Docs for affinely transformed scalar do not match implementation

[martinmodrak]

Summary:

It appears that the transformation in the Affinely transformed scalar section is reversed compared to how it is implemented in Stan math.

Description:

In the documentation, we state that Y = mu + sigma * X where Y is the unconstrained variable as used by Stan and X is what the user sees (at least that's how it is used in the Lower-bounded scalar chapter). However, the implementation (https://github.com/stan-dev/math/blob/92075708b1d1796eb82e3b284cd11e544433518e/stan/math/prim/fun/offset_multiplier_constrain.hpp) and the way it is used suggests that the transformation is inverted, i.e. that Y = (X - mu)/sigma. Consequently the Jacobian in the docs is 1 / sigma while in the code it is sigma.

Additional Information:

Noticed this when inspecting https://discourse.mc-stan.org/t/offset-multiplier-initialization/20712

Current Version:

v2.26.0

[bob-carpenter]

That's right. Do you want to submit the PR to fix it or should I?

[martinmodrak]

Thanks for checking, I created the PR.