# Setting an intercept prior on a regression in brms
**URL:** https://discourse.mc-stan.org/t/setting-an-intercept-prior-on-a-regression-in-brms/40657
**Category:** General
**Created:** [November 19, 2025, 3:12pm UTC](https://discourse.mc-stan.org/t/setting-an-intercept-prior-on-a-regression-in-brms/40657 "2025-11-19T15:12:56Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@kholsinger](https://discourse.mc-stan.org/u/kholsinger)
#### Post date: [November 19, 2025, 3:12pm UTC](https://discourse.mc-stan.org/t/setting-an-intercept-prior-on-a-regression-in-brms/40657/1 "2025-11-19T15:12:56Z")
I have what is probably a very simple problem, but I haven’t found the solution for it yet, and I’d appreciate some help. I’m setting a prior on an intercept, which gives me a `summary()` that confuses me. Here’s a very simple example.
```no-highlight
set.seed(123)
beta_0 <- 5
beta_1 <- 2
sigma <- 10
x <- runif(100, min = 10, max = 100)
mu <- beta_0 + beta_1*x
y <- rnorm(100, mean = mu, sd = sigma)
priors <- c(prior(constant(10), class = "sigma"),
prior(constant(5), class = "Intercept"))
fit <- brm(y ~ x,
data = dat,
prior = priors,
chains = 4,
iter = 2000,
refresh = 0)
summary(fit)
```
This compiles and runs just fine, but look at the output of `summary()`.
```no-highlight
Family: gaussian
Links: mu = identity
Formula: y ~ x
Data: dat (Number of observations: 100)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Regression Coefficients:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept -106.04 2.14 -110.11 -101.81 1.00 1407 1749
x 1.97 0.04 1.89 2.04 1.00 1407 1749
Further Distributional Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 10.00 0.00 10.00 10.00 NA NA NA
Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
```
The estimate for `Intercept` isn’t a constant 5 as I expected. Looking at the underlying Stan code I see that `b_Intercept` is the “actual population-level intercept”, i.e., the intercept after removing the centering that `brms` does internally. If I dump the output to a data frame, and summarize I get this.
```no-highlight
> tmp <- data.frame(fit)
> summary(tmp)
b_Intercept b_x sigma Intercept lprior lp__
Min. :-115.16 Min. :1.843 Min. :10 Min. :5 Min. :0 Min. :-6883
1st Qu.:-107.49 1st Qu.:1.942 1st Qu.:10 1st Qu.:5 1st Qu.:0 1st Qu.:-6875
Median :-106.05 Median :1.968 Median :10 Median :5 Median :0 Median :-6875
Mean :-106.04 Mean :1.968 Mean :10 Mean :5 Mean :0 Mean :-6875
3rd Qu.:-104.58 3rd Qu.:1.994 3rd Qu.:10 3rd Qu.:5 3rd Qu.:0 3rd Qu.:-6874
Max. : -98.99 Max. :2.129 Max. :10 Max. :5 Max. :0 Max. :-6874
>
```
Here `Intercept` is a constant, 5, as I expect, and the mean reported for `Intercept` in `summary(fit)` matches the mean of `b_Intercept` as expected (once you’ve read the Stan code).
_ **BUT** _ since `b_Intercept` is calculated in `generated quantities`, there isn’t a way to put a prior on `b_Intercept`. Do I just have to remember to ignore `Intercept` in a summary when I’ve set a prior on it?
---
### Author:  [@kholsinger](https://discourse.mc-stan.org/u/kholsinger)
#### Post date: [November 19, 2025, 3:49pm UTC](https://discourse.mc-stan.org/t/setting-an-intercept-prior-on-a-regression-in-brms/40657/2 "2025-11-19T15:49:44Z")
I realized that there’s a _ **very** _ simple solution to the problem I posted about 10 minutes after posting it.
If I’m going to treat the intercept as a constant, I simply subtract that constant from the response before fitting the model and remove the intercept from the model with a `-1` in the formula.
That solves my immediate problem, but it leaves the more general problem of setting a prior on the intercept. Using `prior(, class = "Intercept")` places a prior on `Intercept` in the Stan code (which is looking at the centered data), but the reported intercept is `b_Intercept` (which is transformed back to the uncentered data). When, if ever, would it make sense to put a prior on `Intercept`. After all, once the data have been centered, the intercept should be close to 0.
---
### Author:  [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)
#### Post date: [November 19, 2025, 3:54pm UTC](https://discourse.mc-stan.org/t/setting-an-intercept-prior-on-a-regression-in-brms/40657/3 "2025-11-19T15:54:16Z")
Whatever prior you intend to put on `b_Intercept` translates directly to a prior on `Intercept`via only data-derived constants. Thus, there _is_ a way to put a prior on `b_Intercept`. Just figure out what the corresponding prior on `Intercept` is, and apply that prior to `Intercept`.
Saying it doesn’t make sense to put a prior on `Intercept` because it tends to be zero is subtly but exactly analogous to saying it doesn’t make sense to put a prior on `b_Intercept` because it tends to be the mean of the data.
Note that when setting user-defined priors, many users prefer to turn off the automatic centering with `0 + Intercept` syntax in the model formula, to avoid precisely this inconvenience.