Suppose I'm developing a model where the response variable is weight measured in pounds and is Gamma distributed. I would like to specify a prior on my intercept coefficient using other information from previous studies.
Since I am assuming the data generating process is Gamma distributed, I will be using a log-link for my model.
My question is, do I specify my prior in terms of the original measurement, (pounds), or in terms of the transformed space, log(pounds)?
$$ \alpha \sim N(300, 20) $$
$$ \alpha \sim N(5.7, 3) $$