Hi all,

I’m working on the regularized horseshoe and it is throwing about 30 divergent transitions. The effective sample sizes and rhats for all parameters are fine. The regression has 10 predictors and n is 4000. I realize this is not the optimal situation to demonstrate the regularized horseshoe, but I am still getting a tiny bit of additional shrinkage in the estimates compared to the horseshoe. The code is as follows.

```
modelString = "
data {
int <lower=1> n; // number of observations
int <lower=1> p; // number of predictors
real readscore[n]; // outcome
matrix[n,p] X; // inputs
}
transformed data {
real p0 = 5;
// real slab_df = 4;
// real half_slab_df = 0.5 * slab_df;
}
parameters {
vector[p] beta;
vector<lower=0>[p] lambda;
real<lower=0> c2;
real<lower=0> tau;
real alpha;
real<lower=0> sigma;
}
transformed parameters {
real tau0 = (p0 / (p - p0)) * (sigma / sqrt(1.0 * n));
vector[p] lambda_tilde =
sqrt(c2) * lambda ./ sqrt(c2 + square(tau) * square(lambda));
}
model {
beta ~ normal(0, tau * lambda_tilde);
lambda ~ cauchy(0, 1);
c2 ~ inv_gamma(2, 8);
tau ~ cauchy(0, tau0);
alpha ~ normal(0, 2);
sigma ~ cauchy(0, 1);
readscore ~ normal(X * beta + alpha, sigma);
}
// For posterior predictive checking and loo cross-validation
generated quantities {
vector[n] readscore_rep;
vector[n] log_lik;
for (i in 1:n) {
readscore_rep[i] = normal_rng(alpha + X[i,:] * beta, sigma);
log_lik[i] = normal_lpdf(readscore[i] | alpha + X[i,:] * beta, sigma);
}
}
"
```

The code is a slight modification of that given in Betancourt (2018) where instead of specifying the slab scale and slab df, I’m giving c^2 an inverse-gamma (2,8) prior as per a suggestion in Piironen and Vehtari (2017). I have tried the Betancourt code directly and again, the rhats and n_eff values look fine, but it is throwing around the same number of divergent transition warnings. Any thoughts?

Thanks in advance,

David