I have fitted a LASSO regularization logistic regression model as follows :

```
data {
int<lower=1> N;
int<lower=1> K1;
int<lower=0,upper=1> y1[N];
matrix[N,K1] x1;
}
parameters {
real alpha1;
vector[K1] beta1_tilde;
vector<lower=0>[K1] tau_tilde;
real<lower=0> lambda ;
}
transformed parameters {
vector[K1] beta1= beta1_tilde .* tau_tilde*(lambda^2)/2;
}
model {
beta1_tilde ~ normal(0, 1);
tau_tilde ~ exponential(1);
lambda ~ cauchy(0, 1);
alpha1 ~ normal(0, 100);
y1 ~ bernoulli_logit_glm(x1, alpha1, beta1);
}
```

But I am getting the divergent transitions warning. So I increased the `adapt_delta`

parameter .

```
stan(file="logistic_LASSO2.stan", data=data_stan,
control = list(adapt_delta = 0.99999,max_treedepth=15),
iter=2500, chains=4)
```

Still I am getting some divergent transitions. This is the pairs plot for the parameter lambda and the first regression coefficient . The model had 5 divergent transitions.

The divergent transitions appeared to scatter randomly. Can anybody advice how to improve the results so that I can get rid of this divergent transition warning ?

Thank you.