Hello,

I noticed that **rstanarm::stan_lmer** fails to correctly estimate the variance components of a one-way ANOVA model with a random factor when the ratio of the between variance over the within variance is high.

```
mu <- 10000 # grand mean
sigmaWithin <- 1e-3
ratio <- 100
sigmaBetween <- sigmaWithin * ratio
sigmaBetween^2
I <- 10L # number of groups
J <- 5L # sample size per group
set.seed(31415926L)
groupmeans <- rnorm(I, mu, sigmaBetween)
y <- c(
vapply(groupmeans, function(gmean) rnorm(J, gmean, sigmaWithin), numeric(J))
)
dat <- data.frame(
y = y,
group = gl(I, J)
)
stan <- stan_lmer(
y ~ (1|group), data = dat,
prior_aux = cauchy(0, 5)
)
posterior_interval(stan)
```

How would you deal in such a situation? I found that increasing the scale parameter in `prior_covariance = decov(......)`

yields better results.