tensorflow / tensorflow/probability

Copula primer mentions Uniform marginals, but example does not have uniform marginals

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Description

[TFP is awesome, thanks so much for all the amazing functionality!]

I've been reading the copulas primer at https://www.tensorflow.org/probability/examples/Gaussian_Copula

Twice in the first couple of paragraphs it mentions that a copula is a distribution on [0, 1]^n with uniform marginals.

a copula is a multivariate distribution C(U_1, U_2, ...) such that marginalizing gives U_i ~ Uniform(0, 1).

the Gaussian Copula is a distribution over the unit hypercube [0, 1]^n with uniform marginals.

However, in the example just below, the copula pdf pdf = GaussianCopulaTriL(...) doesn't have uniform marginals. The contour plot here is clearly non-uniform in the y direction (the marginal is Normal-like, not Uniform).

Would anyone be able to explain why this is?

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Research direction

Read the Gaussian Copula primer linked in the issue and inspect the GaussianCopulaTriL example alongside its contour plot. Determine whether the example or the surrounding explanation is inconsistent, then document the resolution or identify the required correction so the stated marginal behavior and example agree.

Written by the indexing model from the issue text.

Assessment

Tech stack
jupyter-notebook, tensorflow
Domain
documentation, machine-learning
Issue type
Documentation
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
30/100

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