Bayes Sparse Regression - reg. horseshoe for multinomial model

Modeling
3

Thanks for the paper,

I coding for testing your prior on my data. Just one little question:

I would have thought the data was organised in genes/samples, however “y” is

vector [ n] y; # outputs`

where n is

int < lower =0 > n ; # number of observations

Is this analysis done for each gene separately? Am I missing something?

Here the model I am referring to, in your article

data {
int < lower =0 > n ; # number of observations
int < lower =0 > d ; # number of predictors
vector [ n] y; # outputs
matrix [n ,d] x; # inputs
real < lower =0 > scale_icept ; # prior std for the intercept
real < lower =0 > scale_global ; # scale for the half -t prior for tau
real < lower =1 > nu_global ; # degrees of freedom for the half -t prior
# for tau
real < lower =1 > nu_local ; # degrees of freedom for the half - t priors
# for lambdas
real < lower =0 > slab_scale ; # slab scale for the regularized horseshoe
real < lower =0 > slab_df ; # slab degrees of freedom for the regularized
# horseshoe
}
parameters {
real logsigma ;
real beta0 ;
vector [ d] z;
real < lower =0 > tau ; # global shrinkage parameter
vector < lower =0 >[ d] lambda ; # local shrinkage parameter
real < lower =0 > caux ;
}
transformed parameters {
real < lower =0 > sigma ; # noise std
vector < lower =0 >[ d] lambda_tilde ; # ’ truncated ’ local shrinkage parameter
real < lower =0 > c; # slab scale
vector [ d] beta ; # regression coefficients
vector [ n] f; # latent function values
sigma = exp ( logsigma );
c = slab_scale * sqrt ( caux );
lambda_tilde = sqrt ( c ^2 * square ( lambda ) ./ (c ^2 + tau ^2* square ( lambda )) );
beta = z .* lambda_tilde * tau ;
f = beta0 + x* beta ;
}