Stick breaking process in stan

STB.R

#from BUGS book page 293
#Stick-breaking process
#http://www2.imm.dtu.dk/courses/02443/projects/Roeder_JASA_1990.pdf
library(rstan)

C <- 10
data <-read.csv("data.csv")
N <-nrow(data)
  
model <-stan_model("STB.stan")
fit <- sampling(model,v=data,N=N,C=C,            iter = 1000, chains = 1)
                     
traceplot(fit, ask=T)
print(fit, digit=2)

STB.stan

//from The BUGS book page 293
//Stick-breaking process

  data{
    int<lower=0> C;//num of cludter
    int<lower=0> N;//data num
    real v[N];
  }

  parameters {
   real amu;
   real bmu;
   vector[C] mu_mix;
   vector[C] tau_mix;
   real <lower=0,upper=1>q[C];

  }

  transformed parameters{
     simplex [C] pi;
//     simplex [C] p;
     vector [C]   mu_prec;
  
     pi[1] <- q[1];
     for(j in 2:C)
       pi[j] <- q[j]*(1-q[j-1])*pi[j-1]/q[j-1];

     for(j in 1:C){
//       pi[j] <- p[j]/sum();
       mu_prec[j] <- bmu*tau_mix[j];
     }
  }

  model {
    //    int<lower=0> group[C];
    real bprec;
    real alpha;
    real aprec;

    amu ~ normal(0,0.001);
    bmu ~ gamma(0.5,50);
    bprec~gamma(2,1);

    alpha <- 1;
    aprec<-2;

    for(j in 1:C){
      q[j]~beta(1,alpha);
      mu_mix[j]~normal(amu,mu_prec[j]);
      tau_mix[j]~gamma(aprec,bprec);
    }
    
    //     for(i in 1:N){
    //      group[i]~categorical(pi);

    //       for(j in 1:C)
    // 	if(j==group[i])
    // 	  gind[i,j]<-1;
    // 	else
    // 	  gind[i,j]<-0;

    //      mu[i] <-  mu.mix[group[i]];
    //      tau[i] <- tau.mix[group[i]];
    //      v[i]~normal(mu[i],tau[i]);
    //  }

    for(i in 1:N){
      for(j in 1:C){
	increment_log_prob(
			   pi[j]+normal_log(v[i],mu_mix[j],tau_mix[j])
			   );
      }
    }

  }