Generate data from prior

Modeling
1

Hi all,
I am trying to understand how “fake” data can be generated from priors and to check if the generated dataset is similar to observed data - this is prior predictive check right? So I have used the following simple regression model as an example.

parameters{
   real alpha; 
  real beta; 
  real<lower=0> sigma; 
}
model { 
  alpha ~ normal(0, 10);
  beta ~ normal(0, 10);
  sigma ~ normal(0, 1);
  } 
generated quantities { 
  real y[10]; 
  real x[10]; 
  for (n in 1:10) { 
    x[n] = normal_rng(0, 1); 
    y[n] = normal_rng(alpha * x[n] + beta, sigma); 
  } 
}

I would like to know if the above method for generating data is correct. Or would i need to generate data within mode{} section as below? Which method is correct? After generating data, I would like to use it to check my model too.

data{
real x[10]
}
parameters{
   real alpha; 
  real beta; 
  real<lower=0> sigma; 
real y[10];
}
model { 
  alpha ~ normal(0, 10);
  beta ~ normal(0, 10);
  sigma ~ normal(0, 1);
  y~ normal(alpha * x+ beta, sigma); 
  }

Thanks

2

The first is closer to correct, but you would pass x into the data block rather than drawing it from a distribution in the generated quantities block, unless you intend to model x in your ultimate model.

3

Thanks @bgoodri. That cleared my doubts.

4

I’m encountering the similar problem as you met, still don’t know how it works.
Can you post the whole code after revising?

5

This would be the corrected model, with a couple of amendments (use of vector and std_normal):

data{
  vector[10] x;
}
parameters{
  real alpha; 
  real beta; 
  real<lower=0> sigma; 
}
model { 
  alpha ~ normal(0, 10);
  beta ~ normal(0, 10);
  sigma ~ std_normal();
} 
generated quantities { 
  vector[10] y; 
  for (n in 1:10) { 
    y[n] = normal_rng(alpha * x[n] + beta, sigma); 
  } 
}
6

thanks!