How does brms use the given data to adjust the default priors?

Interfaces brms
1

I have noticed that the parameters of the default priors change with the data. I am curious what the logic is.

library(brms)
set.seed(42)
data <- rskew_normal(1e4, mu = 0, sigma = 1, alpha = -5)

make_stancode(data ~ 1, data, skew_normal)
#  // priors including all constants
#  target += student_t_lpdf(Intercept | 3, 0.2, 2.5);
#  target += student_t_lpdf(sigma | 3, 0, 2.5)
#    - 1 * student_t_lccdf(0 | 3, 0, 2.5);
#  target += normal_lpdf(alpha | 0, 4);

make_stancode(data ~ 1, 100 * data, skew_normal)
#  // priors including all constants
#  target += student_t_lpdf(Intercept | 3, 17.1, 97);
#  target += student_t_lpdf(sigma | 3, 0, 97)
#    - 1 * student_t_lccdf(0 | 3, 0, 97);
#  target += normal_lpdf(alpha | 0, 4);
2

Hi,

I think this might answer your question:

3

Thanks for the reference! So the location parameter is taken to be the median. It does not match the above data, as the median is 0.17, but I suppose it is rounded to one digit after the decimal point. Then the only mystery left is the scale parameter, which is 2.5 and 97 in my example.

4

@paul.buerkner will know :)

5

Somewhat adhoc choices done in the def_scale_prior function (see https://github.com/paul-buerkner/brms/blob/master/R/priors.R).

1 Like
6

That solves it. The logic is roughly as follows:

location <- round(median(data), 1)
scale <- max(round(mad(data), 1), 2.5)

Thanks, everyone!