Is Stan's affine transform type <offset, multiplier> restricted to scalars?

[mitzimorris]

The Stan Reference Manual has sections: "Affinely Transformed Scalar" - https://mc-stan.org/docs/reference-manual/transforms.html#affinely-transformed-scalar and https://mc-stan.org/docs/reference-manual/types.html#affine-transform.section

The following program compiles:

parameters {
  real<multiplier=3> y;
  vector<multiplier=exp(y/2)>[9] x;
}
model {
  y ~ std_normal();
  x ~ std_normal();
}

here x is a vector, not a scalar. scatter plots of x[1] vs x[2] etc look pretty normal...

[bob-carpenter]

Yes, the transform is at the scalar level---it's just $\alpha + \beta \cdot x$ for scalar offset $\alpha$, scalar multiplier $\beta$, and scalar value $x$. This is in contrast to the multivariate affine transform, which we do not support. That is also $\alpha + \beta \cdot x$, but now $\alpha$ is a vector, $\beta$ is a matrix, and $x$ is a vector. We'd want to do the multivariate form to do a non-centered multivariate prior where we'd take the offset to the be a location and the multiplier to be a Cholesky factor of covariance.

Feel free to rewrite to make it clearer that it's a scalar operation that can be applied elementwise to a container of any shape.