added normal mixture of K components to test model in manual

Author: Bob Carpenter

basic_estimators/normal-mixture_k-sim.R

@@ -0,0 +1,17 @@
+K <- 3;
+
+N1 <- 500;
+N2 <- 300;
+N3 <- 200;
+N <- N1 + N2 + N3;
+mu1 <- -2.0;
+mu2 <- 0.5;
+mu3 <- 3.5;
+sigma1 <- 1.0;
+sigma2 <- 0.5;
+sigma3 <- 2;
+
+y <- c(rnorm(N1,mu1,sigma1),rnorm(N2,mu2,sigma2),rnorm(N3,mu3,sigma3));
+
+library("rstan");
+fit <- stan(file="normal_mixture_k.stan", data=("K","N","y"), iter=500, chains=1, init=0);

basic_estimators/normal_mixture_k.stan

@@ -0,0 +1,20 @@
+data {
+  int<lower=1> K;
+  int<lower=1> N;
+  real y[N];
+}
+parameters {
+  simplex[K] theta;
+  real mu[K];
+  real<lower=0,upper=10> sigma[K];
+}
+model {
+  real ps[K];              
+  mu ~ normal(0,10);
+  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);    
+  }
+}