Hi, I have another question about the scale parameter \sigma and it links to this thread prior with brms.
Apologies in advance if I am repeating the question in this thread.
Here is a simple linear model y\sim N(1+x,\tau^2). The prior for the intercept that I got from brms is student_t(3, 84.7, 31.3), where \nu=3, \mu=84.7, and the scale \sigma=31.3. However, the sd of y is 25.6, hence \sigma should be 14.78 according to sd=\sqrt{\frac{\nu}{\nu-2}}\sigma .
Did I misunderstand the formula? Thank you all for your time.