data{
  int N; //number of data
  int K; // number of components
  real x[N]; //data
  vector<lower=0>[K] alpha; //hyperparameter for mixing ratio
  real beta; //hyperparameter for center of component
}

parameters{
  real mu[K]; //parameter for center of componet
  simplex[K] ratio; //parameter for mixing ratio
}

/**
learning model:
p(x|w) = sum_{k=1}^{K} ratio_k N(x-mu_k|1)
priors:
varphi(w|alpha,beta) = Dir(ratio|alpha) prod_k N(mu_k|0,beta)
**/
model{
  real p_comp[K];
  
  //log priors
  ratio ~ dirichlet(alpha);
  for(k in 1:K){
    mu[k] ~ normal(0, beta);
  }
  
  //log likelihood
  for(i in 1:N){
    for(k in 1:K){
      p_comp[k] <- log(ratio[k])+normal_log(x[i], mu[k], 1);
    }
    increment_log_prob(log_sum_exp(p_comp));
  }
}