local level model in Stan reparameterized using Matt's trick

locallevel.stan

// Local Level model in Stan
// parameterized using Matt's Trick
data {
  int n;
  vector[n] y;
  real<lower=0> theta1_mean;
  real<lower=0> theta1_sd;
}
parameters {
  real<lower=0> sigma_v;
  real<lower=0> sigma_w;
  vector[n] theta_innov;
}
transformed parameters {
  vector[n] theta;
  theta[1] <- theta1_mean + theta1_sd * theta_innov[1];
  for (t in 2:n) {
    theta[t] <- theta[t - 1] + sigma_w * theta_innov[i];    
  }
}
model {
  theta_innov ~ normal(0, 1);
  y ~ normal(theta, sigma_v);
}