###################
example1.stan
###################

data {
  int n;
  real y[n];
}

parameters {
  real mu;
  real<lower=0> sigma;
}

model {
  for (i in 1:n)
    y[i] ~ normal(mu,sigma);
  mu ~ normal(1.7,0.3);
  sigma ~ cauchy(0,1);
}




###################
example2.stan
###################

data {
  int n;
  real y[n];
}

parameters {
  real mu;
  real<lower=0> sigma;
  real<lower=0> nu;
}

model {
  for (i in 1:n)
    y[i] ~ student_t(nu,mu,sigma);
  mu ~ normal(0,1);
  sigma ~ inv_gamma(5,1);
  nu ~ gamma(2,0.1);
}



###################
example3.stan
###################

data {
  int<lower=0> n;
  vector[n] y;
}
parameters {
  real alpha;
  real<lower=-1,upper=1> beta;
  real<lower=-1,upper=1> gamma;
  real<lower=0> sigma;
  real<lower=0> nu;
}
model {
  y[3:n] ~ student_t(nu,alpha+beta*y[2:(n-1)]+gamma*y[1:(n-2)],sigma);
  alpha ~ normal(0,1);
  beta ~ normal(0,1);
  gamma ~ normal(0,1);
  sigma ~ inv_gamma(5,1);
  nu ~ gamma(2,0.1);
}