I was wondering which prior I need to use in order to perform inferential tests about the coefficients of a projected model after selecting variables with
projpred and a horseshoe prior? (Is there a tutorial that I missed?) I’m working with the horseshoe prior for the first time, so please excuse me if this is obvious for you more experienced folks.
Say we perform a variable selection as per the tutorial here: https://htmlpreview.github.io/?https://github.com/stan-dev/projpred/blob/master/vignettes/quickstart.html
… and as per the tutorial, we do the projection like so:
proj <- project(vs, nterms = 3, ns = 500)
Given the projection, I would like to compute relative evidence/Bayes factors about, for instance, the coefficient
x1 in the projected model being greater than zero. How to specify the prior?
m <- as.matrix(proj) # I can specify a normal prior easily # my question: what is the correct prior to use here # given the horseshoe prior that was used in the variable selection? prior <- distribution_normal(nrow(m), mean = 0, sd = .1) # Once we go the prior right, we can just test a hypothesis bayesfactor_parameters(m[, "x1"], prior, direction = ">")
I just cannot figure out how to draw from the horseshoe, basically. I feel like this should be simple :p
Thank you for your time!