14.3 Sampling without Parameters

In some situations, such as pure forward data simulation in a directed graphical model (e.g., where you can work down generatively from known hyperpriors to simulate parameters and data), there is no need to declare any parameters in Stan, the model block will be empty, and all output quantities will be produced in the generated quantities block. For example, to generate a sequence of \(N\) draws from a binomial with trials \(K\) and chance of success \(\theta\), the following program suffices.

data {
  real<lower=0,upper=1> theta;
  int<lower=0> K;
  int<lower=0> N;
}
model {
}
generated quantities {
  int<lower=0,upper=K> y[N];
  for (n in 1:N)
    y[n] = binomial_rng(K, theta);
}

This program includes an empty model block because every Stan program must have a model block, even if it’s empty. For this model, the sampler must be configured to use the fixed-parameters setting because there are no parameters. Without parameter sampling there is no need for adaptation and the number of warmup iterations should be set to zero.

Most models that are written to be sampled without parameters will not declare any parameters, instead putting anything parameter-like in the data block. Nevertheless, it is possible to include parameters for fixed-parameters sampling and initialize them in any of the usual ways (randomly, fixed to zero on the unconstrained scale, or with user-specified values). For example, theta in the example above could be declared as a parameter and initialized as a parameter.