Within-chain parallelization in Stan

Hi everyone, I am a Stan newbie.
I need to fit a hierarchical survival model using RSTAN for large data. But, I found sampling is very time-consuming (takes ~ 7 days even for 2000 iteration/500 warmup).

To improve sampling speed, I am going to use more than one CPU per chain and have within-chain parallelization in Stan. Could someone help me to do this within-chain parallelization, please?

My stan code is as below (N=35000, n_grid=350, province=31, number=17,num=12).
In my codes, x[j]'s (j=1,2, …, n_grid) are white noise and It is used only in the calculation of a and there is no need to estimate it.

Thank you in advance!

fit < - stan(“final model.stan”,data = da,iter=iter, warmup=warmup, cores =4, thin = 1, init = “random”)
### Stan codes

data {
  int <lower=0> province;
  int <lower=0> n_grid;
  int <lower=0> N;
  int <lower=0> num;
  int <lower=0> number;
  vector <lower=0> [province] p;
  row_vector[n_grid] kernel[province];
  matrix [N,number] respon;
  vector [num] beta;
  real <lower=0> sigma;
  vector [n_grid] x;
transformed parameters{
  real alpha = 1 / sigma;
  vector [num] time_ratio;
  vector [N] lambdaa;
  vector [n_grid] exp_x;
  vector[province] a; // `a` saved to output
  time_ratio  = exp (beta);
  exp_x = exp(x);
     lambdaa = exp ((-1 * respon[,6:17] * beta) / sigma);
           { // `z` is not part of output
    vector[province] z;
      vector[province] landa;
for (k in 1 : province) {
     landa[k] = kernel[k] * exp_x * p[k];
     a = landa / sum(landa); // assign `a`
  real log_alpha;
  log_alpha = log (alpha);
     target += normal_lpdf(x|0,2);
    target += normal_lpdf(beta | 0, 1000);
    target += normal_lpdf(log_alpha | 0, 5);
for (i in 1:N) {
   vector [province] f_i;
  vector [province] s_i;
for (k in 1:province){
    f_i[k]= a[k]*((lambdaa [i]*alpha*respon[i,4]^(alpha-1))/((1+(lambdaa [i]*respon[i,4]^alpha))^2));
    s_i[k]= a[k]*(1- ((lambdaa [i]*respon[i,4]^alpha)/ (1+(lambdaa [i]*respon[i,4]^alpha))));
    target += respon[i,5] *  (log (f_i)-log(s_i)) + log(s_i)- log_alpha;

In this model (survival model with mentioned RSTAN codes), I want to plot the predicted survival curve and then add the KM curve. Could anyone help me, please?

Thank you!

it looks like your model could be amenable to the reduce_sum approach. Try following the instructions at Reduce Sum: A Minimal Example and if you encoutner problems, feel free to ask here.

I unfortunately don’t understand the model well enough to help directly. What exactly is the model you are trying to implement mathematically?