Horseshoe and regression coefficients with bounds

Modeling
4

It’s pretty neat, you can still mix the constraint with a non-centered param but the bound is a little different - Bob covered over in this thread how to work out the new bound: Non-centered parameterisation with boundaries

And a practical example for lower=0:

data {
    int<lower=0> J; 
    real y[J];                                 
    real<lower=0> sigma[J];                    
}
parameters {
    real mu;          
    real<lower=0> tau;                        
    real<lower=-mu/tau> theta_raw[J]; //Implies lower=0 on theta
}
transformed parameters {
  theta[J] = mu + theta_raw * tau;
}
model {
    theta_raw ~ std_normal();
    y ~ normal(theta, sigma);
}
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