Prior specification for beta distribution in brms

Interfaces brms
2

The thing we recommend people do now is think about their priors in terms of the thing that they’re predicting.

Have a look at: https://www.youtube.com/watch?v=ZRpo41l02KQ&t=2694

I think this is specifically motivated by setting priors in a Bernoulli regression.

We can work a quick example for a model that looks like:

\alpha \sim \text{normal}(0, 1)\\ p = \text{logit}^{-1}(\alpha)\\ y \sim \text{bernoulli}(p)

So this implies a prior on p (the transformed parameter) of:

inverse_logit = function(x) {
  1 / (1 + exp(-x))
}

hist(inverse_logit(rnorm(100, 0, 1)))

And then if we made the prior standard deviation 10, that implies:

hist(inverse_logit(rnorm(100, 0, 10)))
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