Dear all, I noticed a considerable discrepancy between nominal priors (intended priors, theoretical or generated with RNG) and the actually sampled priors. I understand how both methods can differ numerically, but what I observe seems excessive. Perhaps I am misunderstanding something.

The following MRE illustrates the issue well, I hope:

```
library(brms, quietly = TRUE)
#> Loading 'brms' package (version 2.13.0). Useful instructions
#> can be found by typing help('brms'). A more detailed introduction
#> to the package is available through vignette('brms_overview').
#>
#> Attaching package: 'brms'
#> The following object is masked from 'package:stats':
#>
#> ar
library(tidyverse, quietly = TRUE)
dummy_dat <- with(
list(N = 5e3),
data.frame(
mu = 1,
x = gl(2, N/2),
y = 0 # irrelevant, but necessary
)
)
pred_priors <-
brm(y ~ 1 + x,
sample_prior = "only",
prior = c(
set_prior("student_t(3, 0, 2.5)", class = "Intercept"),
set_prior("skew_normal(-1, 1, -4)", class = "b")
),
data = dummy_dat,
iter = 5e3,
refresh = FALSE
)
#> Compiling the C++ model
#> Start sampling
pred_priors %>%
posterior_samples(pars = "b_") %>%
add_column(
nominal_int = rstudent_t(nrow(.), 3, 0, 2.5),
nominal_x = rskew_normal(nrow(.), -1, 1, -4)
) %>%
gather(sample, value) %>%
ggplot(aes(value, colour = sample)) +
geom_vline(xintercept = 0, colour = "grey80") +
geom_density() +
scale_x_continuous(limits = c(-10, 10))
#> Warning: Removed 556 rows containing non-finite values (stat_density).
```

^{Created on 2020-06-22 by the reprex package (v0.3.0)}

I expect the curves would match more closely. In particular, for the Skew-Normal prior, I expected to get some probability above 0 but the support of the realised prior is entirely below 0. This raises the question of which prior I am really using: the one that I specified or the one that has been realised (I guess the latter?).

Thanks in advance for your insights.

Ć’acu.-