I’d like to have a clear understanding of the mathematical model behind a formula and priors. Take for example the following call:

```
fit1 <- brm(brmsformula(time | cens(censored) ~ (1 | 0 | group), shape ~ (1 | 0 | group)),
data = mydata, family = weibull(),
prior = c(set_prior("normal(0,5)", class = "Intercept"),
set_prior("normal(0,4)", dpar="shape", class = "Intercept"),
set_prior("normal(0,0.1)", class = "sd", group="group")),
warmup = 1000, iter = 2000, chains = 4,
control = list(adapt_delta = 0.95))
```

What is the mathematical model here?

time_g = a + a_g

time_g \sim Weibull(\beta_g, \eta) and right-censored

a \sim N(0,5)

a_g \sim N(0,0.1)

\beta_g = b

b\sim N(0,4)

Is this correct?

Also, after fitting the model and calling `summary()`

, I see `cor`

and `sd`

. How do those relate to the mathematical model?