added identified normal mixture

Author: Bob Carpenter

basic_estimators/bernoulli.cpp

@@ -0,0 +1,39 @@
+data {
+  int<lower=1> K;
+  int<lower=1> N;
+  real y[N];
+}
+parameters {
+  simplex[K] theta;
+  simplex[K] mu_prop;
+  real mu_loc;
+  real<lower=0> mu_scale;
+  real<lower=0> sigma[K];
+}
+transformed parameters {
+  ordered[K] mu;
+  mu <- mu_loc + mu_scale * cumulative_sum(mu_prop);
+}
+model {
+  // prior
+  // theta ~ dirichlet(rep_vector(1,K));
+  // mu_prop ~ dirichlet(rep_vector(1,K));
+  mu_loc ~ cauchy(0,5);               
+  mu_scale ~ cauchy(0,5);
+  sigma ~ cauchy(0,5);
+
+  // likelihood
+  { 
+    real ps[K];
+    vector[K] log_theta;
+    log_theta <- log(theta);
+
+    for (n in 1:N) {
+      for (k in 1:K) {
+        ps[k] <- log_theta[k]
+                 + normal_log(y[n],mu[k],sigma[k]);
+      }
+      lp__ <- lp__ + log_sum_exp(ps);    
+    }
+  }
+}