Formulas related to generalized linear model and horseshoe prior

Hello! Currently, I am preparing a paper in which, among other things, I have trained a model using the rstanarm::stan_glm() function and hs() as the prior distribution. I want to describe the main formulas of the model in the manuscript, but, as my statistics background is limited, I would appreciate if someone can corroborate whether the formulas extracted from the documentation are the correct ones:

- Link (logit)


- Likelihood (Binomial(link = logit))

- Posterior (algorithm = ‘sampling’ - MCMC)

- Horseshoe prior (prior = hs())


Thank you very much!!!

Source (link, likelihood, posterior): Estimating Generalized Linear Models for Binary and Binomial Data with rstanarm • rstanarm
Source (horseshoe prior): (Formula #3)

Although it’s named hs(), it implements the regularized horseshoe prior described in Sparsity information and regularization in the horseshoe and other shrinkage priors