|
|
Samples take uncountably many values |
], |
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:
#
Base.length
— Method
length(s::Sampleable)
The length of each sample. Always returns 1
when s
is univariate.
#
Base.size
— Method
size(s::Sampleable)
The size (i.e. shape) of each sample. Always returns ()
when s
is univariate, and (length(s),)
when s
is multivariate.
#
Distributions.nsamples
— Method
nsamples(s::Sampleable)
The number of values contained in one sample of s
. Multiple samples are often organized into an array, depending on the variate form.
#
Base.eltype
— Method
eltype(::Type{Sampleable})
The default element type of a sample. This is the type of elements of the samples generated by the rand
method. However, one can provide an array of different element types to store the samples using rand!
.
#
Base.rand
— Method
rand(::AbstractRNG, ::Sampleable)
Samples from the sampler and returns the result.
#
Random.rand!
— Method
rand!(::AbstractRNG, ::Sampleable, ::AbstractArray)
Samples in-place from the sampler and stores the result in the provided array.
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, multivariates, and matrix for details).