Yes, my data is distributed as Assymetric Laplace. The crux of my question was how to specify the associated parameters. It’s not good enough to model them as half-normal, because we actually have data (the prior data) and we should check empirically for the best distribution.
Regarding the data, each column is annual measurements from a physical location that is similar to the target location described by the observed data. Thus, it’s not the same, but is a good-enough proxy. So, we have annual data from 5 similar sites. From this, we can build out the distribution of the parameters for the priors.
As I described, if I were modeling a beta distribution for the posterior, then I could calculate the alpha and beta parameters.
Namely, each column would have a mu and a standard deviation. I would then use those to calculate alpha and beta according to the formulas here. Then, I would have 5 alphas and betas (in my real dataset I actually have 20 columns) and could fit a distribution.
The problem is that I don’t know how to go from myu and sigma of each column to the parameters in Assymteric Laplace.