When including Stan code in your post it really helps if you make it as readable as possible by using Stan code chunks (```stan) with clear spacing and indentation. For example, use

```
data{
int<lower=1> N; //number of subjects
matrix[N,3] X;
int censor[N];
vector[N] BP;
real<lower=0> hyp_diag;
}
parameters{
real<lower=1> intercept;
vector<lower=0>[3] beta;
real<lower=0> sigma; //regression variance
real intercept_b;
vector[3] beta_p; //binomial parameter coeffs
real<lower=0> trunc_sigmau;
}
model{
intercept ~ normal(0,100);
intercept_b ~ normal(0,20);
trunc_sigmau ~ student_t(3,0,2.5);
sigma ~ student_t(3,0,2.5);
to_vector(beta) ~ multi_normal([0,0,0],diag_matrix(square([5,5,5]')));
to_vector(beta_p) ~ multi_normal([0,0,0],diag_matrix(square([5,5,5]')));
for(n in 1:N){
if (censor[n]==1) {
BP[n] ~ normal(intercept+X[n,1]*beta[1]+X[n,2]*beta[2]+X[n,3]*beta[3],sigma);
if (BP[n]>hyp_diag) {
target += bernoulli_lpmf(1-censor[n]|inv_logit(intercept_b+X[n,1]*beta_p[1]+X[n,2]*beta_p[2]+X[n,3]*beta_p[3]));
}
}else{
target += normal_lccdf(BP[n]|intercept+X[n,1]*beta[1]+X[n,2]*beta[2]+X[n,3]*beta[3],trunc_sigmau);
target += bernoulli_lpmf(1-censor[n]|inv_logit(intercept_b+X[n,1]*beta_p[1]+X[n,2]*beta_p[2]+X[n,3]*beta_p[3]));
}
}
}
```

```
model=stan_model(file = 'H:\\Test Bayes\\BP censored.stan')
nsim=800 #800
age=runif(nsim,min=25,max=74)
sex=rbinom(nsim,size=1,prob=0.5)
gene=rbinom(nsim,size=1,prob=0.51)
sig_err=10
err=rnorm(nsim,mean=0,sd=sig_err)
beta0=123;beta1=0.5;beta2=5;beta3=3
Z=beta0+beta1*age+beta2*sex+beta3*gene+err
betas=c(beta0,beta1,beta2,beta3)
list_hyp=which(Z>130)
num_hyp=length(list_hyp)
treat=rbinom(num_hyp,1,prob=0.6)
old_Z=Z
Z[list_hyp]=Z[list_hyp]+treat*rnormTrunc(num_hyp,mean=-30,sd=20,max=0)
hyp=data.frame(id=1:nsim,age=age,sex=sex,gene=gene,BP=Z,true_BP=old_Z)
hyp$age_g=cut(age,breaks=c(min(age)-1,quantile(age,
#c(1/4,2/4,3/4)),
c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.9)),
max(age)+1))
hyp$censor=1
hyp$censor[list_hyp[as.logical(treat)]]=0
data=list(N=dim(hyp)[1],
X=as.matrix(hyp[,c('age','sex','gene')],ncol=3),
censor=hyp$censor,
BP=hyp$BP,
hyp_diag=130
)
fit_mod=sampling(model,data=data,chains=1,iter=2000,warmup=1000)
```

I am trying to model censored data with normal distribution where mean depends upon covariates. In reality, I will never have information for beta’s all positive in parameters. If I drop that constraint, Stan will give me log(0) posterior density coming from the following part of the stan code within the loop.

```
target += normal_lccdf(BP[n]|intercept+X[n,1]*beta[1]+X[n,2]*beta[2]+X[n,3]*beta[3],trunc_sigmau);
```

Q1: Is there a way to allow me drop the beta’s all positive condition?

Q2: After examining trace plot, it seems that the result did not converge. Is this possibly due to previous normal_lccdf line?

Thanks.