Link function Bijectors.jl

Specific Domains Probabilistic programming
1

Dear All,

I would like to ask probably a stupid question. What exactly does link() function? Documentation: link: maps a sample of a random distribution dist from its support to a value in R^n. Example:
`
How how exactly/according to what key does link() maps this sample from support to R^n?

julia> using Bijectors

julia> dist = Beta(2, 2)
Beta{Float64}(α=2.0, β=2.0)

julia> x = rand(dist)
0.7472542331020509

julia> y = link(dist, x)
1.084021356473311

Best,
Honza

2

For a beta distribution, 0 < x < 1. The link function applies a 1-to-1 transformation to the whole real line. Because the beta distribution has both an upper and lower bound a logit transform is used here:

julia> logit(0.7472542331020509)
1.084021356473311
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3

Thank you very much! Is there some more detailed documentation/tutorial that explains how it works (which transforms does it use)? Does it always transforms some bounded distribution into unbounded one?

4

It looks like the Readme for Bijectors.jl is the primary documentation. The available transformations are listed at the bottom. The general goal is to transform a constrained value to an unconstrained value.

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