I am asking here and not on **brms**’s issue tracker on GitHub because I’m not sure if this is really a bug or if I am just misunderstanding something.

When using an offset in the model formula (e.g.

```
y_var ~ 1 + x_var + offset(offset_var)
```

), then **brms** seems to be still using the same default prior on the intercept as when omitting the offset (i.e.

```
y_var ~ 1 + x_var
```

in the above example). I am considering the `negbinomial(link = "log")`

family, but this probably also applies analogously to other families. For the `negbinomial(link = "log")`

family, the default Student’s t prior for the intercept seems to be centered at the logarithm of the median of the response (`log(median(y_var))`

= `median(log(y_var))`

). Therefore, my question is: If an offset is specified, shouldn’t the center of the default prior for the intercept be adjusted (in the above example e.g. by taking `log(median(y_var)) - median(offset_var)`

or – probably better – by directly taking `median(log(y_var) - offset_var)`

, keeping in mind that the median is not linear and thus the two expressions are in general not the same)? And shouldn’t the scale of the default Student’s t prior for the intercept be adjusted analogously?

(Note: With “intercept”, I am meaning the intercept at centered predictors.)

The same issue also arises when using the additional response information `rate()`

on the left-hand side of the formula instead of `offset()`

on the right-hand side (in the above example, I think this would be

```
y_var | rate(exp(offset_var)) ~ 1 + x_var
```

since `rate()`

automatically takes the logarithm).

My **brms** version is 2.13.0.