Hi,

I defined a model and I want to set a prior on the non-centered intercept. One way to do so in `brms`

, which by default centers the intercept, is to use the formulation `y ~ 0 + Intercept + ...`

. This works fine.

I read in the manual that the same results could be obtained by setting `bf(y ~ 1 + ..., center = FALSE)`

. I noticed that this is true if only for the location parameter of the distribution. If we are also estimating the scale of the distribution with a similar formula, the intercept for this will be centered.

For example:

```
library(tidyverse)
library(brms)
library(tidybayes)
data = read.csv('https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/master/csv/lme4/sleepstudy.csv') %>%
as_tibble(data) %>%
mutate(Subject = factor(Subject))
bf <- bf(Reaction ~ Days + (Days | Subject),
sigma ~ Days + (Days | Subject),
center = FALSE)
get_prior(bf, data = data)
```

will output (notice the `class`

Intercept):

```
prior class coef group resp dpar nlpar bound
1 b
2 b Days
3 b Intercept
4 lkj(1) cor
5 cor Subject
6 student_t(3, 0, 59.3) sd
7 sd Subject
8 sd Days Subject
9 sd Intercept Subject
10 b sigma
11 b Days sigma
12 student_t(3, 0, 2.5) Intercept sigma
13 student_t(3, 0, 59.3) sd sigma
14 sd Subject sigma
15 sd Days Subject sigma
16 sd Intercept Subject sigma
```

Is this the expected behavior?

- Operating System: Win 10
- brms Version: 2.13.13