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Create New Samplers and Distributions

Whereas this package already provides a large collection of common distributions out of box, there are still occasions where you want to create new distributions (e.g your application requires a special kind of distributions, or you want to contribute to this package).

Generally, you don't have to implement every API method listed in the documentation. This package provides a series of generic functions that turn a small number of internal methods into user-end API methods. What you need to do is to implement this small set of internal methods for your distributions.

By default, Discrete sampleables have support of type Int while Continuous sampleables have support of type Float64. If this assumption does not hold for your new distribution or sampler, or its ValueSupport is neither Discrete nor Continuous, you should implement the eltype method in addition to the other methods listed below.

Note: the methods need to be implemented are different for distributions of different variate forms.

Create a Sampler

Unlike a full fledged distributions, a sampler, in general, only provides limited functionalities, mainly to support sampling.

Univariate Sampler

To implement a univariate sampler, one can define a sub type (say Spl) of Sampleable{Univariate,S} (where S can be Discrete or Continuous), and provide a rand method, as

function rand(rng::AbstractRNG, s::Spl)
    # ... generate a single sample from s
end

The package already implements a vectorized version of rand! and rand that repeatedly calls the scalar version to generate multiple samples; as wells as a one arg version that uses the default random number generator.

Multivariate Sampler

To implement a multivariate sampler, one can define a sub type of Sampleable{Multivariate,S}, and provide both length and _rand! methods, as

Base.length(s::Spl) = ... # return the length of each sample

function _rand!(rng::AbstractRNG, s::Spl, x::AbstractVector{T}) where T<:Real
    # ... generate a single vector sample to x
end

This function can assume that the dimension of x is correct, and doesn't need to perform dimension checking.

The package implements both rand and rand! as follows (which you don't need to implement in general):

function _rand!(rng::AbstractRNG, s::Sampleable{Multivariate}, A::DenseMatrix)
    for i = 1:size(A,2)
        _rand!(rng, s, view(A,:,i))
    end
    return A
end

function rand!(rng::AbstractRNG, s::Sampleable{Multivariate}, A::AbstractVector)
    length(A) == length(s) ||
        throw(DimensionMismatch("Output size inconsistent with sample length."))
    _rand!(rng, s, A)
end

function rand!(rng::AbstractRNG, s::Sampleable{Multivariate}, A::DenseMatrix)
    size(A,1) == length(s) ||
        throw(DimensionMismatch("Output size inconsistent with sample length."))
    _rand!(rng, s, A)
end

rand(rng::AbstractRNG, s::Sampleable{Multivariate,S}) where {S<:ValueSupport} =
    _rand!(rng, s, Vector{eltype(S)}(length(s)))

rand(rng::AbstractRNG, s::Sampleable{Multivariate,S}, n::Int) where {S<:ValueSupport} =
    _rand!(rng, s, Matrix{eltype(S)}(length(s), n))

If there is a more efficient method to generate multiple vector samples in batch, one should provide the following method

function _rand!(rng::AbstractRNG, s::Spl, A::DenseMatrix{T}) where T<:Real
    # ... generate multiple vector samples in batch
end

Remember that each column of A is a sample.

Matrix-variate Sampler

To implement a multivariate sampler, one can define a sub type of Sampleable{Multivariate,S}, and provide both size and _rand! method, as

Base.size(s::Spl) = ... # the size of each matrix sample

function _rand!(rng::AbstractRNG, s::Spl, x::DenseMatrix{T}) where T<:Real
    # ... generate a single matrix sample to x
end

Note that you can assume x has correct dimensions in _rand! and don't have to perform dimension checking, the generic rand and rand! will do dimension checking and array allocation for you.

Create a Distribution

Most distributions should implement a sampler method to improve batch sampling efficiency.

Distributions.sampler — Method
sampler(d::Distribution) -> Sampleable
sampler(s::Sampleable) -> s

Samplers can often rely on pre-computed quantities (that are not parameters themselves) to improve efficiency. If such a sampler exists, it can be provided with this sampler method, which would be used for batch sampling. The general fallback is sampler(d::Distribution) = d.

source

Univariate Distribution

A univariate distribution type should be defined as a subtype of DiscreteUnivarateDistribution or ContinuousUnivariateDistribution.

Following methods need to be implemented for each univariate distribution type:

It is also recommended that one also implements the following statistics functions:

You may refer to the source file src/univariates.jl to see details about how generic fallback functions for univariates are implemented.

Create a Multivariate Distribution

A multivariate distribution type should be defined as a subtype of DiscreteMultivarateDistribution or ContinuousMultivariateDistribution.

Following methods need to be implemented for each multivariate distribution type:

Note that if there exists faster methods for batch evaluation, one should override _logpdf! and _pdf!.

Furthermore, the generic loglikelihood function repeatedly calls _logpdf. If there is a better way to compute the log-likelihood, one should override loglikelihood.

It is also recommended that one also implements the following statistics functions:

Create a Matrix-variate Distribution

A multivariate distribution type should be defined as a subtype of DiscreteMatrixDistribution or ContinuousMatrixDistribution.

Following methods need to be implemented for each matrix-variate distribution type: