How to set prior on var in brms

Interfaces brms
,
1

hi, i would like to run a Bayesian hierarchical model. my model is as follows,
y_i \sim Pois(\theta_i P_i) \\ log(\theta_i) \sim N(\mu,\sigma^2) \\ \mu \sim N(\mu_0, \tau^2) \\ \sigma^2 \sim Inv-Gamma(0.001,0.001)
my code is as follows,

model1 <- brm(
  formula = cases ~ 1 + (1 | state) + offset(log(P)),
  family = poisson(link = "log"),
  data = df,
  prior = 
    prior(normal(-7.87, 1), class = "Intercept") +
    prior(inv_gamma(0.001, 0.001), class = "var", group = "state")
)

it can’t wok. the error message is:
The following priors do not correspond to any model parameter:
var_state ~ inv_gamma(0.001, 0.001)
Function ‘default_prior’ might be helpful to you.

I know the code can work if class = “sd”. however, i would like to know the effect of conjugate prior on my model.

so, how to set this prior on var in brms?

Any reply is appreciated!

2

As you indicated, brms parameterizes in terms of \sigma, not \sigma^2. If you really want \sigma^2, I suspect you’d either have to use the non-linear syntax (see here) or perhaps define a custom distribution (see here).

3

Thank you for your reply. I gave up brms and use Stan.