Bijectors.jl

This package implements a set of functions for transforming constrained random variables (e.g. simplexes, intervals) to Euclidean space. The 3 main functions implemented in this package are the link, invlink and logpdf_with_trans for a number of distributions. The distributions supported are:

RealDistribution: Union{Cauchy, Gumbel, Laplace, Logistic, NoncentralT, Normal, NormalCanon, TDist},
PositiveDistribution: Union{BetaPrime, Chi, Chisq, Erlang, Exponential, FDist, Frechet, Gamma, InverseGamma, InverseGaussian, Kolmogorov, LogNormal, NoncentralChisq, NoncentralF, Rayleigh, Weibull},
UnitDistribution: Union{Beta, KSOneSided, NoncentralBeta},
SimplexDistribution: Union{Dirichlet},
PDMatDistribution: Union{InverseWishart, Wishart}, and
TransformDistribution: Union{T, Truncated{T}} where T<:ContinuousUnivariateDistribution.

All exported names from the Distributions.jl package are reexported from Bijectors.

Bijectors.jl also provides a nice interface for working with these maps: composition, inversion, etc. The following table lists mathematical operations for a bijector and the corresponding code in Bijectors.jl.

Operation	Method	Automatic
`b ↦ b⁻¹`	`inverse(b)`	✓
`(b₁, b₂) ↦ (b₁ ∘ b₂)`	`b₁ ∘ b₂`	✓
`(b₁, b₂) ↦ [b₁, b₂]`	`stack(b₁, b₂)`	✓
`x ↦ b(x)`	`b(x)`	×
`y ↦ b⁻¹(y)`	`inverse(b)(y)`	×
`x ↦ log｜det J(b, x)｜`	`logabsdetjac(b, x)`	AD
`x ↦ b(x), log｜det J(b, x)｜`	`with_logabsdet_jacobian(b, x)`	✓
`p ↦ q := b_* p`	`q = transformed(p, b)`	✓
`y ∼ q`	`y = rand(q)`	✓
`p ↦ b` such that `support(b_* p) = ℝᵈ`	`bijector(p)`	✓
`(x ∼ p, b(x), log｜det J(b, x)｜, log q(y))`	`forward(q)`	✓

In this table, b denotes a Bijector, J(b, x) denotes the Jacobian of b evaluated at x, b_* denotes the push-forward of p by b, and x ∼ p denotes x sampled from the distribution with density p.

The "Automatic" column in the table refers to whether or not you are required to implement the feature for a custom Bijector. "AD" refers to the fact that it can be implemented "automatically" using automatic differentiation.