# How to set prior for hyper-parameter

**URL:** <https://discourse.mc-stan.org/t/how-to-set-prior-for-hyper-parameter/15306>\
**Category:** brms\
**Created:** [May 21, 2020, 10:45pm UTC](https://discourse.mc-stan.org/t/how-to-set-prior-for-hyper-parameter/15306 "2020-05-21T22:45:38Z")\
**Posts on this page:** 1\
**Showing post:** 5

<div class="post-metadata">

**Author:** ![wpetry](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/wpetry/32/4852_2.png) [@wpetry](https://discourse.mc-stan.org/u/wpetry)\
**Post date:** [May 23, 2020, 3:53am UTC](https://discourse.mc-stan.org/t/how-to-set-prior-for-hyper-parameter/15306/5 "2020-05-23T03:53:27Z")

</div>

You can do this in `brms` by passing Stan code to `brm()` via two arguments: `prior` and `stanvars` (which adds `tau` as a parameter). Effectively this is exactly what @Jean_Billie recommends, but leans on `brms` to create as much of the Stan code as possible.

```
bpriors <- prior(normal(0, 2), class = "Intercept") +
  prior(normal(0, 4), class = "b", coef = "x1") +
  prior(normal(0, tau), class = "b", coef = "x2")+ # here is where we add tau as a hyperparameter for the standard deviation of x2
  prior("target += exponential_lpdf(tau | 1)", check = FALSE) + # here is where we define the prior for tau; I picked exponential(1)
  prior(exponential(1), class = "sigma")

stanvars <- stanvar(scode = " real<lower=0> tau;", # here is where we add the parameter for tau
                    block = "parameters")

bmod <- brm(y ~ 1 + x1 + x2, family = gaussian(),
            data = dat, chains = 2,
            prior = bpriors, stanvars = stanvars) # this line passes the prior & modified parameter blocks into brm()

summary(bmod)

```

(ht: @paul.buerkner for posting a similar example [https://github.com/paul-buerkner/brms/issues/459#issuecomment-399041581](https://github.com/paul-buerkner/brms/issues/459#issuecomment-399041581))

If your actual model is more complicated than the example you provided, you may find it easier to use the `rethinking` package. Its syntax is very similar to how you wrote your question. `rethinking::ulam` is the workhorse function, and within that `alist` wraps the model (`<-`) & priors (`~`)

```
rmod <- ulam(
  alist(
    y ~ dnorm(mu, sig),
    mu <- a + b*x1 + c*x2,
    a ~ dnorm(0, 2),
    b ~ dnorm(0, 4),
    c ~ dnorm(0, tau),
    tau ~ dexp(1),
    sig ~ dexp(1)
  ),
  data = dat, chains = 2
)
precis(rmod)

```

Finally, this code wouldn’t be complete without the data needed to make it reproducible. Here’s one way to generate a dummy dataset:

```
b0 <- 2
b1 <- 0.5
b2 <- 0.75
sigma <- 1

n <- 50
x1 <- runif(n)
x2 <- runif(n)

lp <- b0 + b1 * x1 + b2 * x2
y <- rnorm(n, lp, sigma)

dat <- data.frame(x1, x2, y)
```

---

_[View the full topic](https://discourse.mc-stan.org/t/how-to-set-prior-for-hyper-parameter/15306)._