Hi all,

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.

**Sample Code**

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!