Hello.

I’ve been teaching myself Bayesian modeling and trying to learn new approaches to solving old problems. For a super basic toy example, let’s say I wanted to estimate the proportion of people who floss at a university and I take a sample size of 1000. 280 respond yes. My non-Bayesian modeling approach would be something like this:

```
> fdf <- data.frame(floss = c(rep(1, 280), rep(0, 1000 - 280)))
> mod1 <- glm(floss ~ 1, data = fdf, family = binomial)
> plogis(confint(mod1))
Waiting for profiling to be done...
2.5 % 97.5 %
0.2527574 0.3083672
```

My confidence interval is about (0.25, 0.31). Pretty much what I get if I use the base R `prop.test`

function.

When implementing the same approach using `stan_glm`

and the default priors, I get the following

```
> bm1 <- stan_glm(floss ~ 1, data = fdf, family = binomial)
[sampling output omitted]
> plogis(posterior_interval(bm1))
5% 95%
(Intercept) 1.197878e-07 0.9999999
```

I’m very surprised the posterior interval is so wide and uninformative. I know the default intercept prior is a weakly information normal(0, 10), but I thought with 1000 observations it would produce an interval of a similar width to the one I got using `glm`

. Am I doing something wrong or misunderstanding how `stan_glm`

works? Thanks for any help!

- Operating System: Win 10, 64-bit
- rstanarm Version: 2.19.2